2.7. Basis Sets

ORCA provides a large number of natively implemented orbital and auxiliary basis sets alongside various effective core potentials (ECPs) that can be combined with them. For use with scalar-relativistic methods like ZORA, DKH, or X2C, specialized relativistic basis sets are available as well. Furthermore, other basis sets can be read from external files. Most built-in basis sets and ECPs were obtained from the Basis Set Exchange[16] or its predecessor, the EMSL library, and the input format in ORCA is closely related to the “GAMESS-US” format.

2.7.1. Basic Usage

The easiest way to use orbital and auxiliary basis sets in ORCA is via the simple input keywords. All available orbital basis set keywords can be found in Section 2.7.2 and all auxiliary basis set options in Section 2.7.4. For example, the Karlsruhe def2-TZVP basis set can be invoked via the def2-TZVP keyword.

! def2-TZVP

Note

Some basis sets like the Karlsruhe def2 employ ECPs by default for heavy elements, in this case the def2-ECP. The explicit control of the ECPs is described in Section 2.7.5.

Auxiliary basis sets needed for resolution-of-the-identity (RI) can be defined in the same way. In this example, Weigend’s universal def2/J auxiliary basis is used.

! def2-TZVP def2/J

Note

Note that for many calculations, RI is activated by default (e.g. RIJCOSX for hybrid DFT). Accordingly, the def2/J auxiliary basis is automatically invoked by default as well if not otherwise specified. In scalar relativistic calculations, the default is SARC/J instead.

Note that there are three separate slots for auxiliary basis sets for RI:

• AuxJ is the Coulomb-fitting basis for the RI-J, RIJDX/RIJONX, and RIJCOSX approximations.

• AuxJK is the Coulomb- and exchange-fitting basis used for RI-JK.

• AuxC is used for RI-based integral generation steps in post-SCF dynamical electron correlation methods, such as RI-MP2, DLPNO-MP2, and DLPNO-CC.

Finally, F12 methods require a complementary auxiliary basis set (CABS), in addition to the specialized orbital basis (and possibly AuxC), for example:

! F12-RI-MP2 cc-pVDZ-F12 cc-pVDZ-F12-CABS cc-pVTZ-F12-MP2Fit

Specifying an auxiliary basis with the simple input keyword, assigns it to the corresponding slot. However, each basis slot, as well as the ECP, can be assigned explicitly in the %basis block. For example, a “/JK” basis may be assigned to AuxJ in this way.

%basis
  Basis "def2-TZVP"         # The orbital expansion basis set
  ECP   "def2-ECP"          # Effective core potential
  AuxJ  "def2/J"            # RI-J auxiliary basis set
  AuxJK "def2/JK"           # RI-JK auxiliary basis set
  AuxC  "def2-TZVP/C"       # Auxiliary basis set for correlated 
                            # calculations, e.g. RI-MP2
  CABS  "cc-pVDZ-F12-OptRI" # complementary auxiliary basis set 
                            # for F12 calculations
end

If required, all basis sets can be decontracted via simple input (e.g. ! DECONTRACT) or the %basis block with the respective keywords below. Note that if your basis set arises from general contraction, it will contain duplicate primitives in several contractions. These will be removed such that only unique primitives remain and there is no problem with redundancy.

%basis
  DecontractBas   false  # if chosen "true" the program will
                         # decontract the orbital basis set
  DecontractAuxJ  false  # if "true" - decontract the AuxJ basis set
  DecontractAuxJK false  # if "true" - decontract the AuxJK basis set
  DecontractAuxC  false  # if "true" - decontract the AuxC basis set
  DecontractCABS  true   # if "false" - do not decontract the CABS
  Decontract      false  # if "true" - decontract all basis sets
end

Tip

• Generally, basis sets can be assigned to specific elements, to individual atoms, or even to structural fragments.

• Any built-in basis can be exported via the orca_exportbasis utility.

• References for the built-in basis sets are usually printed at the start of the ORCA output, as well as by orca_exportbasis.

Warning

ORCA uses pure d and f functions (5D and 7F instead of Cartesian 6D and 10F) for all basis sets. This needs to be taken into account when results are compared with other programs, especially for Pople-style basis sets that were optimized with Cartesian (6D) functions.

2.7.2. Orbital Basis Sets

In the following, we will give an outline of natively implemented basis sets from various families, like the Karlsruhe def2 and correlation consistent basis sets, and list which elements are covered by each. If an ECP is necessary for heavy elements, it is documented in the respective table entries and invoked by default if the basis is selected in the simple input or via the basis keyword in the %basis block.

2.7.2.1. Pople Basis Sets

Various basis sets of the Pople basis set family are available in ORCA. A list of all available Pople-style basis sets is given in Table 2.12.

Naming Convention of Pople Basis Sets

• * or (d) adds one set of first polarization functions on all atoms except H

• ** or (d,p) adds one set of first polarization functions on all atoms

• Further combinations: (2d), (2df), (2d,p), (2d,2p), (2df,2p), (2df,2pd)

• \(+\) before “G” includes diffuse functions on all atoms except H (e.g. 6-31\(+\)G)

• \(++\) before “G” includes diffuse functions on all atoms. Works only when H polarization is already included, e.g. 6-31\(++\)G(d,p)

Table 2.12 Available Pople-style basis sets.

Basis Set	Elem.	ECP	Comment
STO-3G	H–I	–	Minimal basis set
3-21G	H–Cs	–
3-21GSP	H–Ar	–
4-22GSP	H–Ar	–
6-31G	H–Zn	–
6-31G*	H–Kr	–
m6-31G	Sc–Cu	–	Modified 6-31G for 3d transition metals (Sc–Cu)
m6-31G*	Sc–Cu	–
6-31G**	H–Zn	–
6-31G(d)	H–Zn	–
6-31G(d,p)	H–Zn	–
6-31G(2d)	H–Zn	–
6-31G(2d,p)	H–Zn	–
6-31G(2d,2p)	H–Zn	–
6-31G(2df)	H–Zn	–
6-31G(2df,2p)	H–Zn	–
6-31G(2df,2pd)	H–Zn	–
6-31+G*	H–Kr	–
6-31+G**	H–Zn	–
6-31+G(d)	H–Zn	–
6-31+G(d,p)	H–Zn	–
6-31+G(2d)	H–Zn	–
6-31+G(2d,p)	H–Zn	–
6-31+G(2d,2p)	H–Zn	–
6-31+G(2df)	H–Zn	–
6-31+G(2df,2p)	H–Zn	–
6-31+G(2df,2pd)	H–Zn	–
6-31++G**	H–Zn	–
6-31++G(d,p)	H–Zn	–
6-31++G(2d,p)	H–Zn	–
6-31++G(2d,2p)	H–Zn	–
6-31++G(2df,2p)	H–Zn	–
6-31++G(2df,2pd)	H–Zn	–
6-311G	H–Br	–
6-311G*	H–Br	–
6-311G**	H–Br	–
6-311G(d)	H–Br	–
6-311G(d,p)	H–Br	–
6-311G(2d)	H–Br	–
6-311G(2d,p)	H–Br	–
6-311G(2d,2p)	H–Br	–
6-311G(2df)	H–Br	–
6-311G(2df,2p)	H–Br	–
6-311G(2df,2pd)	H–Br	–
6-311G(3df)	H–Br	–
6-311G(3df,3pd)	H–Br	–
6-311+G*	H–Br	–
6-311+G**	H–Br	–
6-311+G(d)	H–Br	–
6-311+G(d,p)	H–Br	–
6-311+G(2d)	H–Br	–
6-311+G(2d,p)	H–Br	–
6-311+G(2d,2p)	H–Br	–
6-311+G(2df)	H–Br	–
6-311+G(2df,2p)	H–Br	–
6-311+G(2df,2pd)	H–Br	–
6-311+G(3df)	H–Br	–
6-311+G(3df,2p)	H–Br	–
6-311+G(3df,3pd)	H–Br	–
6-311++G**	H–Br	–
6-311++G(d,p)	H–Br	–
6-311++G(2d,p)	H–Br	–
6-311++G(2d,2p)	H–Br	–
6-311++G(2df,2p)	H–Br	–
6-311++G(2df,2pd)	H–Br	–
6-311++G(3df,3pd)	H–Br	–

2.7.2.2. Ahlrichs Basis Sets

The older Ahlrichs basis sets implemented in ORCA cover all-electron basis sets and the basis sets automatically employing the def-ECP for all elements beyond Rb. A list of available Ahlrichs basis sets is given in Table 2.13. Relativistically recontracted variants are shown in Section 2.7.3.1.

Note

Past versions of ORCA (ORCA <4.0) used to load all-electron basis sets also for elements Rb-I with the below keywords for double- and triple-\(\zeta\) basis sets. The Rb-I basis sets originated from non-relativistic all-electron basis sets of the Turbomole library (such as “TZVPAlls”). This automatic substitution is now deprecated. However, we offer temporarily the ability to reproduce that behavior by adding the prefix “old-” to the below keywords, e.g. old-TZVP.

Table 2.13 Available all-electron Ahrlichs basis sets.

Basis Set	Elem.	ECP	Comment
SV	H–Kr	–	Valence double-zeta basis set.
SV(P)	H–Kr	–	Valence double-zeta with polarization only on heavy elements.
SVP	H–Kr	–	Polarized valence double-zeta basis set.
TZV	H–Kr	–	Valence triple-zeta basis set.
TZV(P)	H–Kr	–	Valence triple-zeta with polarization on heavy elements.
TZVP	H–Kr	–	Polarized valence triple-zeta basis set.
TZVPP	H–Kr	–	Doubly polarized triple-zeta basis set.
QZVP	H–Kr	–	Polarized valence quadruple-zeta basis set.
QZVPP	H–Kr	–	Doubly polarized quadruple-zeta basis set.
def-SV(P)	H–Lr	def-ECP (Rb–Lr)	Valence double-zeta with polarization only on heavy elements.
def-SVP	H–Lr	def-ECP (Rb–Lr)	Polarized valence double-zeta basis set.
def-TZVP	H–Lr	def-ECP (Rb–Lr)	Valence triple-zeta basis set with polarization functions.
def-TZVPP	H–Lr	def-ECP (Rb–Lr)	Doubly polarized triple-zeta basis set.
Minimally augmented (scheme by Truhlar et al.[17])
ma-def-TZVP	Fr–Lr	def-ECP (Fr–Lr)	Minimally augmented def-TZVP basis set.
Legacy definitions (not recommended!)
old-SV	H–I	–
old-SV(P)	H–I	–
old-SVP	H–I	–
old-TZV	H–I	–
old-TZV(P)	H–I	–
old-TZVP	H–I	–
old-TZVPP	H–I	–

2.7.2.3. Karlsruhe def2 Basis Sets

The valence polarized basis sets of the Karlsruhe def2 family are all-electron for elements H-Kr, and automatically load Stuttgart-Dresden effective core potentials for elements Rb-Rn. A list of available Karlsruhe def2 basis sets is given in Table 2.14. Relativistically recontracted variants are discussed in Section 2.7.3.2.

Table 2.14 Available Karlsruhe def2 basis sets.

Basis Set	Elem.	ECP	Comment
def2-SVP	H–Rn	def2-ECP (Rb–Rn)	Polarized valence double-\(\zeta\).
def2-SV(P)	H–Rn	def2-ECP (Rb–Rn)	def2-SVP with slightly reduced polarization.
def2-TZVP	H–Rn	def2-ECP (Rb–Rn)	Polarized valence triple-\(\zeta\). Quite similar to the older def-TZVPP for main group elements and TZVP for H.
def2-TZVP(-f)	H–Rn	def2-ECP (Rb–Rn)	def2-TZVP with f polarization removed from main group elements.
def2-TZVPP	H–Rn	def2-ECP (Rb–Rn)	Doubly polarized valence triple-\(\zeta\).
def2-QZVP	H–Rn	def2-ECP (Rb–Rn)	Polarized valence quadruple-\(\zeta\).
def2-QZVPP	H–Rn	def2-ECP (Rb–Rn)	Doubly polarized valence quadruple-\(\zeta\).
Diffuse (Rappoport et al.[18, 19])
def2-SVPD	H–Rn	def2-ECP (Rb–Rn)	Diffuse def2-SVP basis set for property calculations
def2-TZVPD	H–Rn	def2-ECP (Rb–Rn)	Diffuse def2-TZVP basis set for property calculations
def2-TZVPPD	H–Rn	def2-ECP (Rb–Rn)	Diffuse def2-TZVPP basis set for property calculations
def2-QZVPD	H–Rn	def2-ECP (Rb–Rn)	Diffuse def2-QZVP basis set for property calculations
def2-QZVPPD	H–Rn	def2-ECP (Rb–Rn)	Diffuse def2-QZVPP basis set for property calculations
Minimally augmented (scheme by Truhlar et al.[17])
ma-def2-SVP	H–Rn	def2-ECP (Rb–Rn)	Minimally augmented def2-SVP basis set.
ma-def2-SV(P)	H–Rn	def2-ECP (Rb–Rn)	Minimally augmented def2-SV(P) basis set.
ma-def2-mSVP	H–Rn	def2-ECP (Rb–Rn)	Minimally augmented def2-mSVP basis set.
ma-def2-TZVP	H–Rn	def2-ECP (Rb–Rn)	Minimally augmented def2-TZVP basis set.
ma-def2-TZVP(-f)	H–Rn	def2-ECP (Rb–Rn)	Minimally augmented def2-TZVP(-f) basis set.
ma-def2-TZVPP	H–Rn	def2-ECP (Rb–Rn)	Minimally augmented def2-TZVPP basis set.
ma-def2-QZVPP	H–Rn	def2-ECP (Rb–Rn)	Minimally augmented def2-QZVPP basis set.

