## The Fastest Way to Accurate Quantum Chemical Energies

Sometimes compromises with respect to accuracy might be acceptable. Sometimes it might be sufficient to just hopefully get the trends right.

But most of the time you want to calculate numbers that are correct and trustworthy. And, most of the time, you don't have time on your hands to wait for these numbers.

This is were DLPNO-CCSD(T) steps in:

DLPNO-CCSD(T) is the fastest – and easiest – way to quantum chemical energies that you can trust.

### What can you expect from DLPNO-CCSD(T)?

CCSD(T) results are widely accepted as the gold-standard in quantum chemistry. DLPNO-CCSD(T) is an approximation to this standard that is

- highly accurate, i.e. it recovers 99.9% of the CCSD(T) correlation energy
- super fast, i.e. its computational cost is similar to DFT and scales linearly with system size
- easy to use, i.e. it operates black box with zero need to adjust parameters.

DLPNO-CCSD(T) is the sole method that combines near-CCSD(T) accuracy with DFT speed in an easy-to-use black-box fashion.

### DLPNO-CCSD(T) – Too Good to be True?

A method that overcomes the compromise between speed and accuracy: Does this sound too good to be true?

There's no need to believe in empty words. DLPNO-CCSD(T) underwent multiple benchmarks and they consistently confirm its performance.

Don't just take our word for it — find out for yourself.

### As Accurate As It Gets: 99.9% of CCSD(T)

DLPNO-CCSD(T) energies are accurate: They reproduce more than 99.9% of the CCSD(T) correlation energy.

#### As Fast As It Gets: near-DFT Cost

DLPNO-CCSD(T) energies are calculated fast: Their computational cost is 2–4 times the cost of a DFT calculation.

#### CCSD(T) Accuracy at DFT Cost.

DLPNO-CCSD(T) takes only 2-4 times as long as a DFT calculation — and produces 99.9% of the CCSD(T) correlation energy.

For four different test sets DLPNO-CCSD(T) results are compared to canonical CCSD(T) results at complete basis set limit. The performance of the DLPNO results is compared against the performance of state-of-the-art density functionals in terms of accuracy and speed. The test sets are established benchmark sets containing nontrivial problems with weak interactions that were specifically proposed for evaluating DFT functionals – DLPNO-CCSD(T) is meeting DFT on its homeground. With NormalPNO thresholds, DLPNO-CCSD(T) is about a factor of 2 slower than B3LYP and shows a mean absolute deviation of less than 1 kcal/mol from the reference data for the four different, difficult data sets used. The robustness and accuracy of DLPNO-CCSD(T) for all data sets tested were consistently better than those with even the most advanced functionals used. TightPNO calculations are more expensive than B3LYP by about 3 to 4.5 times. Together with the triple-zeta basis set, it produces results close to the CCSD(T)/CBS level while being orders of magnitude more efficient.

Figure 8:Computation Time DLPNO-CCSD(T) versus DFT.

#### Linear Scaling

DLPNO-CCSD(T) scales linear — and becomes as fast as fast DFT.

The DLPNO-CCSD(T) methodology is shown to be linear scaling up to 1000 atoms for a set of linear carbon chains. Comparison with RIJCOSX-B3LYP shows a crossover in computing time at about 500 atoms. Due to linear scaling calculations at DLPNO-CCSD(T) level on very large systems, like the crambin molecule, become feasible.

Figure 7: DLPNO-CCSD(T) — as fast as DFT.

#### World Record: Calculating Proteins At CCSD(T) Level

The original DLPNO-CCSD(T) implementation completes the first CCSD(T) calculation ever on an entire protein with 644 atoms with a double-zeta basis within 30 days. The new implementation completes this world record calculation now within 30 hours on 4 CPUs. The corresponding triple-zeta calculation is completed in 2 weeks.

The first CCSD(T) calculation with a double-zeta basis on an entire protein with 644 atoms is completed within 30 days.

Figure 6: Crambin, the first protein calculated at 99.9% CCSD(T) accuracy.

#### As Easy As It Gets: Single Keyword Access

DLPNO-CCSD(T) energies are calculated easily: Simply specify the keyword DLPNO-CCSD(T) in the input keyword line.

! DLPNO-CCSD(T) cc-pVTZ cc-pVTZ/C * int 0 1 O 0 0 0 0.0 0.000 0.000 H 1 0 0 1.0 0.000 0.000 H 1 2 0 1.0 104.060 0.000 *

That's it.

