3.6. Semiempirical Methods

Semi-empirical quantum mechanical methods (SQM) are very useful to deal with many of very large systems. They use tailored approximations to reduce the computational cost drastically while keeping a reasonable level of accuracy for large parts of the chemical space. They are specifically useful to simulate raction paths with NEB-TS or to define a SQM region in multi-scale approaches like ONIOM.

3.6.1. Neglect of Differential Overlap: CNDO, INDO, NDDO

A number of methods based on the “neglect of differential overlap” [289, 290] are currently implemented for energies and analytic gradients inluding AM1[291], PM3[292], MNDO[293, 294, 295] and other variants of CNDO, INDO, and NDDO.The methods MNDO , AM1, and PM3 are available for main group elements only and arise from the work of the Dewar group. They have been optimized to reproduce molecular structure and energetics. The older CNDO/1,2 and INDO/1,2 were developed by the Pople group [296, 297, 298, 299, 300, 301, 302, 303, 304] and were designed to roughly mimic minimal basis ab initio calculations. The methods of the Zerner group (ZINDO/1,2 and ZINDO/S) are closely related to the older methods but have been well parameterized for transition metals too [305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315]. ZINDO/1 (and less so ZINDO/2) are suitable for geometry optimization. ZINDO/S gives good results for electronically excited states at moderate configuration interaction levels and is also successful for the calculation of electron and spin distributions in large transition metal complexes [310, 311, 312, 313, 314, 315]. The ZNDDO/1,2 methods have been implemented into ORCA as straightforward extensions of the corresponding INDO methods without changing any parameter. However, the methods benefit from the somewhat more accurate representation of the Coulomb interaction within the NDDO approximation [316, 317]. The preliminary experience with these methods is that they are better than the corresponding INDO methods for calculation of transition metal complex structures but on the whole have also similar deficiencies. The analytic gradients are available for all of these methods and can be used to produce reasonable molecular structures at low computational cost or to get preliminary insight in the behavior of the system under investigation. However, do not try to use ZINDO/S (or CNDO/S) for structure optimizations - it does not make sense and will lead to disastrous results because there is no accurate representation of nuclear repulsion in these methods.

Tip

Even though ORCA has no implementation of newer MNDO methods like PM6 or RM1, they can be used via ORCA’s External Optimizer feature and MOPAC. This way, MOPAC can be interfaced to provide ORCA with energies and gradients via the respective wrapper script that can be downloaded from the ORCA external tools GitHub repository.

3.6.1.1. Basic Usage

The NDDO-based MNDO, AM1, and PM3 methods can be invoked via the simple input keywords !MNDO, !AM1 and !PM3.

!MNDO

!AM1

!PM3

These and other methods can be further defined via the %method block, e.g. INDO with the INDO/1 parameter set as:

%method
   METHOD   INDO
   VERSION  INDO_1
end

Or by directly invoking the respective parameterization as METHOD

%method
   METHOD   INDO_1
end

Note

If you want you can also combine semiempirical methods with MP2 (energies only). For example use Method AM1 and DoMP2 true. It is questionable if this makes the results of semiempirical calculations any better but at least it is possible in ORCA.

3.6.1.2. Custom Parameters

You can change the built-in semiempirical parameters in a straightforward fashion via the %ndoparas block. To do so, any element sepcific parameters can be defined via an array “P”:

%ndoparas  
   P[<atomic number>,<parameter number>] <real>
end

For example, we can set the resonance integral parameter BS (s shell beta) with the number 25 for Carbon (Z = 6) to 20 eV:

%ndoparas  
   P[6,25] 20
end

A full list of parameters that can be modified can be found below. Most of them will only be interesting for expert users. The most commonly modified parameters are the Beta’s (number 25 through 28). Note that most programs require a negative number here. In ORCA the resonance integrals are defined in a way that makes the Beta’s positive.

Table 3.21 List of parameters that can be set in the %ndoparas block.