2.7.2.4. Karlsruhe dhf Basis Sets

These basis sets are derived from the def2-XVP ones with small modifications for 5s, 6s, 4d, and 5d elements and iodine.[20] They are optimized for the revised Dirac-Fock ECPs (dhf-ECP) as opposed to the Wood–Boring ones (def2-ECP). For elements H–Kr these basis sets are equivalent to the respective def2-XVP basis set. Versions for two-component methods are also available, e.g. dhf-TZVP-2c, however, such methods are currently not implemented in ORCA. A list of available Karlsruhe dhf basis sets is given in Table 2.15.

Table 2.15 Available dhf basis sets.

Basis Set	Elem.	ECP	Comment
dhf-SV(P)	H–Rn	dhf-ECP (Rb–Rn)	based on def2-SV(P)
dhf-SVP	H–Rn	dhf-ECP (Rb–Rn)	based on def2-SVP
dhf-TZVP	H–Rn	dhf-ECP (Rb–Rn)	based on def2-TZVP
dhf-TZVPP	H–Rn	dhf-ECP (Rb–Rn)	based on def2-TZVPP
dhf-QZVP	H–Rn	dhf-ECP (Rb–Rn)	based on def2-QZVP
dhf-QZVPP	H–Rn	dhf-ECP (Rb–Rn)	based on def2-QZVPP
Two-component variants:
dhf-SVP-2c	H–Rn	dhf-ECP-2c (Rb–Rn)	based on def2-SVP
dhf-TZVP-2c	H–Rn	dhf-ECP-2c (Rb–Rn)	based on def2-TZVP
dhf-TZVPP-2c	H–Rn	dhf-ECP-2c (Rb–Rn)	based on def2-TZVPP
dhf-QZVP-2c	H–Rn	dhf-ECP-2c (Rb–Rn)	based on def2-QZVP
dhf-QZVPP-2c	H–Rn	dhf-ECP-2c (Rb–Rn)	based on def2-QZVPP

2.7.2.5. Jensen Basis Sets

Jensen’s polarization-consistent generally contracted basis sets include various general purpose and sepcialized variants. A list of available Jensen basis sets is given in Table 2.16.[21, 22, 23, 24, 25, 26, 27]

Table 2.16 Available Jensen basis sets.

Basis Set	Elem.	ECP	Comment
pc-0	H–Ca, Ga–Kr	–
pc-1	H–Kr	–
pc-2	H–Kr	–
pc-3	H–Kr	–
pc-4	H–Kr	–
aug-pc-0	H–Ca, Ga–Kr	–	pc-0 augmented by diffuse functions
aug-pc-1	H–Kr	–	pc-1 augmented by diffuse functions
aug-pc-2	H–Kr	–	pc-2 augmented by diffuse functions
aug-pc-3	H–Kr	–	pc-3 augmented by diffuse functions
aug-pc-4	H–Kr	–	pc-4 augmented by diffuse functions
Segmented contraction variants:
pcseg-0	H–Kr	–
pcseg-1	H–Kr	–
pcseg-2	H–Kr	–
pcseg-3	H–Kr	–
pcseg-4	H–Kr	–
aug-pcseg-0	H–Kr	–	pcseg-0 augmented by diffuse functions
aug-pcseg-1	H–Kr	–	pcseg-1 augmented by diffuse functions
aug-pcseg-2	H–Kr	–	pcseg-2 augmented by diffuse functions
aug-pcseg-3	H–Kr	–	pcseg-3 augmented by diffuse functions
aug-pcseg-4	H–Kr	–	pcseg-4 augmented by diffuse functions
Optimized for nuclear magnetic shieldings:
pcSseg-0	H–Kr	–
pcSseg-1	H–Kr	–
pcSseg-2	H–Kr	–
pcSseg-3	H–Kr	–
pcSseg-4	H–Kr	–
aug-pcSseg-0	H–Kr	–	pcSseg-0 augmented by diffuse functions
aug-pcSseg-1	H–Kr	–	pcSseg-1 augmented by diffuse functions
aug-pcSseg-2	H–Kr	–	pcSseg-2 augmented by diffuse functions
aug-pcSseg-3	H–Kr	–	pcSseg-3 augmented by diffuse functions
aug-pcSseg-4	H–Kr	–	pcSseg-4 augmented by diffuse functions
Optimized for spin-spin coupling constants:
pcJ-0	H–He, B–Ne, Al–Ar	–
pcJ-1	H–He, B–Ne, Al–Ar	–
pcJ-2	H–He, B–Ne, Al–Ar	–
pcJ-3	H–He, B–Ne, Al–Ar	–
pcJ-4	H–He, B–Ne, Al–Ar	–
aug-pcJ-0	H–He, B–Ne, Al–Ar	–	pcJ-0 augmented by diffuse functions
aug-pcJ-1	H–He, B–Ne, Al–Ar	–	pcJ-1 augmented by diffuse functions
aug-pcJ-2	H–He, B–Ne, Al–Ar	–	pcJ-2 augmented by diffuse functions
aug-pcJ-3	H–He, B–Ne, Al–Ar	–	pcJ-3 augmented by diffuse functions
aug-pcJ-4	H–He, B–Ne, Al–Ar	–	pcJ-4 augmented by diffuse functions
Optimized for hyperfine coupling constants:
pcH-1	H, He, B–Ne, Al–Ar	–
pcH-2	H, He, B–Ne, Al–Ar	–
pcH-3	H, He, B–Ne, Al–Ar	–
pcH-4	H, He, B–Ne, Al–Ar	–
aug-pcH-1	H, He, B–Ne, Al–Ar	–	pcH-1 augmented by diffuse functions
aug-pcH-2	H, He, B–Ne, Al–Ar	–	pcH-2 augmented by diffuse functions
aug-pcH-3	H, He, B–Ne, Al–Ar	–	pcH-3 augmented by diffuse functions
aug-pcH-4	H, He, B–Ne, Al–Ar	–	pcH-4 augmented by diffuse functions
Optimized for core-spectroscopy:
pcX-1	Li–Ar	–
pcX-2	Li–Ar	–
pcX-3	Li–Ar	–
pcX-4	Li–Ar	–
aug-pcX-1	Li–Ar	–	pcX-1 augmented by diffuse functions
aug-pcX-2	Li–Ar	–	pcX-2 augmented by diffuse functions
aug-pcX-3	Li–Ar	–	pcX-3 augmented by diffuse functions
aug-pcX-4	Li–Ar	–	pcX-4 augmented by diffuse functions

2.7.2.6. Hydrogenic Gaussian Basis Sets

Lehtolas hydrogenic Gaussian basis sets (HGBS) were constructed as widely transferable and accurate basis sets based on one-electron model systems imitating real atoms and molecules.[28] A list of available HGBS basis sets is given in Table 2.17.

Naming convention of HGBS basis sets

• \(m\): represents the energy optimization threshold \(10^{-m}\)

• P\(n\): represents the number of polarization shells

• \(A\): indicates explicit augmentation by diffuse functions

Table 2.17 Karlsruhe HGBS, HGBSP, AHGBS, and AHGBSP basis sets.

Basis Set	Elem.	ECP	Comment
HGBS-5	H–Og	–
HGBS-7	H–Og	–
HGBS-9	H–Og	–
HGBSP1-5	H–Og	–	Polarized variant
HGBSP1-7	H–Og	–
HGBSP1-9	H–Og	–
HGBSP2-5	H–Og	–
HGBSP2-7	H–Og	–
HGBSP2-9	H–Og	–
HGBSP3-5	H–Og	–
HGBSP3-7	H–Og	–
HGBSP3-9	H–Og	–
AHGBS-5	H–Og	–	Augmented by diffuse functions
AHGBS-7	H–Og	–
AHGBS-9	H–Og	–
AHGBSP1-5	H–Og	–	Polarized variant augmented by diffuse functions
AHGBSP1-7	H–Og	–
AHGBSP1-9	H–Og	–
AHGBSP2-5	H–Og	–
AHGBSP2-7	H–Og	–
AHGBSP2-9	H–Og	–
AHGBSP3-5	H–Og	–
AHGBSP3-7	H–Og	–
AHGBSP3-9	H–Og	–

2.7.2.7. Sapporo Basis Sets

The Sapporo basis set family, named after the city of Sapporo, Japan, comprises segmented contracted all-electron Gaussian basis sets up to quadruple-\(\zeta\) quality.[29, 30, 31] They were developed as compact yet accurate basis sets focusing on calculations with correlated wavefunction methods. Variants optimized for the scalar-relativistic DKH3 Hamiltonian are also available. A list of available Sapporo basis sets is given in Table 2.18. Relativistic variants are discussed in Section 2.7.3.6.

Table 2.18 List of available Sapporo basis sets.

Basis Set	Elem.	ECP	Comment
Sapporo-DZP-2012	H–Xe	–
Sapporo-TZP-2012	H–Xe	–
Sapporo-QZP-2012	H–Xe	–

2.7.2.8. Partridge Basis Sets

The basis sets of the Partridge family are uncontracted RHF groundstate energy-optimized.[32, 33] A list of available Partridge basis sets is given in Table 2.19.

Table 2.19 AvailablePartridge basis sets.

Basis Set	Elem.	ECP	Comment
Partridge-1	H, Li–Sr	–
Partridge-2	H, Li–Kr	–
Partridge-3	H, Li–Zn	–
Partridge-4	Sc–Zn	–

2.7.2.9. CRENB Basis Sets

The Christiansen-Ross-Ermler-Nash-Bursten (CRENB) basis sets and effective core potentials are available for most elements.[34, 35, 36, 37, 38, 39, 40] Note that while the ECPs were originally designed for spin-orbit coupling (SOC) interactions, SOC calculations with ECPs are currently not implemented in ORCA. A list of availble CRENB basis sets is given in Table 2.20.

Table 2.20 List of available CRENB basis sets.

Basis Set	Elem.	ECP	Comment
CRENBL	H, Li–Og	CRENBL-ECP (Li–Og)	Large basis version for use with small-core ECP

2.7.2.10. LANL Basis Sets

The Los Alamos National Laboratory (LANL) basis sets and effective core potentials were originally introduced in 1985 by Hay and Wadt.[41, 42, 43] Later polarized variants were proposed[44, 45] and the basis sets were extended by Roy et al.[46]. A list of available LANL basis sets is given in Table 2.21.

Table 2.21 List of available LANL basis sets.

Basis Set	Elem.	ECP	Comment
LANL08	Na–La, Hf–Bi	HayWadt (Na–La, Hf–Bi)	uncontracted
LANL08(f)	Sc–Cu, Y–Ag, La, Hf–Au	HayWadt (Sc–Cu, Y–Ag, La, Hf–Au)	uncontracted + polarization
LANL2DZ	H, Li–La, Hf–Bi, U–Pu	HayWadt (Na–La, Hf–Bi, U–Pu)	double-\(\zeta\), D95V for H–Ne
LANL2TZ	Sc–Zn, Y–Cd, La, Hf–Hg	HayWadt (Sc–Zn, Y–Cd, La, Hf–Hg)	triple-\(\zeta\)
LANL2TZ(f)	Sc–Cu, Y–Ag, La, Hf–Au	HayWadt (Sc–Cu, Y–Ag, La, Hf–Au)	triple-\(\zeta\) + polarization

2.7.2.11. Correlation-consistent Basis Sets

The correlation-consistent basis sets were pioneered by Dunning and co-workers and manifold variants have been developed since. They are among the most widely used for application with correlated wave-function methods and are particularly suited for basis set extrapolation. A list of available correlation-consisten basis sets is given in Table 2.22. Relativistic variants are discussed in Section 2.7.3.7.

Table 2.22 List of available correlation-consistent basis sets.

