Accuracy and Reliability in the Simulation of Vibrational Spectra: A Comprehensive Benchmark of Energies and Intensities Issuing From Generalized Vibrational Perturbation Theory to Second Order (GVPT2)

Vibrational spectroscopy represents an active frontier for the identification and characterization of molecular species in the context of astrochemistry and astrobiology. As new missions will provide more data over broader ranges and at higher resolution, especially in the infrared region, which could be complemented with new spectrometers in the future, support from laboratory experiments and theory is crucial. In particular, computational spectroscopy is playing an increasing role in deepening our understanding of the origin and nature of the observed bands in extreme conditions characterizing the interstellar medium or some planetary atmospheres, not easily reproducible on Earth. In this connection, the best compromise between reliability, feasibility and ease of interpretation is still a matter of concern due to the interplay of several factors in determining the final spectral outcome, with larger molecular systems and non-covalent complexes further exacerbating the dichotomy between accuracy and computational cost. In this context, second-order vibrational perturbation theory (VPT2) together with density functional theory (DFT) has become particularly appealing. The well-known problem of the reliability of exchange-correlation functionals, coupled with the treatment of resonances in VPT2, represents a challenge for the determination of standardized or “black-box” protocols, despite successful examples in the literature. With the aim of getting a clear picture of the achievable accuracy and reliability of DFT-based VPT2 calculations, a multi-step study will be carried out here. Beyond the definition of the functional, the impact of the basis set and the influence of the resonance treatment in VPT2 will be analyzed. For a better understanding of the computational aspects and the results, a short summary of vibrational perturbation theory and the overall treatment of resonances for both energies and intensities will be given. The first part of the benchmark will focus on small molecules, for which very accurate experimental and theoretical data are available, to investigate electronic structure calculation methods. Beyond the reliability of energies, widely used for such systems, the issue of intensities will also be investigated in detail. The best performing electronic structure methods will then be used to treat larger molecular systems, with more complex topologies and resonance patterns.

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Spin-component-scaled and dispersion-corrected second-order Møller-Plesset perturbation theory: A path toward chemical accuracy

10.33774/chemrxiv-2021-jdv3c ◽

2021 ◽

Author(s):

Chandler Greenwell ◽

Jan Rezac ◽

Gregory Beran

Keyword(s):

Perturbation Theory ◽

Density Functional ◽

Correlation Energy ◽

Computational Cost ◽

Second Order ◽

Spin Component ◽

Dispersion Interactions ◽

Reaction Energies ◽

Moller Plesset ◽

Plesset Perturbation Theory

Second-order Møller-Plesset perturbation theory (MP2) provides a valuable alternative to density functional theory for modeing problems in organic and biological chemistry. However, MP2 suffers from known lim- itations in the description of van der Waals dispersion interactions and reaction thermochemistry. Here, a spin-component-scaled, dispersion-corrected MP2 model (SCS-MP2D) is proposed that addresses these weaknesses. The dispersion correction, which is based on Grimme’s D3 formalism, replaces the uncoupled Hartree-Fock dispersion inherent in MP2 with a more robust coupled Kohn-Sham treatment. The spin- component scaling of the residual MP2 correlation energy then reduces the remaining errors in the model. This two-part correction strategy solves the problem found in earlier spin-component-scaled MP2 models where completely different spin-scaling parameters were needed for describing reaction energies versus in- termolecular interactions. Results on 18 benchmark data sets and two challenging potential energy curves demonstrate that SCS-MP2D considerably improves upon the accuracy of MP2 for intermolecular interac- tions, conformational energies, and reaction energies. Its accuracy and computational cost are competitive with state-of-the-art density functionals such as DSD-BLYP-D3(BJ), revDSD-PBEP86-D3(BJ), ωB97X-V, and ωB97M-V for systems with ∼100 atoms.

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Divergence of Many-Body Perturbation Theory for Noncovalent Interactions of Large Molecules

10.26434/chemrxiv.11124251.v1 ◽

2019 ◽

Author(s):

Brian Nguyen ◽

Guo P Chen ◽

Matthew M. Agee ◽

Asbjörn M. Burow ◽

Matthew Tang ◽

...