Parameter	Number	Description
Core Integrals (in eV):
US	0
UP	1
UD	2
UF	3
Basis Set Parameters (double-zeta):
NSH	4	Number of shells for the element
NZS	5	Number of Slater type orbitals for the s shell
ZS1	6	First exponent
ZS2	7	Second exponent
CS1	8	First contraction coefficient
CS2	9	Second contraction coefficient
NZP	10	Number of Slater type orbitals for the p shell
ZP1	11
ZP2	12
CP1	13
CP2	14
NZD	15	Number of Slater type orbitals for the d shell
ZD1	16
ZD2	17
CD1	18
CD2	19
NZF	20	Number of Slater type orbitals for the f shell
ZF1	21
ZF2	22
CF1	23
CF2	24
Resonance integral parameters (in eV):
BS	25	s shell beta
BP	26	p shell beta
BD	27	d shell beta
BF	28	f shell beta
Number of electrons in the ground state:
NEL	29	Total number of electrons (integer)
NS	30	Fractional occupation number of the s shell
NP	31	Fractional occupation number of the p shell
ND	32	Fractional occupation number of the d shell
NF	33	Fractional occupation number of the f shell
One center repulsion (gamma) integrals (in eV):
GSS	34
GSP	35
GSD	36
GSF	37
GPP	38
GPD	39
GPF	40
GDD	41
GDF	42
GFF	43
Slater Condon parameters (in eV):
F2PP	44
F2PD	45
F2DD	46
F4DD	47
G1SP	48
G1PD	49
G2SD	50
G3PD	51
R1SPPD	52
R2SDPP	53
R2SDDD	54
The nuclear repulsion parameters for Dewar type models:
NR1	55
NR2	56
NR3	57
NR4	58
NR5	59
NR6	60
NR7	61
NR8	62
NR9	63
NR10	64
NR11	65
NR12	66
NR13	67
Nuclear attraction/repulsion parameter for MNDO/d:
RHO	68
Spin orbit coupling parameters:
SOCP	69	SOC for the p shell
SOCD	70	SOC for the d shell
SOCF	71	SOC for the f shell

The “molecular” parameters are also set in the %ndoparas block using “INTFA” (“interaction factors”);

%ndoparas  
   INTFA[PP_PI] 0.585
  # The interaction factors exist for
  #  ss_sigma
  #  sp_sigma
  #  sd_sigma
  #  pp_sigma
  #  pd_sigma
  #  dd_sigma
  #  pp_pi
  #  pd_pi
  #  dd_pi
  #  dd_delta
  # the parameter entering the Coulomb integrals
  # in INDO/S
   FGAMMA 1.2
end

3.6.1.3. Keywords

Table 3.22 Simple input keywords for the NDO-based methods.

Keyword	Description
AM1	Activates AM1
PM3	Activates PM3
MNDO	Activates MNDO
ZINDO/1	Activates ZINDO/1
ZINDO/2	Activates ZINDO/2
ZINDO/S	Activates ZINDO/S
ZNDDO/1	Activates ZNDDO/1
ZNDDO/2	Activates ZNDDO/2

Table 3.23 %method block input keywords for the NDO-based methods.

Keyword	Options	Description
METHOD	AM1	Activates AM1
	PM3	Activates PM3
	MNDO	Activates MNDO
	CNDO_1	Activates CNDO/1
	CNDO_2	Activates CNDO/2
	CNDO_S	Activates CNDO/S
	INDO_1	Activates INDO/1
	INDO_2	Activates INDO/2
	INDO_S	Activates INDO/S
	ZINDO_1	Activates ZINDO/1
	ZINDO_2	Activates ZINDO/2
	ZINDO_S	Activates ZINDO/S
	ZNDDO_1	Activates ZNDDO/1
	ZNDDO_2	Activates ZNDDO/2
	CNDO	Activates CNDO, requires a VERSION to be set
	INDO	Activates INDO, requires a VERSION to be set
	NDDO	Activates NDDO, requires a VERSION to be set
VERSION	CNDO_1	Sets the parameter set for CNDO to CNDO_1
	CNDO_2	Sets the parameter set for CNDO to CNDO_2
	CNDO_S	Sets the parameter set for CNDO to CNDO_S
	INDO_1	Sets the parameter set for INDO to INDO_1
	INDO_2	Sets the parameter set for INDO to INDO_2
	INDO_S	Sets the parameter set for INDO to INDO_S
	ZINDO_1	Sets the parameter set for INDO to ZINDO_1
	ZINDO_2	Sets the parameter set for INDO to ZINDO_2
	ZINDO_S	Sets the parameter set for INDO to ZINDO_S
	ZNDDO_1	Sets the parameter set for NDDO to ZNDDO_1
	ZNDDO_2	Sets the parameter set for NDDO to ZNDDO_2
	MNDO	Sets the parameter set for NDDO to MNDO
	AM1	Sets the parameter set for NDDO to AM1
	PM3	Sets the parameter set for NDDO to PM3