Basis Set	Elem.	ECP	Comment
cc-pVDZ	H–Ar, Ca–Kr	–	Dunning correlation-consistent polarized double-\(\zeta\)
cc-pVTZ	H–Ar, Ca–Kr, Y, Ag, Au	–	Dunning correlation-consistent polarized triple-\(\zeta\)
cc-pVQZ	H–Ar, Ca–Kr	–	Dunning correlation-consistent polarized quadruple-\(\zeta\)
cc-pV5Z	H–Ar, Ca–Kr	–	Dunning correlation-consistent polarized quintuple-\(\zeta\)
cc-pV6Z	H–He, Be–Ne, Al–Ar	–	Dunning correlation-consistent polarized sextuple-\(\zeta\)
aug-cc-pVDZ	H–Ar, Sc–Kr	–	cc-pVDZ augmented by diffuse functions
aug-cc-pVTZ	H–Ar, Sc–Kr, Ag, Au	–	cc-pVTZ augmented by diffuse functions
aug-cc-pVQZ	H–Ar, Sc–Kr	–	cc-pVQZ augmented by diffuse functions
aug-cc-pV5Z	H–Ar, Sc–Kr	–	cc-pV5Z augmented by diffuse functions
aug-cc-pV6Z	H–He, B–Ne, Al–Ar	–	cc-pV6Z augmented by diffuse functions
With tight d functions:
cc-pVD(+d)Z	Na–Ar	–
cc-pVT(+d)Z	Na–Ar	–
cc-pVQ(+d)Z	Na–Ar	–
cc-pV5(+d)Z	Na–Ar	–
aug-cc-pVD(+d)Z	Al–Ar	–	cc-pVD(+d)Z augmented by diffuse functions
aug-cc-pVT(+d)Z	Al–Ar	–	cc-pVT(+d)Z augmented by diffuse functions
aug-cc-pVQ(+d)Z	Al–Ar	–	cc-pVQ(+d)Z augmented by diffuse functions
aug-cc-pV5(+d)Z	Al–Ar	–	cc-pV5(+d)Z augmented by diffuse functions
aug-cc-pV6(+d)Z	Al–Ar	–	cc-pV6(+d)Z augmented by diffuse functions
Partially augmented according to Truhlar et al.[47]:
apr-cc-pV(Q+d)Z	H–Ar	–	Augmented with sp diffuse functions on Li–Ca
may-cc-pV(T+d)Z	H–Ar	–	Augmented with sp diffuse functions on Li–Ca
may-cc-pV(Q+d)Z	H–Ar	–	Augmented with spd diffuse functions on Li–Ca
jun-cc-pV(D+d)Z	H–Ar	–	Augmented with sp diffuse functions on Li–Ca
jun-cc-pV(T+d)Z	H–Ar	–	Augmented with spd diffuse functions on Li–Ca
jun-cc-pV(Q+d)Z	H–Ar	–	Augmented with spdf diffuse functions on Li–Ca
jul-cc-pV(D+d)Z	H–Ar	–	Augmented with spd diffuse functions on Li–Ca
jul-cc-pV(T+d)Z	H–Ar	–	Augmented with spdf diffuse functions on Li–Ca
jul-cc-pV(Q+d)Z	H–Ar	–	Augmented with spdfg diffuse functions on Li–Ca
maug-cc-pV(D+d)Z	H–Ar	–	Equals jun-cc-pV(D+d)Z
maug-cc-pV(T+d)Z	H–Ar	–	Equals may-cc-pV(T+d)Z
maug-cc-pV(Q+d)Z	H–Ar	–	Equals apr-cc-pV(Q+d)Z
Core-polarized for core-valence electron correlation:
cc-pCVDZ	H–Ar, Ca, Ga–Kr	–	Equals cc-pVDZ for H and He
cc-pCVTZ	H–Ar, Ca, Ga–Kr	–	Equals cc-pVTZ for H and He
cc-pCVQZ	H–Ar, Ca, Ga–Kr	–	Equals cc-pVQZ for H and He
cc-pCV5Z	H–Ar, Ca, Ga–Kr	–	Equals cc-pV5Z for H and He
cc-pCV6Z	H–He, B–Ne, Al–Ar	–	Equals cc-pV6Z for H and He
aug-cc-pCVDZ	H–Ar, Ga–Kr	–	cc-pCVDZ augmented by diffuse functions, equals aug-cc-pVDZ for H and He
aug-cc-pCVTZ	H–Ar, Ga–Kr	–	cc-pCVTZ augmented by diffuse functions, equals aug-cc-pVTZ for H and He
aug-cc-pCVQZ	H–Ar, Ga–Kr	–	cc-pCVQZ augmented by diffuse functions, equals aug-cc-pVQZ for H and He
aug-cc-pCV5Z	H–Ar, Ga–Kr	–	cc-pCV5Z augmented by diffuse functions, equals aug-cc-pV5Z for H and He
aug-cc-pCV6Z	H–He, B–Ne, Al–Ar	–	cc-pCV6Z augmented by diffuse functions, equals aug-cc-pV6Z for H and He
Core-polarized with weighted core functions:
cc-pwCVDZ	H–Ar, Ca, Ga–Kr	–	Equals cc-pVDZ for H and He
cc-pwCVTZ	H–Ar, Ca–Kr, Ag, Au	–	Equals cc-pVTZ for H and He
cc-pwCVQZ	H–Ar, Ca–Kr	–	Equals cc-pVQZ for H and He
cc-pwCV5Z	H–Ar, Ca–Kr	–	Equals cc-pV5Z for H and He
aug-cc-pwCVDZ	H–Ar, Ga–Kr	–	cc-pwCVDZ augmented by diffuse functions, equals aug-cc-pVDZ for H and He
aug-cc-pwCVTZ	H–Ar, Sc–Kr, Ag, Au	–	cc-pwCVTZ augmented by diffuse functions, equals aug-cc-pVTZ for H and He
aug-cc-pwCVQZ	H–Ar, Sc–Kr	–	cc-pwCVQZ augmented by diffuse functions, equals aug-cc-pVQZ for H and He
aug-cc-pwCV5Z	H–Ar, Sc–Kr	–	cc-pwCV5Z augmented by diffuse functions, equals aug-cc-pV5Z for H and He
Pseudo-potential (ECP) variants:
cc-pVDZ-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra, U	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)
cc-pVTZ-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra, U	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)
cc-pVQZ-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra, U	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)
cc-pV5Z-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)
aug-cc-pVDZ-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)	cc-pVDZ-PP augmented by diffuse functions
aug-cc-pVTZ-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)	cc-pVTZ-PP augmented by diffuse functions
aug-cc-pVQZ-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)	cc-pVQZ-PP augmented by diffuse functions
aug-cc-pV5Z-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)	cc-pV5Z-PP augmented by diffuse functions
cc-pCVDZ-PP	Ca, Sr, Ba, Ra	SK-MCDHF-RSC (Ca, Sr, Ba, Ra)
cc-pCVTZ-PP	Ca, Sr, Ba, Ra	SK-MCDHF-RSC (Ca, Sr, Ba, Ra)
cc-pCVQZ-PP	Ca, Sr, Ba, Ra	SK-MCDHF-RSC (Ca, Sr, Ba, Ra)
cc-pCV5Z-PP	Ca, Sr, Ba, Ra	SK-MCDHF-RSC (Ca, Sr, Ba, Ra)
aug-cc-pCVDZ-PP	Ca, Sr, Ba, Ra	SK-MCDHF-RSC (Ca, Sr, Ba, Ra)	cc-pCVDZ-PP augmented by diffuse functions
aug-cc-pCVTZ-PP	Ca, Sr, Ba, Ra	SK-MCDHF-RSC (Ca, Sr, Ba, Ra)	cc-pCVTZ-PP augmented by diffuse functions
aug-cc-pCVQZ-PP	Ca, Sr, Ba, Ra	SK-MCDHF-RSC (Ca, Sr, Ba, Ra)	cc-pCVQZ-PP augmented by diffuse functions
aug-cc-pCV5Z-PP	Ca, Sr, Ba, Ra	SK-MCDHF-RSC (Ca, Sr, Ba, Ra)	cc-pCV5Z-PP augmented by diffuse functions
cc-pwCVDZ-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra, U	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)
cc-pwCVTZ-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra, U	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)
cc-pwCVQZ-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra, U	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)
cc-pwCV5Z-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)
aug-cc-pwCVDZ-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)	cc-pwCVDZ-PP augmented by diffuse functions
aug-cc-pwCVTZ-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)	cc-pwCVTZ-PP augmented by diffuse functions
aug-cc-pwCVQZ-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)	cc-pwCVQZ-PP augmented by diffuse functions
aug-cc-pwCV5Z-PP	Ca, Cu–Kr, Sr–Xe, Ba, Hf–Rn, Ra	SK-MCDHF-RSC (Ca, Cu–Kr, Sr–Xe, Ba, Hf–Ra, U)	cc-pwCV5Z-PP augmented by diffuse functions
Optimized for hyperfine coupling constants:
aug-cc-pVTZ-J	H, B–F, Al–Cl, Sc–Zn, Se	–	Sauer’s basis set for accurate hyperfine coupling
W4 theory:
haV(T+d)Z	H–Ar	–	cc-pVTZ (H–Be, Na, Mg), aug-cc-pVTZ (B–Ne), aug-cc-pVT(+d)Z (Al–Ar)
haV(Q+d)Z	H–Ar	–	cc-pVQZ (H–Be, Na, Mg), aug-cc-pVQZ (B–Ne), aug-cc-pVQ(+d)Z (Al–Ar)
haV(5+d)Z	H–Ar	–	cc-pV5Z (H–Be, Na, Mg), aug-cc-pV5Z (B–Ne), aug-cc-pV5(+d)Z (Al–Ar)

2.7.2.12. F12 Basis Sets

Special orbital basis sets for F12 calculations (larger than the regular D, T, Q-zeta basis sets!). A list of available F12 basis sets is given in Table 2.23. See Table 2.37 for the necessary complementary auxiliary basis sets (CABS).

Table 2.23 F12 basis sets.

Basis Set	Elem.	ECP	Comment
cc-pVDZ-F12	H–Ar	–
cc-pVTZ-F12	H–Ar	–
cc-pVQZ-F12	H–Ar	–
Core-polarized:
cc-pCVDZ-F12	Li–Ar	–
cc-pCVTZ-F12	Li–Ar	–
cc-pCVQZ-F12	Li–Ar	–
Pseudo-potential (ECP) variants:
cc-pVDZ-PP-F12	Ga–Kr, In–Xe, Tl–Rn	SK-MCDHF-RSC (Ga–Kr, In–Xe, Tl–Rn)
cc-pVTZ-PP-F12	Ga–Kr, In–Xe, Tl–Rn	SK-MCDHF-RSC (Ga–Kr, In–Xe, Tl–Rn)
cc-pVQZ-PP-F12	Ga–Kr, In–Xe, Tl–Rn	SK-MCDHF-RSC (Ga–Kr, In–Xe, Tl–Rn)

2.7.2.13. Atomic Natural Orbital Basis Sets

Atomic natural orbitals are a special class of basis sets. They are represented by the orthonormal set of orbitals that diagonalizes a spherically symmetric, correlated atomic density. The idea is to put as much information as possible into each basis functions such that one obtains the best possible result with the given number of basis functions. This is particularly important for correlated calculations where the number of primitives is less an issue than the number of basis functions. ORCA features some ANO basis sets on the basis of the cc-pV6Z (or pc-4 where missing) basis set primitives.[48] These are very accurate and significantly better than the cc-pV\(n\)Z counterparts for the same number of basis functions (but much larger number of primitives). A list of available ANO basis sets is given in Table 2.24.

Note

• aug-ANO-pV\(n\)Z: full augmentation with spd, spdf, spdfg set of polarization functions. Almost as expensive as the next higher basis set. In fact, aug-ANO-pV\(n\)Z \(=\) ANO-pV(\(n+1\))Z with the highest angular momentum polarization function deleted.

• saug-ANO-pV\(n\)Z: augmentation with a single set of sp functions. Greatly enhances the accuracy of the SCF energies but not for correlation energies.

Table 2.24 Available atomic natural orbital (ANO) basis sets.

Basis Set	Elem.	ECP	Comment
ANO-SZ	H–Ar, Sc–Zn	–
ANO-pVDZ	H–Ar, Sc–Zn	–
ANO-pVTZ	H–Ar, Sc–Zn	–
ANO-pVQZ	H–Ar, Sc–Zn	–
ANO-pV5Z	H–Ar, Sc–Zn	–
ANO-pV6Z	H–Ar, Sc–Zn	–
aug-ANO-pVDZ	H–Ar, Sc–Zn	–	ANO-pVDZ augmented by diffuse functions
aug-ANO-pVTZ	H–Ar, Sc–Zn	–	ANO-pVTZ augmented by diffuse functions
aug-ANO-pVQZ	H–Ar, Sc–Zn	–	ANO-pVQZ augmented by diffuse functions
aug-ANO-pV5Z	H–Ar, Sc–Zn	–	ANO-pV5Z augmented by diffuse functions
saug-ANO-pVDZ	H–Ar, Sc–Zn	–	ANO-pVDZ augmented by by a single set of diffuse sp functions
saug-ANO-pVTZ	H–Ar, Sc–Zn	–	ANO-pVTZ augmented by by a single set of diffuse sp functions
saug-ANO-pVQZ	H–Ar, Sc–Zn	–	ANO-pVQZ augmented by by a single set of diffuse sp functions
saug-ANO-pV5Z	H–Ar, Sc–Zn	–	ANO-pV5Z augmented by by a single set of diffuse sp functions

2.7.2.13.1. Efficient Calculations with ANO Basis Sets

Usually, ANO basis sets are “generally contracted” which means that for any given angular momentum all primitives contribute to all basis functions. Since the concept of ANOs only makes sense if the underlying set of primitives is large, the calculations readily become very expensive unless special precaution is taken in the integral evaluation algorithms. ORCA features special algorithms for ANO basis sets together with accurate ANO basis sets for non-relativistic calculations. However, even then the integral evaluation is so expensive that efficiency can only be realized if all integrals are stored on disk and are re-used as needed.

Currently, the use of ANOs is restricted to the built-in ANO basis sets. These are built upon the cc-pV6Z primitives and hence, the calculations take significant time.