Keyword(s):

Perturbation Theory ◽

System Size ◽

State Density ◽

Second Order ◽

Binding Energies ◽

Basis Set ◽

Many Body ◽

Many Body Perturbation Theory ◽

Relative Errors ◽

Ground State Density

Prompted by recent reports of large errors in noncovalent interaction (NI) energies obtained from many-body perturbation theory (MBPT), we compare the performance of second-order Møller–Plesset MBPT (MP2), spin-scaled MP2, dispersion-corrected semilocal density functional approximations (DFA), and the post-Kohn–Sham random phase approximation (RPA) for predicting binding energies of supramolecular complexes contained in the S66, L7, and S30L benchmarks. All binding energies are extrapolated to the basis set limit, corrected for basis set superposition errors, and compared to reference results of the domain-based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)) or better quality. Our results confirm that MP2 severely overestimates binding energies of large complexes, producing relative errors of over 100% for several benchmark compounds. RPA relative errors consistently range between 5-10%, significantly less than reported previously using smaller basis sets, whereas spin-scaled MP2 methods show limitations similar to MP2, albeit less pronounced, and empirically dispersion-corrected DFAs perform almost as well as RPA. Regression analysis reveals a systematic increase of relative MP2 binding energy errors with the system size at a rate of approximately 1‰ per valence electron, whereas the RPA and dispersion-corrected DFA relative errors are virtually independent of the system size. These observations are corroborated by a comparison of computed rotational constants of organic molecules to gas-phase spectroscopy data contained in the ROT34 benchmark. To analyze these results, an asymptotic adiabatic connection symmetry-adapted perturbation theory (AC-SAPT) is developed which uses monomers at full coupling whose ground-state density is constrained to the ground-state density of the complex. Using the fluctuation–dissipation theorem, we obtain a nonperturbative “screened second-order” expression for the dispersion energy in terms of monomer quantities which is exact for non-overlapping subsystems and free of induction terms; a first-order RPA-like approximation to the Hartree, exchange, and correlation kernel recovers the macroscopic Lifshitz limit. The AC-SAPT expansion of the interaction energy is obtained from Taylor expansion of the coupling strength integrand. Explicit expressions for the convergence radius of the AC-SAPT series are derived within RPA and MBPT and numerically evaluated. Whereas the AC-SAPT expansion is always convergent for nondegenerate monomers when RPA is used, it is found to spuriously diverge for second-order MBPT, except for the smallest and least polarizable monomers. The divergence of the AC-SAPT series within MBPT is numerically confirmed within RPA; prior numerical results on the convergence of the SAPT expansion for MBPT methods are revisited and support this conclusion once sufficiently high orders are included. The cause of the failure of MBPT methods for NIs of large systems is missing or incomplete “electrodynamic” screening of the Coulomb interaction due to induced particle–hole pairs between electrons in different monomers, leaving the effective interaction too strong for AC-SAPT to converge. Hence, MBPT cannot be considered reliable for quantitative predictions of NIs, even in moderately polarizable molecules with a few tens of atoms. The failure to accurately account for electrodynamic polarization makes MBPT qualitatively unsuitable for applications such as NIs of nanostructures, macromolecules, and soft materials; more robust non-perturbative approaches such as RPA or coupled cluster methods should be used instead whenever possible.

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Evaluating Transition Metal Barrier Heights with the Latest DFT Exchange–Correlation Functionals – the MOBH35 Benchmark Dataset

10.26434/chemrxiv.7732262.v1 ◽

2019 ◽

Author(s):

Mark Iron ◽

Trevor Janes

Keyword(s):