3.6.2. Extended Tight-Binding: GFN0-xTB, GFN-xTB, GFN2-xTB

ORCA is interfaced to the xtb program by Grimme and coworkers, allowing the user to request all kinds of calculations using the popular GFN0-xTB, GFN-xTB and GFN2-xTB Hamiltonians.[161, 318, 319] From the technical side, the user has to provide the executable provided by the Grimme group. The xtb program package can be obtained free of charge from https://github.com/grimme-lab/xtb/releases and detailed information on the usage of the xtb standalone program and its utilities can be found at https://xtb-docs.readthedocs.io/en/latest/contents.html. Only the file bin/xtb is used by ORCA . The user should copy this file into the directory where the other ORCA executables are located, and rename it as otool_xtb.

Warning

Please use the 6.7.1 version (or any later version) of xtb; older versions are not fully compatible with ORCA anymore or are missing features, for example it may not be possible to invoke the solvation model! Additionally, Windows users should copy libiomp5md.dll from the XTB directory to the ORCA directory.

The xTB method can be invoked via the GFN0-xTB, GFN-xTB, and GFN2-xTB keywords. The GFN-FF generic force-field can be invoked via GFN-FF:

! GFN0-xTB  # Synonym: XTB0

! GFN-xTB  # Synonym: XTB1

! GFN2-xTB  # Synonym: XTB2

! GFN-FF # Synonym: XTBFF

The following methods can be used in conjunction with XTB:

• Single Point Energy

• Energy and Gradient

• Optimization, using all kinds of constraints, relaxed surface scans, etc.

• Nudged-Elastic Band calculations

• Numerical Frequency Calculations

• Intrinsic Reaction Coordinate

• Molecular Dynamics Calculations

• QM/MM calculations

Note

• XTB0 is a non-self-consistent tight-binding method, and as such, its accuracy is generally inferior to XTB1 and XTB2 (and sometimes even XTBFF), despite that it is a few times faster than XTB1 and XTB2. From our experience, we only recommend XTB0 when both XTB1 and XTB2 exhibit qualitative failures for the system of interest.

• Please note that XTB0, XTB1 and XTB2 can also be used for the initial path generation or for the calculation of an initial TS structure on XTB level, both as input for the subsequent NEB calculation on a higher level of theory. For more details, please consult section Nudged Elastic Band Method.

3.6.2.1. Solvation in xTB

Three implicit solvation models can be requested in xTB calculations:

1. the analytical linearized Poisson-Boltzmann (ALPB)[320] solvation model

2. the domain decomposition COSMO (ddCOSMO)[321]

3. the extended conductor-like polarizable continuum model (CPCM-X).[149]

These models can be requested via the simple keyword input:

! ALPB(solvent) # use ALPB

! DDCOSMO(solvent) # use ddCOSMO

! CPCMX(solvent) # use CPCMX

where solvent is any of the solvents in Table 3.24.

They can further be envoked via the %xtb block, here exemplarily shown for ALPB:

%xtb
  DOALPB true
  ALPBSOLVENT "water"
end

Table 3.24 List of available solvents for the different implicit solvation methods that can be used with xtb.