Hint

Geometry optimizations with ANOs are discouraged; they will be very inefficient.

The use of ANOs is recommended in the following way:

! ano-pVTZ Conv TightSCF CCSD(T)
%maxcore 2000 
* int 0 1
C  0 0 0    0   0   0
O  1 0 0  1.2   0   0
H  1 2 0  1.1 120   0
H  1 2 3  1.1 120 180
*

This yields:

ano-pVTZ:
E(SCF) = -113.920388785
E(corr)=   -0.427730189

Compare to the cc-pVTZ value of:

cc-pVTZ:
E(SCF) = -113.911870901
E(corr)=   -0.421354947

Thus, the ANO-based SCF energy is ca. 8–9 mEh lower and the correlation energy almost 2 mEh lower than with the cc-basis set of the same size. Usually, the ANO results are much closer to the basis set limit than the cc-results. Also, ANO values extrapolate very well (see section Automatic extrapolation to the basis set limit)

Importantly, the integrals are all stored in this job. Depending on your system and your patience, this may be possible up to 300–500 basis functions. The ORCA correlation modules have been rewritten such that they deal efficiently with these stored integrals. Thus, we might as well have used ! MO-CCSD(T) or ! AO-CCSD(T) , both of which would perform well.

Yet, the burden of generating and storing all four-index integrals quickly becomes rather heavy. Hence, the combination of ANO basis sets with the RI-JK technique is particularly powerful and efficient. For example:

! ano-pVTZ cc-pVTZ/JK RI-JK Conv TightSCF RI-CCSD(T)

For the SCF, this works very well and allows for much larger ANO based calculations to be done efficiently. Also, RI-MP2 can be done very efficiently in this way. However, for higher order correlation methods such as CCSD(T) the logical choice would be RI-CCSD(T) which is distinctly less efficient than the AO or MO based CCSD(T) (roughly a factor of two slower). Hence, ORCA implements a hybrid method where the RI approximation is used to generate all four index integrals. This is done via the “RI-AO” keyword:

! ano-pVTZ cc-pVTZ/JK RI-AO Conv TightSCF AO-CCSD(T)

In this case either AO-CCSD(T) or MO-CCSD(T) would both work well. This does not solve the storage bottleneck with respect to the four index integrals of course. If this becomes a real issue, then RI-CCSD(T) is mandatory. The error in the total energy is less than 0.1 mEh in the present example.

Warning

With conventional RI calculations the use of a second fit basis set is not possible and inconsistent results will be obtained. Hence, stick to one auxiliary basis!

2.7.2.14. Miscellaneous and Specialized Basis Sets

A list of further available specialized and miscellaneous basis sets is given in Table 2.25.

Table 2.25 Collection of available miscellaneous and specialized basis sets.

Basis Set	Elem.	ECP	Comment
D95	H, Li, B–Ne, Al–Cl	–	Dunning’s double-\(\zeta\) basis set
D95p	H, Li, B–Ne, Al–Cl	–	Polarized version of D95
EPR-II	H, B–F	–	Barone’s double-\(\zeta\) basis set for EPR calculations
EPR-III	H, B–F	–	Barone’s triple-\(\zeta\) basis set for EPR calculations
IGLO-II	H, B–F, Al–Cl	–	Kutzelnigg’s basis set for NMR and EPR calculations.
IGLO-III	H, B–F, Al–Cl	–	Kutzelnigg’s larger basis set for NMR and EPR calculations.
UGBS	H–Th, Pu–Am, Cf–Lr	–	Universal Gaussian basis set.
CP	Sc–Zn	–
CP(PPP)	Sc–Zn	–
Wachters+f	Sc–Cu	–
W1-mtsmall	H–Ar	–	W1 theory basis set
W1-DZ	H–Ar	–	W1 theory basis set
W1-TZ	H–Ar	–	W1 theory basis set
W1-QZ	H–Ar	–	W1 theory basis set
W1-Opt	H–Ar	–	W1 theory basis set
MINI	H–Ca	–	Huzinaga’s minimal basis set.
MINIS	H–Ca	–	Scaled version of the MINI
MIDI	H–Na, Al–K	–	Huzinaga’s valence double-\(\zeta\) basis set
MINIX	H–Rn	def-ECP (Rb–Lr)	Combination of small basis sets by Grimme (see Table 3.30). Used in HF-3c.
def2-mSVP	H–Rn	def2-ECP (Rb–Rn), def-ECP (Fr–Lr)	Used in PBEh-3c and B3LYP-3c
def2-mTZVP	H–Rn	def2-ECP (Rb–Rn), def-ECP (Fr–Lr)	Used in B97-3c
def2-mTZVPP	H–Lr	def2-ECP (Rb–Rn), def-ECP (Fr–Lr)	Used in r²SCAN-3c
vDZP	H–Rn	vDZP-ECP (B–Rn)	Molecule-optimized polarized valence double-\(\zeta\) basis set by Grimme et al. Used in \(\omega\)B97X-3c.[49]

2.7.3. Relativistic Basis Sets

Scalar-relativistic calculations with the DKH, ZORA or X2C approaches typically require specifically optimized or recontracted basis sets – see Basis Sets in Relativistic Calculations for details. ORCA provides various suitable basis sets for such calculations like the recontracted Karlsruhe, the SARC, and SARC2, and various optimized all-electron correlation-consistent basis sets. Suitable auxiliary basis options like SARC/J or AutoAux can be found in Section 2.7.4.

2.7.3.1. Recontracted Ahlrichs Basis Sets

A list of available relativistically recontracted variants of the original Ahlrichs basis sets is given in Table 2.26. Refer to the section Ahlrichs Basis Sets for the origin of the legacy definitions with the prefix “old-“.

Table 2.26 Relativistically recontracted Ahlrichs basis sets. RH = relativistic Hamiltonian.

Basis Set	Elem.	RH	Comment
DKH-SV(P)	H–Kr	DKH2
DKH-SVP	H–Kr	DKH2
DKH-TZV(P)	H–Kr	DKH2
DKH-TZVP	H–Kr	DKH2
DKH-TZVPP	H–Kr	DKH2
DKH-QZVP	H–Kr	DKH2
DKH-QZVPP	H–Kr	DKH2
ZORA-SV(P)	H–Kr	ZORA
ZORA-SVP	H–Kr	ZORA
ZORA-TZV(P)	H–Kr	ZORA
ZORA-TZVP	H–Kr	ZORA
ZORA-TZVPP	H–Kr	ZORA
ZORA-QZVP	H–Kr	ZORA
ZORA-QZVPP	H–Kr	ZORA
Legacy definitions (not recommended!)
old-DKH-SV(P)	H–I	DKH2
old-DKH-SVP	H–I	DKH2
old-DKH-TZV(P)	H–I	DKH2
old-DKH-TZVP	H–I	DKH2
old-DKH-TZVPP	H–I	DKH2
old-ZORA-SV(P)	H–I	ZORA
old-ZORA-SVP	H–I	ZORA
old-ZORA-TZV(P)	H–I	ZORA
old-ZORA-TZVP	H–I	ZORA
old-ZORA-TZVPP	H–I	ZORA

2.7.3.2. Recontracted Karlsruhe def2 Basis Sets

A list of available adapted DKH and ZORA versions of the def2 basis sets (i.e., for the all-electron def2 basis sets) is given in Table 2.27. These basis sets retain the original def2 exponents but have only one contracted function per angular momentum (and hence are somewhat larger), with contraction coefficients suitable for the respective scalar relativistic Hamiltonian. These basis sets can be combined with the SARC and SARC2 basis sets for the heavier elements.

Table 2.27 Relativistically recontracted Karlsruhe basis sets. RH = relativistic Hamiltonian.

Basis Set	Elem.	RH	Comment
DKH-def2-SVP	H–Kr	DKH2
DKH-def2-SV(P)	H–Kr	DKH2
DKH-def2-TZVP	H–Kr	DKH2
DKH-def2-TZVP(-f)	H–Kr	DKH2
DKH-def2-TZVPP	H–Kr	DKH2
DKH-def2-QZVPP	H–Kr	DKH2
ZORA-def2-SVP	H–Kr	ZORA
ZORA-def2-SV(P)	H–Kr	ZORA
ZORA-def2-TZVP	H–Kr	ZORA
ZORA-def2-TZVP(-f)	H–Kr	ZORA
ZORA-def2-TZVPP	H–Kr	ZORA
ZORA-def2-QZVPP	H–Kr	ZORA
Minimally augmented (scheme by Truhlar et al.[17])
ma-DKH-def2-SVP	H–Kr	DKH2
ma-DKH-def2-SV(P)	H–Kr	DKH2
ma-DKH-def2-TZVP	H–Kr	DKH2
ma-DKH-def2-TZVP(-f)	H–Kr	DKH2
ma-DKH-def2-TZVPP	H–Kr	DKH2
ma-DKH-def2-QZVPP	H–Kr	DKH2
ma-ZORA-def2-SVP	H–Kr	ZORA
ma-ZORA-def2-SV(P)	H–Kr	ZORA
ma-ZORA-def2-TZVP	H–Kr	ZORA
ma-ZORA-def2-TZVP(-f)	H–Kr	ZORA
ma-ZORA-def2-TZVPP	H–Kr	ZORA
ma-ZORA-def2-QZVPP	H–Kr	ZORA

2.7.3.3. SARC Basis Sets

Segmented all-electron relativistically contracted (SARC) basis sets for use with the DKH2 and ZORA Hamiltonians.[50, 51, 52, 53, 54, 55] A list of available SARC basis sets is given in Table 2.28.

Tip

Specifically for wavefunction-based calculations of lanthanide systems we recommend the more heavily polarized SARC2 basis sets [56].

Table 2.28 Relativistic SARC basis sets. RH = relativistic Hamiltonian.

Basis Set	Elem.	RH	Comment
SARC-DKH-SVP	Hf–Hg	DKH2
SARC-DKH-TZVP	Rb–Rn, Ac–Lr	DKH2
SARC-DKH-TZVPP	Rb–Rn, Ac–Lr	DKH2
SARC-ZORA-SVP	Hf–Hg	ZORA
SARC-ZORA-TZVP	Rb–Rn, Ac–Lr	ZORA
SARC-ZORA-TZVPP	Rb–Rn, Ac–Lr	ZORA

Note

SARC/J is the general-purpose Coulomb-fitting auxiliary for all SARC orbital basis sets.

2.7.3.4. SARC2 Basis Sets

SARC basis sets of valence quadruple-zeta quality for lanthanides, with NEVPT2-optimized (3g2h) polarization functions (SARC2).[56] Suitable for accurate calculations using correlated wavefunction methods. A list of available SARC2 basis sets is given in Table 2.29.

Table 2.29 Relativistic SARC2 basis sets. RH = relativistic Hamiltonian.

Basis Set	Elem.	ECP	Comment
SARC2-DKH-QZV	La–Lu	DKH2
SARC2-DKH-QZVP	La–Lu	DKH2
SARC2-ZORA-QZV	La–Lu	ZORA
SARC2-ZORA-QZVP	La–Lu	ZORA

Note

Each basis set has a large dedicated /JK auxiliary basis set for simultaneous Coulomb and exchange fitting (cf. Table 2.35).

2.7.3.5. Karlsruhe x2c Basis Sets

For calculations with the X2C Hamiltonian, all-electron basis sets up to Rn are available.[57] The “-s” variants, e.g. x2c-TZVPall-s, are augmented with additional tight functions for NMR shielding calculations.[58] The “-2c” variants, e.g. x2c-TZVPall-2c, are intended for two-component calculations including spin-orbit coupling (Note that two-component calculations are not implemented in ORCA). A list of available basis sets of this family is given in Table 2.30.

Tip

The x2c/J and AutoAux auxiliary basis set options can be used for these basis sets.

Table 2.30 Karlsruhe basis sets optimized for the x2c Hamiltonian.[57] RH = relativistic Hamiltonian.

Basis Set	Elem.	RH	Comment
x2c-SV(P)all	H–Rn	X2C
x2c-SVPall	H–Rn	X2C
x2c-TZVPall	H–Rn	X2C
x2c-TZVPPall	H–Rn	X2C
x2c-QZVPall	H–Rn	X2C
x2c-QZVPPall	H–Rn	X2C
NMR shielding optimized[58]
x2c-SV(P)all-s	H–Rn	X2C
x2c-SVPall-s	H–Rn	X2C
x2c-TZVPall-s	H–Rn	X2C
x2c-TZVPPall-s	H–Rn	X2C
x2c-QZVPall-s	H–Rn	X2C
x2c-QZVPPall-s	H–Rn	X2C
Two-component variants (no matching Hamiltonian yet!)
x2c-SV(P)all-2c	H–Rn	SO-X2C
x2c-SVPall-2c	H–Rn	SO-X2C
x2c-TZVPall-2c	H–Rn	SO-X2C
x2c-TZVPPall-2c	H–Rn	SO-X2C
x2c-QZVPall-2c	H–Rn	SO-X2C
x2c-QZVPPall-2c	H–Rn	SO-X2C
x2c-QZVPall-2c-s	H–Rn	SO-X2C
x2c-QZVPPall-2c-s	H–Rn	SO-X2C

2.7.3.6. Relativistic Sapporo Basis Sets

A list of relativistic variants of the Sapporo basis sets that were optimized for the DKH3 Hamiltonian and finite nucleus are given in Table 2.31.