A few seconds later, you can retrieve the following output:

------------------------------------------- DLPNO BASED TRIPLES CORRECTION ------------------------------------------- ⁝ Triples Correction (T) ... -0.007718230 Final correlation energy ... -0.278154390 E(CCSD) ... -76.321436435 E(CCSD(T)) ... -76.329154666 ⁝

#### Conclusion

DLPNO-CCSD(T) is the fastest — and easiest — way to highly accurate energies.

- It recovers more than 99.9% of the CCSD(T) energy.
- It scales linearly.
- It operates black box with a single keyword.

Plus: It is embedded in a powerful quantum-chemical software Suite — ORCA.

Have Fun with ORCA!

#### Discover More

We do not stop at closed-shell, single-point energies, however. Profit from DLPNO-CCSD(T) speed and accuracy in

- Multi-Level Schemes
- Local Energy Decomposition
- Embedding Schemes for Solids
- Easy Integration into QM/MM
- Open-Shell Energies
- Density/Properties
- Excited States
- Combination with Implicit Solvation Models (available soon)

## Accurate Absolute and Relative Energies

I Want to Read the Paper!

## Smooth Potential Energy Surfaces

Smoothness of potential energy surfaces has been demonstrated through bond dissociation and bond rotation involving weak molecular interactions. Other local methods fail to produce smooth potential energy surfaces in these cases.

I Want to Read the Paper!

Figure 1: Rotation Barrier for Ethane–1,2–diphenyl.

Figure 2: Potential Energy Surface of the Dissociation of Ketene.

## Optimal Trade-Off Between Speed and Accuracy

With the DLPNO-CCSD(T) accuracy levels TightPNO, NormalPNO and LoosePNO you determine the optimal trade-off between speed and accuracy yourself. Because only you know what you need.

DLPNO-CCSD(T) reproduces CCSD(T) reaction energies as well as relative energies with a mean absolute deviation of 0.1 kcal/mol, 0.2 kcal/mol and 0.4 kcal/mol for TightPNO, NormalPNO and LoosePNO, respectively, over four test sets covering more than 200 reactions.

For four different test sets DLPNO-CCSD(T) results are compared to canonical CCSD(T) results. The test sets include more than 200 reactions and relative energies covering a wide range of interactions, e.g. charge transfer, hydrogen bonding, dipole and weak interactions, π-π stacking complexes and conjugated Schiff bases. Three black box settings are suggested for different levels of accuracy and speed. LoosePNO for preliminary studies, e.g. initial screenings and exploration of potential energy surfaces. NormalPNO for reaction energies and PESs that are not dominated by dispersion interactions and TightPNO for very accurate calculations with nonbonding interactions. For the four test sets the mean absolute deviations with respect to the CCSD(T) results are consistently about 0.1 kcal/mol for the TightPNO calculations, range from 0.1 to 0.3 kcal/mol for the NormalPNO calculations, and from 0.3 to 0.6 kcal/mol for the LoosePNO settings.

I Want to Read the Paper!

Figure 3: Distribution of Errors for the Different DLPNO Settings.

## Coupled-Cluster Accuracy At DFT Cost

DLPNO-CCSD(T) reproduces CCSD(T) reaction energies and relative energies with a mean absolute deviation of 0.3 kcal/mol for TightPNO, 0.5 kcal/mol for NormalPNO and 1.0 kcal/mol for LoosePNO settings over four test sets covering 57 reactions.

For four different test sets DLPNO-CCSD(T) results are compared to canonical CCSD(T) results at complete basis set limit. The performance of the DLPNO results is compared against the performance of state-of-the-art density functionals in terms of accuracy and speed. The test sets are established benchmark sets containing nontrivial problems with weak interactions that were specifically proposed for evaluating DFT functionals — DLPNO-CCSD(T) is meeting DFT on its homeground. With NormalPNO thresholds, DLPNO-CCSD(T) is about a factor of 2 slower than B3LYP and shows a mean absolute deviation of less than 1 kcal/mol from the reference data for the four different, difficult data sets used. The robustness and accuracy of DLPNO-CCSD(T) for all data sets tested were consistently better than those with even the most advanced functionals used. TightPNO calculations are more expensive than B3LYP by about 3 to 4.5 times. Together with the triple-zeta basis set, it produces results close to CCSD(T) at the complete basis set limit while being orders of magnitude more efficient.

I Want to Read the Paper!

Figure 4: Accuracy of DLPNO-CCSD(T) versus DFT.

Figure 5: Failure Rate of DLPNO-CCSD(T) versus DFT-D3.

Further Benchmarks

I'm Convinced!