Solvent	ALPB	ddCOSMO	CPCM-X
1,2,4-trimethylbenzene			X
1,2-dichloroethane			X
1,4-dioxane / dioxane	X	X
1-butanol / butanol			X
1-chlorohexane / chlorohexane			X
1-decanol / decanol			X
1-fluorooctane			X
1-heptanol / heptanol			X
1-hexanol / hexanol			X
1-iodohexadecane / hexadecyliodide			X
1-nonanol / nonanol			X
1-octanol / octanol	X	X	X
1-pentanol / pentanol			X
1-propanol / propanol			X
2,2,4-trimethylpentane / isooctane			X
2,6-dimethylpyridine			X
2-butanol / secbutanol			X
2-methoxyethanol / methoxyethanol			X
2-methyl-1-propanol / isobutanol			X
2-methylpyridine / 2methylpyridine			X
2-propanol / isopropanol			X
4-methyl-2-pentanone / 4methyl2pentanone			X
acetic acid / aceticacid			X
acetone	X	X
acetonitrile / mecn / ch3cn	X	X	X
acetophenone			X
aniline	X	X	X
anisole			X
benzaldehyde	X	X
benzene	X	X	X
benzonitrile			X
benzyl alcohol / benzylalcohol			X
bromobenzene			X
bromoethane			X
bromoform			X
butanone			X
butyl ethanoate / butyl acetate / butylacetate			X
n-butylbenzene / butylbenzene			X
sec-butylbenzene / secbutylbenzene			X
tert-butylbenzene / tbutylbenzene			X
carbon disulfide / carbondisulfide / cs2	X	X	X
carbon tetrachloride / ccl4			X
chlorobenzene			X
chloroform / chcl3	X	X	X
conductor		X
m-cresol / mcresol			X
cyclohexane			X
cyclohexanone			X
decalin			X
n-decane / decane			X
dibromomethane			X
dibutylether			X
o-dichlorobenzene / odichlorobenzene			X
dichloromethane / ch2cl2 / dcm	X	X	X
diethyl ether / diethylether	X	X	X
diisopropyl ether / diisopropylether			X
n,n-dimethylacetamide / dimethylacetamide			X
n,n-dimethylformamide / dimethylformamide / dmf	X	X	X
dimethylsulfoxide / dmso	X	X	X
diphenylether			X
n-dodecane / dodecane			X
ethanol	X	X	X
ethyl acetate / ethylacetate / ethanoate	X	X	X
ethyl phenyl ether / ethoxybenzene			X
ethylbenzene			X
fluorobenzene			X
furan / furane	X	X
n-heptane / heptane			X
n-hexadecane / hexadecane	X	X	X
n-hexane / hexane	X	X	X
iodobenzene			X
isopropylbenzene			X
p-isopropyltoluene / isopropyltoluene			X
mesitylene			X
methanol	X	X	X
n-methylformamide / methylformamide			X
nitrobenzene / phno2			X
nitroethane			X
nitromethane / meno2	X	X	X
o-nitrotoluene / onitrotoluene			X
n-nonane / nonane			X
n-octane / octane			X
n-pentadecane / pentadecane			X
octanol(wet) / wetoctanol / woctanol	X	X
n-pentane / pentane			X
perfluorobenzene / hexafluorobenzene			X
phenol	X	X
pyridine			X
tetrachloroethene / c2cl4			X
tetrahydrofuran / thf	X	X	X
tetrahydrothiophene-s,s-dioxide / tetrahydrothiophenedioxide / sulfolane			X
tetralin			X
toluene	X	X	X
tributylphosphate			X
triethylamine			X
n-undecane / undecane			X
water / h2o	X	X	X
xylene			X

Note

• If jobs are run over several nodes, the number of cores used by the XTB tool might be lower than requested via the pal keyword.

3.6.2.2. Keywords

Table 3.25 Simple input keywords for the extended tight-binding methods.

Keyword	Description
XTB	Activates GFN2-xTB
XTB0	Activates GFN0-xTB
GFN0-XTB	Activates GFN0-xTB
XTB1	Activates GFN1-xTB
GFN1-XTB	Activates GFN1-xTB
XTB2	Activates GFN2-xTB
GFN2-XTB	Activates GFN2-xTB
XTBFF	Activates GFN-FF
GFN-FF	Activates GFN-FF
ALPB(<solvent>)	Activates ALPB solvation for a <solvent>, e.g. ALPB(Water)
DDCOSMO(<solvent>)	Activates DDCOSMO solvation for a <solvent>, e.g. DDCOSMO(Water)
CPCMX(<solvent>)	Activates CPCMX solvation for a <solvent>, e.g. CPCMX(Water)

Table 3.26 %xtb block input keywords for the extended tight-binding methods.