Table 2.31 Relativistic Sapporo basis sets. RH = relativistic Hamiltonian.

Basis Set	Elem.	RH	Comment
Sapporo-DKH3-DZP-2012	K–Rn	DKH3	Optimized for DKH3 and finite nucleus
Sapporo-DKH3-TZP-2012	K–Rn	DKH3
Sapporo-DKH3-QZP-2012	K–Rn	DKH3

2.7.3.7. Relativistic Correlation-Consistent Basis Sets

A list of relativistic variants of the correlation-consistent basis sets is given in Table 2.32.

Table 2.32 Relativistic correlation-consistent basis sets. RH = relativistic Hamiltonian.

Basis Set	Elem.	RH	Comment
cc-pVDZ-DK	H–Ar, Sc–Kr	DKH2
cc-pVTZ-DK	H–Ar, Sc–Kr, Y–Xe, Hf–Rn	DKH2
cc-pVQZ-DK	H–Ar, Sc–Kr, In–Xe, Tl–Rn	DKH2
cc-pV5Z-DK	H–Ar, Sc–Kr	DKH2
cc-pVDZ-DK3	U	DKH3	For use with 3rd-order DKH
cc-pVTZ-DK3	U	DKH3
cc-pVQZ-DK3	U	DKH3
aug-cc-pVDZ-DK	H–Ar, Sc–Kr	DKH2	cc-pVDZ-DK augmented by diffuse functions
aug-cc-pVTZ-DK	H–Ar, Sc–Kr, Y–Xe, Hf–Rn	DKH2	cc-pVTZ-DK augmented by diffuse functions
aug-cc-pVQZ-DK	H–Ar, Sc–Kr, In–Xe, Tl–Rn	DKH2	cc-pVQZ-DK augmented by diffuse functions
aug-cc-pV5Z-DK	H–Ar, Sc–Kr	DKH2	cc-pV5Z-DK augmented by diffuse functions
cc-pwCVDZ-DK	H–Be, Na–Mg, Ca–Zn	DKH2	Equals cc-pVDZ-DK for H and He
cc-pwCVTZ-DK	H–Be, Na–Mg, Ca–Zn, Y–Xe, Hf–Rn	DKH2	Equals cc-pVTZ-DK for H and He
cc-pwCVQZ-DK	H–Be, Na–Mg, Ca–Zn, In–Xe, Tl–Rn	DKH2	Equals cc-pVQZ-DK for H and He
cc-pwCV5Z-DK	H–Be, Na–Mg, Ca–Zn	DKH2	Equals cc-pV5Z-DK for H and He
cc-pwCVDZ-DK3	U	DKH3
cc-pwCVTZ-DK3	U	DKH3
cc-pwCVQZ-DK3	U	DKH3
aug-cc-pwCVDZ-DK	H–Be, Na–Mg, Sc–Zn	DKH3	cc-pwCVDZ-DK augmented by diffuse functions, equals aug-cc-pVDZ-DK for H and He
aug-cc-pwCVTZ-DK	H–Be, Na–Mg, Sc–Zn, Y–Xe, Hf–Rn	DKH2	cc-pwCVTZ-DK augmented by diffuse functions, equals aug-cc-pVTZ-DK for H and He
aug-cc-pwCVQZ-DK	H–Be, Na–Mg, Sc–Zn, In–Xe, Tl–Rn	DKH2	cc-pwCVQZ-DK augmented by diffuse functions, equals aug-cc-pVQZ-DK for H and He
aug-cc-pwCV5Z-DK	H–Be, Na–Mg, Sc–Zn	DKH2	cc-pwCV5Z-DK augmented by diffuse functions, equals aug-cc-pV5Z-DK for H and He

2.7.3.8. Relativistically Contracted ANO Basis Sets

The relativistic contracted ANO basis sets of Roos and coworkers were developed for the DKH2 Hamiltonian. The full list is given in Table 2.33.

Table 2.33 Relativistic contracted ANO basis sets. RH = relativistic Hamiltonian.

Basis Set	Elem.	RH	Comment
ANO-RCC-Full	H–Cm	DKH2	Complete ANO-RCC basis sets.
ANO-RCC-DZP	H–Cm	DKH2	Double-\(\zeta\) contraction of ANO-RCC-Full.
ANO-RCC-TZP	H–Cm	DKH2	Triple-\(\zeta\) contraction of ANO-RCC-Full.
ANO-RCC-QZP	H–Cm	DKH2	Quadruple-\(\zeta\) contraction of ANO-RCC-Full.

2.7.4. Auxiliary Basis Sets

Resolution-of-the-idendity (RI) techniques can be used to speed up various types of calculations. Any RI method requires the definition of a reasonable auxiliary basis set in addition to the chosen orbital basis set. ORCA provides various built-in auxiliary basis set options for AuxJ, AuxJK, AuxC, and CABS and an automatic auxiliary basis set generation called AutoAux. Auxiliary basis sets can further be read from external files as described in Section 2.7.9.

Note

The distinction beweeen AuxJ, AuxJK, AuxC, and CABS, as well as how to correctly assign them, is explained above.

2.7.4.1. Coulomb-fitting auxiliary basis sets (AuxJ)

The auxiliary basis sets listed in Table 2.34 are suitable for the RI-J, RIJDX/RIJONX, and RIJCOSX approximations.

Table 2.34 Available Coulomb-fitting auxiliary basis sets.

Keyword	Elements	Comment
def2/J	H–Lr	Weigend’s “universal” Coulomb-fitting basis suitable for all def2 and def type basis sets. Assumes the use of ECPs beyond Kr (do not use with DKH/ZORA/X2C).
def2-mTZVP/J	H–Lr
def2-mTZVPP/J	H–Lr
x2c/J	H–Rn	Weigend’s Coulomb-fitting basis for the all-electron x2c-XVPall basis sets
SARC/J	H–Rn, Ac–Lr	General-purpose Coulomb-fitting basis set for all-electron calculations. Consists of the decontracted def2/J up to Kr and of our own auxiliary basis sets for the rest of the periodic table. Appropriate for use in DKH or ZORA calculations with the recontracted versions of the all-electron def2 basis sets (up to Kr) and the SARC basis sets for the heavier elements.

2.7.4.2. Coulomb- and exchange-fitting auxiliary basis sets (AuxJK)

The auxiliary basis sets listed in Table 2.35 are optimized for the RI-JK approximation. They can safely be used for RI-J, RIJDX/RIJONX, or RIJCOSX, but in that case they must be assigned to AuxJ via the %basis block.

Table 2.35 Available Coulomb- and exchange-fitting auxiliary basis sets.

Keyword	Elements	Comment
def2/JK	H–Rn	Coulomb+Exchange fitting for all def2 basis sets
def2/JKsmall	H–Ra, Th–Lr	reduced version of def2/JK
cc-pVTZ/JK	H, B–F, Al–Cl, Ga–Br	For use with the respective cc-pV\(n\)Z orbital basis
cc-pVQZ/JK	H, B–F, Al–Cl, Ga–Br
cc-pV5Z/JK	H, B–F, Al–Cl, Ga–Br
aug-cc-pVTZ/JK	H, B–F, Al–Cl, Ga–Br	For use with the respective aug-cc-pV\(n\)Z orbital basis
aug-cc-pVQZ/JK	H, B–F, Al–Cl, Ga–Br
aug-cc-pV5Z/JK	H, B–F, Al–Cl, Ga–Br
SARC2-DKH-QZV/JK	La–Lu
SARC2-DKH-QZVP/JK	La–Lu
SARC2-ZORA-QZV/JK	La–Lu
SARC2-ZORA-QZVP/JK	La–Lu

2.7.4.3. Auxiliary basis sets for correlated methods (AuxC)

The available auxiliary basis sets suitable for post-(CAS)SCF dynamical electron correlation methods are listed in Table 2.36.

Table 2.36 Available auxiliary basis sets for correlated methods.

Keyword	Elements	Comment
def2-SVP/C	H–Rn	For use with the respective def2 orbital basis
def2-TZVP/C	H–Rn
def2-TZVPP/C	H–Rn
def2-QZVPP/C	H–Rn
def2-SVPD/C	H–La, Hf–Rn
def2-TZVPD/C	H–La, Hf–Rn
def2-TZVPPD/C	H–La, Hf–Rn
def2-QZVPPD/C	H–La, Hf–Rn
cc-pVDZ/C	H–Ar, Ga–Kr	For use with the respective cc-pV\(n\)Z orbital basis
cc-pVTZ/C	H–Ar, Sc–Kr
cc-pVQZ/C	H–Ar, Sc–Kr
cc-pV5Z/C	H–Ar, Ga–Kr
cc-pV6Z/C	H–He, B–Ne, Al–Ar
aug-cc-pVDZ/C	H–He, Be–Ne, Mg–Ar, Ga–Kr	For use with the respective aug-cc-pV\(n\)Z orbital basis
aug-cc-pVTZ/C	H–He, Be–Ne, Mg–Ar, Sc–Kr
aug-cc-pVQZ/C	H–He, Be–Ne, Mg–Ar, Sc–Kr
aug-cc-pV5Z/C	H–Ne, Al–Ar, Ga–Kr
aug-cc-pV6Z/C	H–He, B–Ne, Al–Ar
cc-pwCVDZ/C	H–He, B–Ne, Al–Ar, Ga–Kr	For use with the respective cc-pwCV\(n\)Z orbital basis, equals cc-pV$n$Z/C for H and He
cc-pwCVTZ/C	H–He, B–Ne, Al–Ar, Sc–Kr
cc-pwCVQZ/C	H–He, B–Ne, Al–Ar, Ga–Kr
cc-pwCV5Z/C	H–Ne, Al–Ar
aug-cc-pwCVDZ/C	H–He, B–Ne, Al–Ar, Ga–Kr	For use with the respective aug-cc-pwCV\(n\)Z orbital basis, equals aug-cc-pV$n$Z/C for H and He
aug-cc-pwCVTZ/C	H–He, B–Ne, Al–Ar, Sc–Kr
aug-cc-pwCVQZ/C	H–He, B–Ne, Al–Ar, Ga–Kr
aug-cc-pwCV5Z/C	H–Ne, Al–Ar
cc-pVDZ-PP/C	Cu–Kr, Y–Xe, Hf–Rn	For use with the respective cc-pV\(n\)Z-PP orbital basis
cc-pVTZ-PP/C	Cu–Kr, Y–Xe, Hf–Rn
cc-pVQZ-PP/C	Cu–Kr, Y–Xe, Hf–Rn
aug-cc-pVDZ-PP/C	Cu–Kr, Y–Xe, Hf–Rn	For use with the respective aug-cc-pV\(n\)Z-PP orbital basis
aug-cc-pVTZ-PP/C	Cu–Kr, Y–Xe, Hf–Rn
aug-cc-pVQZ-PP/C	Cu–Kr, Y–Xe, Hf–Rn
cc-pwCVDZ-PP/C	Cu–Kr, Y–Xe, Hf–Rn	For use with the respective cc-pwCV\(n\)Z-PP orbital basis
cc-pwCVTZ-PP/C	Cu–Kr, Y–Xe, Hf–Rn
cc-pwCVQZ-PP/C	Cu–Kr, Y–Xe, Hf–Rn
aug-cc-pwCVDZ-PP/C	Cu–Kr, Y–Xe, Hf–Rn	For use with the respective aug-cc-pwCV\(n\)Z-PP orbital basis
aug-cc-pwCVTZ-PP/C	Cu–Kr, Y–Xe, Hf–Rn
aug-cc-pwCVQZ-PP/C	Cu–Kr, Y–Xe, Hf–Rn
cc-pVDZ-F12-MP2Fit	H–Ar	For use with the respective cc-pV\(n\)Z-F12 orbital basis
cc-pVTZ-F12-MP2Fit	H–Ar
cc-pVQZ-F12-MP2Fit	H–Ar
cc-pVDZ-PP-F12-MP2Fit	Ga–Kr, In–Xe, Tl–Rn	For use with the respective cc-pV\(n\)Z-PP-F12 orbital basis
cc-pVTZ-PP-F12-MP2Fit	Ga–Kr, In–Xe, Tl–Rn
cc-pVQZ-PP-F12-MP2Fit	Ga–Kr, In–Xe, Tl–Rn
cc-pCVDZ-F12-MP2Fit	Li–Ar	For use with the respective cc-pCV\(n\)Z-F12 orbital basis
cc-pCVTZ-F12-MP2Fit	Li–Ar
cc-pCVQZ-F12-MP2Fit	Li–Ar

2.7.4.4. Complementary auxiliary basis sets for F12 (CABS)

The available CABS options for F12 methods are listed in Table 2.37.

Table 2.37 Available complementary auxiliary basis sets for F12 methods.

Keyword	Elements	Comment
cc-pVDZ-F12-CABS	H, B–Ne, Al–Ar	For use with the respective cc-pV\(n\)Z-F12 orbital basis
cc-pVTZ-F12-CABS	H, B–Ne, Al–Ar
cc-pVQZ-F12-CABS	H, B–Ne, Al–Ar
cc-pVDZ-F12-OptRI	H–Ar	Identical to the cc-pV\(n\)Z-F12-CABS basis above
cc-pVTZ-F12-OptRI	H–Ar
cc-pVQZ-F12-OptRI	H–Ar
cc-pVDZ-PP-F12-OptRI	Ga–Kr, In–Xe, Tl–Rn	For use with the respective cc-pV\(n\)Z-PP-F12 orbital basis
cc-pVTZ-PP-F12-OptRI	Ga–Kr, In–Xe, Tl–Rn
cc-pVQZ-PP-F12-OptRI	Ga–Kr, In–Xe, Tl–Rn
aug-cc-pVDZ-PP-OptRI	Cu–Zn, Ag–Cd, Au–Hg	For use with the respective aug-cc-pV\(n\)Z-PP-F12 orbital basis
aug-cc-pVTZ-PP-OptRI	Cu–Zn, Ag–Cd, Au–Hg
aug-cc-pVQZ-PP-OptRI	Cu–Zn, Ag–Cd, Au–Hg
aug-cc-pV5Z-PP-OptRI	Cu–Zn, Ag–Cd, Au–Hg
cc-pCVDZ-F12-OptRI	Li–Ar	For use with the respective cc-pCV\(n\)Z-PP-F12 orbital basis
cc-pCVTZ-F12-OptRI	Li–Ar
cc-pCVQZ-F12-OptRI	Li–Ar
aug-cc-pwCVDZ-PP-OptRI	Cu–Zn, Ag–Cd, Au–Hg	For use with the respective aug-cc-pwCV\(n\)Z-PP-F12 orbital basis
aug-cc-pwCVTZ-PP-OptRI	Cu–Zn, Ag–Cd, Au–Hg
aug-cc-pwCVQZ-PP-OptRI	Cu–Zn, Ag–Cd, Au–Hg
aug-cc-pwCV5Z-PP-OptRI	Cu–Zn, Ag–Cd, Au–Hg

2.7.4.5. Automatic Generation of Auxiliary Basis Sets (AutoAux)

If no auxiliary basis set is available for your chosen orbital basis set, one can be generated automatically by ORCA using the keyword AutoAux. This is specified as any other fitting basis set: as a value to the AuxJ/AuxJK/AuxC variables in the %basis block or as a separate keyword in the simple input line (in which case all three Aux slots are populated with identical fitting basis sets). AutoAux can also be assigned to individual elements or atoms – see sections Assigning or Adding Basis Functions to an Element and Assigning or Adding Basis Functions to Individual Atoms. The generated basis sets can be used for Coulomb, exchange and correlation fitting and are as accurate as the optimized auxiliary basis sets at the cost of being up to twice as large.[59] The available settings for AutoAux are given in Table 2.41 with their default values.

Note

The generation procedure in ORCA 3.1 was significantly different and does not produce the same results! For compatibility, the old version is still accessible via the setting OldAutoAux true in the %basis block.

Note that if the orbital basis set contains diffuse functions, as is the case for the aug-cc-pVXZ sets, the AutoAux fitting basis may contain (near-)linear dependencies. In this case, the Cholesky decomposition of the Coulomb metric will fail and the program will likely crash. One may print the offending auxiliary basis using !PrintBasis and manually remove the most diffuse s- and/or p-functions, which will usually resolve the problem. An alternative, automatic solution is also implemented – see section Removal of Redundant Basis Functions.

2.7.5. Effective Core Potentials

Starting from version 2.8.0, ORCA features effective core potentials (ECPs). They are a good alternative to scalar relativistic all-electron calculations if heavy elements are involved. This pertains to geometry optimizations and energy calculations but may not be true for property calculations.

In order to reduce the computational effort, the usually highly contracted and chemically inert core basis functions can be eliminated by employing ECPs. ECP calculations comprise a “valence-only” basis and thus are subject to the frozen core approximation. Contributions due to the core orbitals are accounted for by an effective one-electron operator \(U^{\text{core} }\) which replaces the interactions between core and valence electrons and accounts for the indistinguishability of the electrons. Its radial parts \(U_l(r)\) are generally expressed as a linear combination of Gaussian functions, while the angular dependence is included through angular momentum projectors \(|S^l_m\rangle\).

\[U^{\text{core} } = U_L(r) + \sum\limits_{l=0}^{L-1} \sum\limits_{m=-l}^{l}\left|S^l_m \rangle \left[U_l(r) - U_L(r)\right]\langle S^l_m\right|\]

\[U_l = \sum\limits_k d_{kl}r^{n_{kl} } \exp (-\alpha_{kl}r^2)\]

The maximum angular momentum \(L\) is generally defined as \(l_{\text{max} }^{\text{atom} } + 1\). The parameters \(n_{kl}\), \(\alpha_{kl}\) and \(d_{kl}\) that are necessary to evaluate the ECP integrals have been published by various authors, among them the well-known Los Alamos (LANL) [41] and Stuttgart–Dresden (SD) [60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105] parameter sets. Depending on the specific parametrization of the ECP, relativistic effects can be included in a semiempirical fashion in an otherwise nonrelativistic calculation. Introducing \(U^{\text{core} }\) into the electronic Hamiltonian yields two types of ECP integrals, the local (or type-1) integrals that arise because of the maximum angular momentum potential \(U_L\) and the semi-local (or type-2) integrals that result from the projected potential terms. The evaluation of these integrals in ORCA proceeds according to the scheme published by Flores-Moreno et al.[106].

A selection of ECP parameters and associated basis sets is directly accessible in ORCA through the internal ECP library (see Table 2.38 for a listing of keywords).

Table 2.38 Overview of library keywords for ECPs and associated basis sets available in ORCA.

ECP keyword	Core size[1]	Elements	Valence basis sets
Recommended
def-ECP	78	Fr–Ra	Karlsruhe def2 basis sets: def-SV(P), def-SVP, def-TZVP, def-TZVPP, ma-def-TZVP MINIX
	60	Ac–Lr
def2-ECP	28	Rb–Xe	Karlsruhe basis sets: def2-SVP, def2-TZVP, etc. def2-SVPD, def2-TZVPD, etc. ma-def2-SVP, ma-def2-TZVP, etc.
	46	Cs–La
	28	Ce–Lu
	60	Hf–Rn
SK-MCDHF-RSC	10	Ca, Cu–Kr	Correlation-consistent basis sets: cc-pV\(n\)Z-PP, aug-cc-pV\(n\)Z-PP, cc-pCV\(n\)Z-PP, aug-cc-pCV\(n\)Z-PP, cc-pwCV\(n\)Z-PP, aug-cc-pwCV\(n\)Z-PP (\(n=\) D, T, Q, 5) cc-pV\(n\)Z-PP (\(n=\) D, T, Q)
	28	Sr–Xe
	46	Ba
	60	Hf–Rn
	78	Ra
	60	U
HayWadt[2]	10	Na–Cu	LANL basis sets: LANL2DZ, LANL2TZ, LANL2TZ(f), LANL08, LANL08(f)
	18	Zn
	28	Ga–Ag
	36	Cd
	46	In–La
	60	Hf–Au
	68	Hg–Tl
	78	Pb–Bi, U–Pu
dhf-ECP	28	Rb–Xe	Karlsruhe dhf basis sets: dhf-SVP, dhf-TZVP, etc.
	46	Cs–Ba
	60	Hf–Rn, U
vDZP-ECP	2	B–Mg	vDZP uniquely compiled for the use with vDZP
	10	Al–Zn
	28	Ga–Cd
	46	In–Lu
	60	Hf–Hg
	78	Tl–Rn
CRENBL-ECP	2	Li–Mg	CRENBL
	10	Al–Zn
	28	Rb–Cd
	36	In–Xe
	46	Cs–La
	54	Ce–Lu
	60	Hf-Hg
	68	Tl-Rn
	78	Fr-Ts
	92	Og
Legacy definitions
def2-SD	28,MWB	Rb–Cd
	28,MDF[3]	In–Xe
	46,MWB	Cs–La
	60,MWB	Hf–Pt
	60,MDF[4]	Au–Rn
def-SD	28,MWB	Rb–Cd
	46,MWB	In–La
	28,MWB	Ce–Lu
	60,MWB	Hf–Pt
	60,MDF[4]	Au, Hg, Rn
	78,MWB	Tl–At
	78,MDF	Fr, Ra
	60,MWB	Ac–Lr
SDD	2,SDF	Li, Be
	2,MWB	B–Ne
	10,SDF	Na, Mg
	10,MWB	Al–Ca
	10,MDF	Sc–Ni
	10,MWB	Cu-Zn
	28,MWB	Ga–Sr
	28,MHF	Y–Cd
	28,MDF	Ge–Br, Rb–Xe
	46,MWB	In–Ba
	28,MWB	La–Lu
	60,MWB	Hf–Hg
	78,MWB	Tl–Rn
	60,MWB	Ac–Lr
LANL1	10	Na–Ar
	18	K–Zn
	28	Ga–Kr
	36	Rb–Cd
	46	In–Xe
	54	Cs–La
	68	Hf–Tl
	78	Pb, Bi
LANL2	10	K–Cu
	28	Rb–Ag
	46	Cs–La
	60	Hf–Au

Note

Requesting some basis sets automatically assigns the matching ECP (except when using the NewGTO keyword): for example, “def2” basis sets use the def2-ECP. For others, see the respective basis set table entries.

The simplest way to assign ECPs is by using the ECP keyword within the simple input line. The ECP keyword itself assigns only the effective core potential, not a valence basis set! As an example for an explicitly named ECP you could use

! def2-TZVP def2-SD

This would assign the def2-SD ECP according to the definition given in the table above. Without the def2-SD keyword ORCA would default to def2-ECP.

Assignment of ECPs can be done within the %basis block using the ECP and NewECP keywords, as in the following example:

%basis
  ECP       "def2-ECP"     # All elements (for which the ECP is defined)
  NewECP Pt "def2-SD" end  # Different ECP for Pt
end

A variant of the NewECP keyword can be used for individual atoms inside the geometry definition:

* xyz ...
  ...
  S   0.0  0.0  0.0  NewECP "SDD" end
  ...
*

Note that these keywords also only affect the ECP and not the valence basis set!

In case the basis set for an element/atom has been changed using the NewGTO keyword (see sections Assigning or Adding Basis Functions to an Element and Assigning or Adding Basis Functions to Individual Atoms above) it may be necessary to remove the ECP from that element/atom. This can be done with the DelECP keyword in the %basis block or coordinates input, respectively:

! LANL2DZ                   # Uses HayWadt ECPs by default, starting from Na
%basis
  NewGTO S "def2-TZVP" end  # All-electron up to Kr
  DelECP S                  # Remove HayWadt ECP
end
* xyz ...
...
Cu   0.0  0.0  0.0  
  DelECP                    # Remove HayWadt ECP
  NewGTO "def2-QZVPP" end   # All-electron up to Kr
...
*

To remove all ECPs loaded by default (e.g. in case no global basis set is chosen) you can use the !NoECP simple keyword.

2.7.5.1. Manual Input of ECP Parameters

To manually specify ECP parameters, the NewECP keyword is followed by the element for which an ECP is to be entered, the number of core electrons to be replaced (N_core) and the maximum angular momentum (lmax). The ECP specification is finished by giving the definitions of the individual shells that constitute the angular dependent potentials U\(_l\).

%basis 
    NewECP <element>
      N_core <number of core electrons>
      lmax <max. angular momentum>
      [shells]
    end
end

For each ECP shell, first the angular momentum \(l\) has to be given, followed by the number of primitives. The primitives themselves are then specified by giving a running index and the respective tuple of exponent \(a_{kl}\), expansion coefficient \(d_{kl}\) and radial power \(n_{kl}\).

# ECP shell 
      l <number of primitives>
      1    a1l    d1l    n1l
      2    a2l    d2l    n3l
      ...

As an example, consider the SD(10,MDF) for Vanadium. The name indicates a Stuttgart–Dresden type ECP that replaces 10 core electrons and is derived from a relativistic calculation for the neutral atom. It consists of 4 shells with angular momentum s, p, d, and f. Note that the f shell has an expansion coefficient of 0.0 and thus will not contribute at all to this effective core potential. This is typical for all SD potentials (but may be different for program packages like TURBOMOLE that do not support arbitrary angular momentum with respect to the ECP and therefore use recontractions of the original parameter sets).

%basis 
  # ECP SD(10,MDF) for V 
  # M. Dolg, U. Wedig, H. Stoll, H. Preuss,
  # J. Chem. Phys. 86, 866 (1987).  
  NewECP V 
    N_core 10 
    lmax f 
    s 2 
      1      14.4900000000    178.4479710000  2 
      2       6.5240000000     19.8313750000  2 
    p 2 
      1      14.3000000000    109.5297630000  2 
      2       6.0210000000     12.5703100000  2 
    d 2 
      1      17.4800000000    -19.2196570000  2 
      2       5.7090000000     -0.6427750000  2 
    f 1 
      1       1.0000000000      0.0000000000  2 
  end
end

2.7.5.2. ECPs and Ghost Atoms

When ghost atoms are defined in the input (see section Special definitions), ECPs are not added to these atoms by default. If that is somehow needed, please add GhostECP true under the %basis block.