Keyword	Options	Description
XTBINPUTSTRING	"<string>"	Parses string to the otool_xtb call
XTBINPUTSTRING2	"<string>"	Parses string to the otool_xtb call
NPROCS	<integer>	Controls number of processors for the otool_xtb run, default is ORCA’s PAL setting
MAXCORE	<integer>	Memory in MB reserved for the xtb run, default is ORCA’s maxcore setting
ACCURACY	<real>	Accuracy setting for --acc in otool_xtb, default is ORCA’s accuracy x 1.e6
DOALPB	true/false	Activates ALPB solvation in xtb run
ALPBSOLVENT	"<solvent>"	Controls the <solvent> used for ALPB
DODDCOSMO	true/false	Activates DDCOSMO solvation in xtb run
DDCOSMOSOLVENT	"<solvent>"	Controls the <solvent> used for DDCOSMO
EPSILON	<real>	Controls the dielectric constant, only for ddCOSMO
DOCPCMX	true/false	Activates CPCMX solvation in xtb run
CPCMXSOLVENT	"<solvent>"	Controls the <solvent> used in CPCMX
ETEMP	<real>	Controls electronic temperature --etemp in otool_xtb

3.6.3. Native GFN-xTB and GFN2-xTB

Added in version 6.1.0: Native implementation of GFN1-xTB and GFN2-xTB

ORCA features its own native implementation of GFN-xTB and GFN2-xTB. Unlike the interface to the xtb program, the native xTB implementation can use the SCF and plotting infrastructure.

The native xTB methods can be invoked via the !Native-GFN-xTB, !Native-GFN2-xTB simple keywords:

! Native-GFN-xTB  # Synonym: Native-GFN1-xTB, Native-XTB1

! Native-GFN2-xTB # Synonym: Native-XTB2

Warning

For a faster SCF restart based on atomic charges and multipole moments, the native xTB methods write a basename.xtbw file. If such an .xtbw file is present, it will be used for the restart instead of the .gbw file.

3.6.3.1. Custom parameterization

The native implementations feature the use of custom semi-empirical parameters by reading a JSON parameter file with the name basename.xtb.json. This file has the same format as the JSON file in the dxtb program (dxtb documentation), and can be generated by writing the internal parameters. Reading and writing of semi-empirical parameters can be turned on and off via the %method block:

%method
  XTBParamFile "orca.xtb.json" # set parameter filename to orca.xtb.json
  WriteXTBParam true      # if true: write parameters to orca.xtb.json file
  WriteXTBParamDry false  # if true: write parameters to orca.xtb.json file and exit
  ReadXTBParam false      # if true: read parameters from orca.xtb.json file
end

By default the parameter file will be named according to the basename of your calculation (basename.xtb.json), but other names can be chosen ẁith the XTBParamFile option in the method block. For a dry run that just generates the parameter file from default parameters set WriteXTBParamDry true.

Warning

Please note that the native xTB implementation does not allow changes in the basis.

3.6.3.2. Spin-polarized native xTB

The energy expressions of the original GFNn-xTB methods are spin-independent. Therefore, calculations are typically performed using RHF/RKS-type wavefunctions, even for open-shell systems. Since spin does not enter the energy expression, electronic states with higher spin multiplicity will always be higher in energy compared to the respective low-spin states. This shortcoming is addressed by the spin-polarized xTB methods. The spin-polarized variants [322], termed spGFN1-xTB and spGFN2-xTB, employ a simple on-site spin-dependent term, which can stabilize high-spin states and allows for screening of potential high-spin configurations using xTB methods.

The native spin-polarized xTB methods can be invoked via the !Native-spGFN1-xTB, !Native-spGFN2-xTB simple keywords:

! Native-spGFN1-xTB  # Synonym: Native-spGFN-xTB, Native-spXTB1

! Native-spGFN2-xTB # Synonym: Native-spXTB2

Note that the spin-polarization term will only affect high-spin states. The computational cost increases compared to RHF/RKS-type calculations, as the underlying UHF/UKS-type wavefunctions require two Fock matrix diagonalizations instead of one—approximately doubling the cost.