%basis 
 GhostECP true
 AllowGhostECP true # synonym
end

2.7.5.3. ECP Embedding

Computations on cluster models sometimes require the presence of embedding potentials in order to account for otherwise neglected repulsive terms at the border [107]. In order to simplify these kind of calculations with ORCA the ECP embedding can be accomplished quite easily:

*xyz ...
# atom>  charge x    y    z    optional ECP declaration
Zr>      4.0    0.0  0.0  0.0  NewECP "SDD" end
...
*

The declaration of such a coreless ECP center takes place in the coordinates section by appending a bracket “>” to the element symbol. Note that embedding ECPs are treated as point charges in ORCA, so the charge has to be given next. The coordinates of the coreless ECP center have to be specified as usual and may be followed by an optional ECP assignment. In general, calculations that employ an ECP embedding procedure should be single point calculations. However if the need arises to perform a geometry optimization, make sure to set up explicit Cartesian constraints for the coreless ECP centers.

2.7.6. Assigning or Adding Basis Functions to an Element

In order to assign a new basis set to a given element, use:

%basis
  NewGTO 8    # New basis for oxygen.
# NewGTO O    # This works as well.
   S   3      # s-shell
    1  910.10034975         0.03280967
    2  137.19711335         0.23422391
    3   30.85279077         0.81490980
   0   2      # also an s-shell
    1     1.72885887         0.27389659
    2     0.39954770         0.79112437
   P   1
    1     8.35065975         1.00000000
  end
end

For simplicity and consistency the input format is the same as that used in the basis set files. In this format, the first line carries the angular momentum of the shell to be added – either as an integer, or as a label (s, p, d, f, g, h, i, k) – and the number of primitives. Then for each primitive one line follows which has (a) the index of the primitive (1, 2, 3, …) (b) the exponent of the primitive and (c) the contraction coefficient (unnormalized). There also is the possibility to include a SCALE X statement after the number of primitives in the first line to indicate that the basis function exponents should be scaled.

Warning

• ORCA always uses spherical harmonic Gaussian functions.

• Angular momentum 7 is labeled as “k” – there are no j-shells in accepted spectroscopic conventions.

• Combined s- and p-shells are sometimes labelled as “L-shells” in other programs. This is not supported in the NewGTO format and to avoid confusion, shells with angular momentum 8 can only be specified with a number, and not with the label “l”.

In order to add basis functions to the basis of a given element (for example because you do not like the standard polarization functions) use AddGTO instead of NewGTO. In NewGTO or AddGTO you can also use the nicknames of internally stored basis sets. An example is:

%basis
  NewGTO 8    # new basis for oxygen
   "6-31G"
    D  1 
    1  0.4  1.0
  end
end

In this example the 6-31G basis is assigned to oxygen and in addition a polarization function with exponent 0.4 is added to the oxygen basis.

Note that the NewGTO keyword does not change the ECP for the given element – you must use NewECP or DelECP (see section Effective Core Potentials).

A similar mechanism was established for the auxiliary basis sets in RI calculations:

%basis
  NewAuxJGTO 8    # new auxiliary basis for oxygen
    s  1 
    1  350  1.0
    ... etc
  end
  AddAuxJGTO 8   # add a shell to the auxiliary basis for 
                # oxygen
    D  1 
    1  0.8  1.0
  end
end

New basis functions can be specifically assigned to any auxiliary basis sets. The keywords NewAuxCGTO, AddAuxCGTO, NewAuxJKGTO, AddAuxJKGTO, NewCABSGTO, AddCABSGTO are used in the same way. The keywords NewAuxGTO and AddAuxGTO are the same as NewAuxJGTO and AddAuxJGTO, that is, they only influence the Coulomb auxiliary basis (AuxJ)!

2.7.7. Assigning or Adding Basis Functions to Individual Atoms

Sometimes you may want to not treat all atoms of the same element with the same basis set but to assign a specific basis set to a specific atom in the molecules. This is also possible in ORCA and takes place in the coordinate section (%coords, *xyz, etc.). The format is the same as described above. An example may help to make things clear:

*int 0 1
  C  0 0 0 0.00   0.0   0.00
   AddGTO
     D  1 
      1  1.0  1.0
   end
  O  1 0 0 1.13   0.0   0.00
   NewGTO
     "6-311G"
     D  1 
      1  1.2  1.0
   end
*

In this example an extra d-shell with exponent 1.0 is added to the first carbon atom and the basis for the oxygen atom is changed to 6-311G with an extra d-function of exponent 1.2 added.

Analogously, AUX basis functions can be assigned or added to individual atoms using the keywords NewAuxJGTO, AddAuxJGTO, NewAuxCGTO, AddAuxCGTO, NewAuxJKGTO, AddAuxJKGTO, NewCABSGTO, AddCABSGTO.

A note on the use of AutoAux: if you change the basis set on a given atom and want to generate a fitting basis, you have to specify it again in the coordinates section, even if AutoAux is already present in the simple input line or in the %basis block. For example:

! def2-SVP def2/JK
%basis
  NewAuxJKGTO H
    "AutoAux"
  end
end
*xyz 0 1
  O  0.00 0.00 0.00
  H -0.25 0.93 0.00
  H  0.96 0.00 0.00
   AddGTO
     P 1
      1 1.6 1.0
     D 1
      1 1.0 1.0
   end
   NewAuxJKGTO
     "AutoAux"
   end
*

Here the oxygen atom is assigned the def2-SVP basis and the def2/JK fitting basis, the first hydrogen atom is assigned the def2-SVP basis and an automatically generated fitting basis and the second hydrogen atom is assigned the def2-SVP basis with two additional polarization functions and a larger automatically generated fitting basis that accounts for these functions.

Tip

When assigning custom basis sets it is always a good idea to print the basis set information (%output print[p_basis] 2 end or simply !PrintBasis) and check that everything is correct.

2.7.8. Assigning Basis Sets and ECPs to Fragments

In multi-level or QM/QM calculations it may be convenient to assign different basis sets to different fragments. This can be done with the keywords FragBasis, FragAuxJ, FragAuxJK, FragAuxC, FragCABS, and FragECP in the %basis block, followed by the number of the fragment (numbering starts at 1!) and a standard basis set or ECP from the ORCA library (see Section 2.7.2 and Table 2.38). Note that unlike the NewGTO keyword, FragBasis also changes the ECP, if applicable. Fragment basis sets will overload the global or element-specific (Section 2.7.6) choice but can be overloaded for individual atoms (Section 2.7.7). If AutoAux is requested for a fragment, it will be generated for the actual orbital basis set chosen for each atom, even if it is changed in the coordinates section. However, if AutoAux was requested for an element or in the simple input, the auxiliary basis will be generated before the fragment basis is assigned (which is not desired), therefore AutoAux must be requested again for the fragment. An example is given below:

! PrintBasis BP86 NoIter
! def2-SVP def2/J
%basis
  FragBasis 1 "def2-TZVP"
  FragBasis 2 "cc-pVTZ-PP"
  FragAuxJ  2 "AutoAux"
  FragECP   3 "SK-MCDHF-RSC"
  FragAuxJ  3 "def2/JK"
end
*xyz 0 1
  H(1) 0 0 0
  I(1) 0 0 1.6
  H(2) 0 5 0   NewGTO "cc-pVTZ" end
  I(2) 0 5 1.6
  H(3) 5 0 0
  I(3) 5 0 1.6
*
# Final basis sets:
# Atom Basis      ECP          AuxJ
# 0H   def2-TZVP  def2-ECP     def2/J
# 1I   def2-TZVP  def2-ECP     def2/J
# 2H   cc-pVTZ    -            AutoAux(cc-pVTZ)
# 3I   cc-pVTZ-PP SK-MCDHF-RSC AutoAux(cc-pVTZ-PP)
# 4H   def2-SVP   -            def2/JK
# 5I   def2-SVP   SK-MCDHF-RSC def2/JK

It is also possible to read fragment-specific basis sets from a file. The syntax is analogous, using the keywords ReadFragBasis, ReadFragAuxJ, ReadFragAuxJK, ReadFragAuxC, ReadFragCABS, and ReadFragECP. In this case, the input string is expected to be an existing basis set file in GAMESS-US format (see section Reading Basis Sets from a File). All other details above (e.g., regarding ECPs and AutoAux) also apply here.

Note

• Details regarding the assignment of fragments can be found in Fragment Specification section.

2.7.9. Reading Basis Sets from a File

By using the variables GTOName, GTOAuxJName, GTOAuxJKName, GTOAuxCName, and GTOCABSName (GTOAuxName is a synonym for GTOAuxJName) a basis set can be read from an ASCII file. In this way you can construct or modify your favorite standard basis set and load it easily into the program.

%basis
  GTOName      = "MyBasis.bas"      # read orbital basis
  GTOAuxJName  = "MyAuxJBasis.bas"  # read Coulomb-fitting basis
  GTOAuxJKName = "MyAuxJKBasis.bas" # read Coulomb- and exchange-fitting basis
  GTOAuxCName  = "MyAuxCBasis.bas"  # read correlation-fitting basis
  GTOCABSName  = "MyCABSBasis.bas"  # read complementary auxiliary basis set
end

A word of caution: under Windows, backslashes directory assignments must be given twice to be correctly understood! The format is that used for “GAMESS-US” in the EMSL library [108]. To give an example of what this format looks like here is a part of the 3-21GSP basis of Buenker and coworkers [109, 110]:

!                         lines in the beginning with '!' or '#' are comments
! BASIS="3-21GSP"
!Elements                             References                                
!--------                             ----------                                
! H - Ne: A.V. Mitin, G. Hirsch, R. J. Buenker, Chem. Phys. Lett. 259, 151 (1996)
! Na - Ar: A.V. Mitin, G. Hirsch, R. J. Buenker, J. Comp. Chem. 18, 1200 (1997). 
!
$DATA        ! Optional
HYDROGEN     ! (3s) -> [2s]      Element symbols are also recognized
 S   2
  1           4.50036231         0.15631167
  2           0.68128924         0.90466909
 S   1
  1           0.15137639         1.00000000
CARBON       ! (6s,3p) -> [3s,2p]                                
 S   3
  1         499.24042249         0.03330322
  2          75.25419194         0.23617745
  3          16.86538669         0.81336259
 L   2       ! L shells are a s and a p shell with identical exponents
  1           0.89739483         0.24008573         0.46214684
  2           0.21746772         0.81603757         0.66529098
 L   1
  1           4.52660451         1.00000000         1.00000000
$END         ! Optional

The file format for the auxiliary basis sets is exactly the same. Basis sets can be also exported in GAMESS-US format by the orca_exportbasis utility (section orca_exportbasis). Note that in order to read basis sets printed by ORCA (using !PrintBasis), the NewGTO and end keywords must be removed.

Warning

• Angular momentum 7 is labeled as “k” – there are no j-shells in accepted spectroscopic conventions.

• To avoid confusion with combined s- and p-shells, shells with angular momentum 8 can only be specified with a number, and not with the label “l”.

2.7.10. Linear Dependence

The previous sections describe the assessment of a desired molecular basis set from appropriately parametrized functions at various locations within the molecule (normally centered on atoms). The parametrization of these functions is such that the chance for redundancy is minimal. Since however, one is limited to work with finite numerical precision, and furthermore these parameters also depend on the molecular geometry, redundancies cannot be completely eliminated in advance. Redundancy means that the subspace spanned by the given basis functions at given values of parameters (including geometry), can be identically spanned by a smaller number of linear independent basis functions. Linear dependent (redundant) function sets however may cause numerical instabilities. Linear dependence is normally identified by searching for zero eigenvalues of the overlap matrix. Note that the inverse of the overlap (or related matrices) are used for orthogonalization purposes, and it follows that if near zero eigenvalues are not treated properly, the inverse becomes ill-defined, and the SCF procedure numerically unstable.

From the previous discussion, it is evident that the crucial parameter for curing linear dependence is the threshold below which an overlap eigenvalue is considered zero. This parameter may be changed using the following keyword

%scf
  sthresh 1e-6 # default 1e-7
end

Although there is no strict limit for the value of the above parameter, it should reasonably be somewhere between 1e-5 and 1e-8 (the default is 1e-7). One may get away with 1e-9 or perhaps even lower without convergence problem, but there is a risk that the result is contaminated with noise caused by the near zero vectors. In difficult cases, an 1e-6 threshold was often found to work smoothly, and above that one risks throwing away more and more functions, which also influence comparability of results with other calculations. To monitor the behavior of the small eigenvalues, one should look for the following block in the output

Diagonalization of the overlap matrix:
Smallest eigenvalue                        ... -1.340e-17
Time for diagonalization                   ...    0.313 sec
Threshold for overlap eigenvalues          ... 1.000e-07
Number of eigenvalues below threshold      ... 1
Smallest eigenvalue above threshold        ... 6.013e-07
Time for construction of square roots      ...    0.073 sec
Total time needed                          ...    0.387 sec

Here, the smallest eigenvalue is printed, along with the currently used overlap threshold, and the number of functions below this (which will be dropped). It is a recommended consistency check to look for an equal number of zero entries among orbital energies once the SCF procedure converged. Note that for functions belonging to zero eigenvalues no level shifts are applied!

In case that redundant vectors were removed from the basis, ! MORead NoIter should only be used in conjunction with the same SThresh as in the original calculation, otherwise the results will be inconsistent. ! MORead may still be used together with a change in SThresh, but a few SCF iterations will be required.

2.7.10.1. Automatic Adjustments for Near Linear-Dependent Cases

Starting from ORCA6, there is now a keyword called DiffSThresh, which controls an automatic tightening of the integral cutoff parameters Thresh and TCut in case small eigenvalues of the overlap matrix are found. We found this to be important in some calculations using diffuse basis, and these parameters are set to a minimum value of Thresh=1e-12 and TCut=1e-13 in case the “Smallest eigenvalue” shown above gets below that number. If the cutoffs are already tighter than that, for instance when using !VeryTightSCF, than nothing will happen.

We found empirically that these are safe numbers to mitigate noise and increase the robustness of the SCF procedure, thus they are enforced by default. The default is 1e-6 and this can be turned off by setting %SCF DiffSThresh -1 END on the input in case you don’t want this automatic adjustment to happen.

2.7.10.2. Removal of Redundant Basis Functions

While the approach described above is usually successful in removing linear dependencies from the orbital basis set, the auxiliary basis used in RI is not orthogonalized the same way. Instead, the RI linear equation system is solved using a Cholesky decomposition (CD) of the auxiliary basis Coulomb metric. If the auxiliary basis is redundant, the CD fails and the program usually aborts. One simple solution implemented in ORCA is to perform a pivoted Cholesky decomposition (PCD) of the metric, terminating at a given threshold. Then, the shells contributing to the nullspace are removed from the basis at the beginning of the calculation. This can be requested for any of the basis sets using either the overlap or the Coulomb metric. It is most appropriate for the AuxJ/AuxJK/AuxC basis using the Coulomb metric. The truncated basis can be examined using the !PrintBasis keyword. Often, functions may be removed for some atoms of a given element, but kept for others. As long as the threshold is low enough, i.e. only truly redundant functions are removed, this should not affect the molecular symmetry of the results.

%basis
  PCDTrimBas   Overlap # Trim the orbital basis in the overlap metric
  PCDTrimAuxJ  Coulomb # Trim the AuxJ basis in the Coulomb metric
  PCDTrimAuxJK Coulomb # Trim the AuxJK basis in the Coulomb metric
  PCDTrimAuxC  Coulomb # Trim the AuxC basis in the Coulomb metric
  PCDThresh    -1      # Threshold for the PCD: chosen automatically if <0
end

2.7.11. Which Methods Need Which Basis Sets?

ORCA offers a variety of methods and a large choice of orbital and auxiliary basis sets to go with them. Pure (GGA or meta-GGA) DFT functionals only require the calculation of Coulomb integrals, while hybrid DFT, HF (and by extension, all post-HF electron correlation methods, such as MP2 and coupled cluster), as well as CASSCF (and NEVPT2), require the calculation of Coulomb and exchange integrals.

• An orbital basis set (<basis>) is always needed for these methods.

• If RI is used for Coulomb integrals (RI-J, RIJDX/RIJONX, RIJCOSX), AuxJ is needed (usually <basis>/J or def2/J).

• If RI is also used for exchange integrals (RI-JK), AuxJK is needed instead (usually <basis>/JK or def2/JK).

• If RI is used for integral generation in post-SCF correlation methods, as in RI-MP2 (including double-hybrid DFT), DLPNO-MP2, and DLPNO-CC, AuxC is also needed (usually <basis/C>).

• In F12 methods, a specialized orbital basis is used (<basis>-F12) and CABS is needed in addition (usually <basis>-F12-CABS or <basis>-F12-OptRI).

An overview of auxiliary basis requirements for an inexhaustive list of methods and approximations is given in Table 2.39.

Table 2.39 Simple input keywords for basis sets and ECPs.

Method	Approximation	Basis sets
HF	NoRI (default)	<basis>
HF	RIJONX or RIJCOSX	<basis> + <basis>/J
HF	RI-JK	<basis> + <basis>/JK
pure DFT	RI (default)	<basis> + <basis>/J
hybrid DFT	NoRI	<basis>
hybrid DFT	RIJCOSX (default)	<basis> + <basis>/J
hybrid DFT	RI-JK	<basis> + <basis>/JK
CASSCF/NEVPT2		<basis>
CASSCF/NEVPT2	RI-JK	<basis> + <basis>/JK
CASSCF/NEVPT2	RIJCOSX	<basis> + <basis>/J + <basis>/C
CASSCF/NEVPT2	TrafoStep RI	<basis> + <basis>/JK or <basis>/C
NEVPT2-F12	TrafoStep RI	<basis>-F12 + <basis>-F12-CABS + <basis>/JK or <basis>/C
TDDFT		<basis>
MP2		<basis>
RI-MP2		<basis> + <basis>/C
RI-MP2	RI-JK	<basis> + <basis>/C + <basis>/JK
F12-MP2		<basis>-F12 + <basis>-F12-CABS
F12-RI-MP2		<basis>-F12 + <basis>-F12-CABS + <basis>/C
DLPNO-MP2		<basis> + <basis>/C
DLPNO-MP2	RIJCOSX	<basis> + <basis>/C + <basis>/J
F12-DLPNO-MP2		<basis>-F12 + <basis>-F12-CABS + <basis>/C
CCSD		<basis>
RI-CCSD		<basis> + <basis>/C
DLPNO-CCSD		<basis> + <basis>/C
DLPNO-CCSD	RIJCOSX	<basis> + <basis>/C + <basis>/J
F12-CCSD		<basis>-F12 + <basis>-F12-CABS
F12-RI-CCSD		<basis>-F12 + <basis>-F12-CABS + <basis>/C
F12-RI-CCSD	RI-JK	<basis>-F12 + <basis>-F12-CABS + <basis>/C + <basis>/JK

2.7.12. Keywords

Table 2.40 Simple input keywords for basis sets and ECPs.

Keyword	Description
<BasisName>	Assign the respective orbial basis set to all elements
<AUXJName>	Assign the respective AuxJ basis set to all elements
<AUXJKName>	Assign the respective AuxJK basis set to all elements
<AUXCName>	Assign the respective AuxJC basis set to all elements
<CABSName>	Assign the respective CABS to all elements
AutoAux	Automatically generate AuxJ, AuxJK, and AuxC auxiliary basis sets (see Section 2.7.4.5)
<ECPName>	Assign the respective ECP to all elements for which it is defined
NoECP	Remove the default ECP
Decontract	Decontract all (orbital and auxiliary) basis sets
DecontractBas	Decontract the orbital basis sets
NoDecontractBas	Do not decontract the basis set
DecontractAuxJ	Decontract the AuxJ basis set
NoDecontractAuxJ	Do not decontract the AuxJ basis
DecontractAuxJK	Decontract the AuxJK basis set
NoDecontractAuxJK	Do not decontract the AuxJK basis
DecontractAuxC	Decontract the AuxC basis set
NoDecontractAuxC	Do not decontract the AuxC basis

Table 2.41 %basis block input keywords for basis sets and ECPs.

Keyword	Options	Description
Basis	"<BasisName>"	Define the orbital basis set
AuxJ	"<AuxName>"	Define the J auxiliary basis set
AuxJK	"<AuxName>"	Define the JK auxiliary basis set
AuxC	"<AuxName>"	Define the correlation auxiliary basis set
CABS	"<CABSName>"	Define the complementary auxiliary basis set for F12 calculations
ECP	"<ECPName>"	Assign the respective ECP to all elements for which it is available
GhostECP	false	Activate ECPs on ghost atoms
AllowGhostECP	false	Equivalent to GhostECP
Decontraction options
Decontract	false	If true, decontract all basis sets
DecontractBas	false	If true, decontract the orbital basis set
DecontractAuxJ	false	If true, decontract the AuxJ basis set
DecontractAuxJK	false	If true, decontract the AuxJK basis set
DecontractAuxC	false	If true, decontract the AuxC basis set
DecontractCABS	true	If false, do not decontract the CABS
Setting basis sets for elements (see Section 2.7.6)
NewGTO	<Element> "<BasisName>" <shells> End	Define new Basis for element via built-in name and/or custom shells
AddGTO	<Element> <shells> End	Add GTO shells to basis for element
NewAuxJGTO	<Element> "<AuxName>" <shells> End	Define new AuxJ set for element via built-in name and/or custom shells
AddAuxJGTO	<Element> <shells> End	Add GTO shells to AuxJ for element
NewAuxJKGTO	<Element> "<AuxName>" <shells> End	Define new AuxJK set for element via built-in name and/or custom shells
AddAuxJKGTO	<Element> <shells> End	Add GTO shells to AuxJK for element
NewAuxCGTO	<Element> "<AuxName>" <shells> End	Define new AuxC set for element via built-in name and/or custom shells
AddAuxCGTO	<Element> <shells> End	Add GTO shells to AuxC for element
NewCABSGTO	<Element> "<CABSName>" <shells> End	Define new CABS set for element via built-in name and/or custom shells
AddCABSGTO	<Element> <shells> End	Add GTO shells to CABS for element
NewECP	<Element> "<ECPName>" End	Define new built-in ECP for element
	<Element> <shells> End	Manually define new ECP for element (see Section 2.7.5.1)
DelECP	<Element>	Remove the ECP for the element
Setting basis sets for fragments (see Section 2.7.8)
FragBasis	<FragID> "<BasisName>"	Define Basis for fragment
FragAuxJ	<FragID> "<AuxName>"	Define AuxJ for fragment
FragAuxJK	<FragID> "<AuxName>"	Define AuxJK for fragment
FragAuxC	<FragID> "<AuxName>"	Define AuxC for fragment
FragCABS	<FragID> "<CABSName>"	Define CABS for fragment
FragECP	<FragID> "<ECPName>"	Define ECP for fragment
ReadFragBasis	<FragID> "<filename.bas>"	Read Basis for fragment from file
ReadFragAuxJ	<FragID> "<filename.bas>"	Read AuxJ for fragment from file
ReadFragAuxJK	<FragID> "<filename.bas>"	Read AuxJK for fragment from file
ReadFragAuxC	<FragID> "<filename.bas>"	Read AuxC for fragment from file
ReadFragCABS	<FragID> "<filename.bas>"	Read CABS for fragment from file
ReadFragECP	<FragID> "<filename.bas>"	Read ECP for fragment from file
Reading basis sets from a file (see Section 2.7.9)
GTOName	<filename.bas>	Read orbital basis from file
GTOAuxJName	<filename.bas>	Read AuxJ from file
GTOAuxName	<filename.bas>	Equivalent to GTOAuxJName
GTOAuxJKName	<filename.bas>	Read AuxJK from file
GTOAuxCName	<filename.bas>	Read AuxC from file
GTOCABSName	<filename.bas>	Read CABS from file
Removal of linear dependence (see Section 2.7.10.2)
PCDTrimBas	Overlap	Trim the orbital basis in the overlap metric
PCDTrimAuxJ	Coulomb	Trim the AuxJ basis in the Coulomb metric
PCDTrimAuxJK	Coulomb	Trim the AuxJK basis in the Coulomb metric
PCDTrimAuxC	Coulomb	Trim the AuxC basis in the Coulomb metric
PCDThresh	-1	Threshold for the PCD (1e-16 to 1e-10 makes sense): chosen automatically if <0
AutoAux-related keywords (see Section 2.7.4.5)
AutoAuxSize	0	Use minimal effective rather than minimal primitive exponent (suitable for ANO basis sets)
	1	(default) Increases the maximal exponent for the shells with low angular momenta.
	2	Increases the maximal exponent for all shells
	3	Directly uses the primitives and produces the largest fitting basis
AutoAuxLmax	false	If true, increase the maximal angular momentum of the fitting basis set to the highest value permitted by ORCA and by the orbital basis set.
AutoAuxLLimit	-1	If >0, do not exceed the given angular momentum.
AutoAuxF[0]	20.0	The factor to increase the maximal s-exponent
AutoAuxF[1]	7.0	Same for the p-shell
AutoAuxF[2]	4.0	Same for the d-shell
AutoAuxF[3]	4.0	Same for the f-shell
AutoAuxF[4]	3.5	Same for the g-shell
AutoAuxF[5]	2.5	Same for the h-shell
AutoAuxF[6]	2.0	Same for the i-shell
AutoAuxF[7]	2.0	Same for the j-shell
AutoAuxB[0]	1.8	Even-tempered expansion factor for the s-shell
AutoAuxB[1]	2.0	Same for the p-shell
AutoAuxB[2]	2.2	Same for the d-shell
AutoAuxB[3]	2.2	Same for the f-shell
AutoAuxB[4]	2.2	Same for the g-shell
AutoAuxB[5]	2.3	Same for the h-shell
AutoAuxB[6]	3.0	Same for the i-shell
AutoAuxB[7]	3.0	Same for the j-shell
AutoAuxTightB	true	Only use AutoAuxB[l] for shells with high l and AutoAuxB[0] for the rest
OldAutoAux	false	If true, selects the ORCA 3.1 generation procedure (deprecated)

---

[1]

Where applicable, reference method and data are given (S: single-valence-electron ion; M: neutral atom; HF: Hartree–Fock; WB: quasi-relativistic; DF: relativistic).

[2]

Corresponds to LANL2 and to LANL1 where LANL2 is unavailable.

[3]

I: OLD-SD(28,MDF) for compatibility with TURBOMOLE.

[4] (1,2)

Au, Hg: OLD-SD(60,MDF) for compatibility with TURBOMOLE.