3.6.3.3. SCF with native xTB

The native xTB methods, by default, employ special SCF settings that mimic the SCF procedure of the xtb program and override all other ORCA SCF settings. These special settings take advantage of xTB-specific features, most notably, that the Fock matrix can be constructed from atomic charges and multipole moments alone. Due to these shortcuts, the special SCF settings are typically faster for xTB methods than the default ORCA SCF. However, the default SCF is more robust and may succeed in converging problematic cases where the xtb SCF fails.

To use the standard ORCA SCF infrastructure instead, set UseXTBMixer to false in the %scf block:

%scf
  UseXTBMixer false    # if true (default): special xTB SCF is used
end

With the ORCA default SCF infrastructure, challenging electronic structures can often be converged, but the results should be used with caution. In cases where SCF convergence has to be forced, the GFNn-xTB Hamiltonians are often not adequate to describe the system at hand. In such cases, Mulliken charges should be checked for sanity, and it might be helpful to slightly adjust the element-wise pair parameters via the parameter file described above.

Warning

Note that all SCF iterations are direct with xTB methods.

3.6.3.4. FOD with native xTB

To better account for static correlation, the xTB methods use finite temperature SCF by default, with an electronic temperature of 300 K. The corresponding fractional occupation number weighted density (FOD) is not printed by default, since 300 K is a too low temperature to use it as a diagnostic tool. The FOD printout can be enabled by setting XTBFOD to true in the %scf input block. The electronic temperature can be controlled–just as for other methods–via the SmearTemp keyword:

%scf
  XTBFOD true    # if true: Enable FOD printout and add FOD to density container
  SmearTemp 5000 # 5000 K is typically used for FOD plots with xTB methods
end

3.6.3.5. Solvation in native xTB

The native implementation of xTB includes the ALPB solvation model with the same solvents available as in the xtb program (see above). It is controlled with the same keywords as the external ALPB via the simple keyword input:

! ALPB(solvent) # use ALPB

In addition, the native implementations can be used with other solvation models available in ORCA, but one should consider that the CPCM and SMD models are quite expensive compared to an xTB calculation, and therefore the faster ALPB solvation model is recommended.

3.6.3.6. Keywords

Table 3.27 Simple input keywords for the native extended tight-binding methods.

Keyword	Description
NATIVE-XTB	Activates native GFN2-xTB
NATIVE-spXTB	Activates native spGFN2-xTB
NATIVE-XTB1	Activates native GFN1-xTB
NATIVE-spXTB1	Activates native spGFN1-xTB
NATIVE-GFN-XTB	Activates native GFN1-xTB
NATIVE-spGFN-XTB	Activates native spGFN1-xTB
NATIVE-GFN1-XTB	Activates native GFN1-xTB
NATIVE-spGFN1-XTB	Activates native spGFN1-xTB
NATIVE-XTB2	Activates native GFN2-xTB
NATIVE-spXTB2	Activates native spGFN2-xTB
NATIVE-GFN2-XTB	Activates native GFN2-xTB
NATIVE-spGFN2-XTB	Activates native spGFN2-xTB
ALPB(<solvent>)	Activates ALPB solvation for a <solvent>, e.g. ALPB(Water)

Table 3.28 %method block input keywords for the native extended tight-binding methods.

Keyword	Options	Description
WRITEXTBPARAM	true/false	Write semi-empirical parameters to xtb.json file
WRITEXTBPARAMDRY	true/false	Write semi-empirical parameters to xtb.json file and abort
READXTBPARAM	true/false	Read semi-empirical parameters from xtb.json file
XTBPARAMFILE	"filename.xtb.json"	Specifies xtb.json filename to “filename.xtb.json”

Table 3.29 %scf block input keywords for the native extended tight-binding methods.

Keyword	Options	Description
XTBFOD	true/false	Enable FOD printout
UseXTBMixer	true/false	Use special SCF settings similar to the ones in xtb