Transition Metal ◽

Density Functional ◽

Computational Cost ◽

Basis Set ◽

Functional Theory ◽

Exchange Correlation ◽

Barrier Heights ◽

Complete Basis Set ◽

Complete Basis Set Limit ◽

Hybrid Functionals

A new database of transition metal reaction barrier heights – MOBH35 – is presented. Benchmark energies (forward and reverse barriers and reaction energy) are calculated using DLPNO-CCSD(T) extrapolated to the complete basis set limit using a Weizmann1-like scheme. Using these benchmark energies, the performance of a wide selection of density functional theory (DFT) exchange–correlation functionals, including the latest from the Truhlar and Head-Gordon groups, is evaluated. It was found, using the def2-TZVPP basis set, that the ωB97M-V (MAD 1.8 kcal/mol), ωB97X-V (MAD 2.1 kcal/mol) and SCAN0 (MAD 2.1 kcal/mol) hybrid functionals are recommended. The double-hybrid functionals PWPB95 (MAD 1.6 kcal/mol) and B2K-PLYP (MAD 1.8 kcal/mol) did perform slightly better but this has to be balanced by their increased computational cost.

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The Sternheimer approach to all-electron real-space density-functional perturbation theory with atomic basis set

AIP Advances ◽

10.1063/5.0029361 ◽

2021 ◽

Vol 11 (1) ◽

pp. 015224

Author(s):

Honghui Shang

Keyword(s):

Perturbation Theory ◽

Density Functional ◽

Real Space ◽

Basis Set ◽

Space Density ◽

Density Functional Perturbation Theory

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Accurate quadruple-ζ basis-set approximation for double-hybrid density functional theory with an order of magnitude reduction in computational cost

Theoretical Chemistry Accounts ◽

10.1007/s00214-013-1426-9 ◽

2013 ◽

Vol 133 (2) ◽

Cited By ~ 18

Author(s):

Bun Chan ◽

Leo Radom

Keyword(s):

Density Functional Theory ◽

Density Functional ◽

Computational Cost ◽

Basis Set ◽

Hybrid Density Functional Theory ◽

Functional Theory ◽

Order Of Magnitude ◽

Set Approximation ◽

Hybrid Density Functional

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r2SCAN-3c: An Efficient “Swiss Army Knife” Composite Electronic-Structure Method

10.26434/chemrxiv.13333520.v1 ◽

2020 ◽

Author(s):

Stefan Grimme ◽

Andreas Hansen ◽

Sebastian Ehlert ◽

Jan-Michael Mewes

Keyword(s):

Electronic Structure ◽

Density Functional ◽

Chemical Space ◽

Noncovalent Interactions ◽

New Method ◽

Basis Set ◽

Basis Set Superposition Error ◽

Benchmark Database ◽

The Cost ◽

Conformational Energies

The recently proposed second revision of the SCAN meta-GGA density-functional approximation (DFA) {Furness et al., J. Phys. Chem. Lett. 2020, 11, 8208-8215, termed r2SCAN} is used to construct an efficient composite electronic-structure method termed r2SCAN-3c, expanding the "3c'' series (hybrid: HSE/PBEh-3c, GGA: B97-3c, HF: HF-3c) to themGGA level. To this end, the unaltered r2SCAN functional is combined with a tailor-made triple-zeta Gaussian AO-basis as well as with refitted D4 and gCP corrections for London-dispersion and basis-set superposition error. The performance of the new method is evaluated for the GMTKN55 thermochemical database covering large parts of chemical space with about 1500 data points, as well as additional benchmarks for noncovalent interactions, organometallic reactions, lattice energies of organic molecules and ices, as well as for the adsorption on polar salt and non-polar coinage-metal surfaces. These comprehensive tests reveal a spectacular performance and robustness of r2SCAN-3c for reaction energies and noncovalent interactions in molecular and periodic systems, as well as outstanding conformational energies, and consistent structures. At just one tenth of the cost, r2SCAN-3c provides one of the best results of all semi-local DFT/QZ methods ever tested for the GMTKN55 benchmark database. Specifically for reaction and conformational energies as well as for noncovalent interactions, the new method outperforms hybrid-DFT/QZ approaches, compared to which the computational savings are even larger (factor 100-1000). In relation to other "3c'' methods, r2SCAN-3c by far surpasses the accuracy of its predecessor B97-3c at only about twice the cost. The perhaps most relevant remaining systematic deviation of r2SCAN-3c is due to self-interaction-error, owing to its mGGA nature. However, SIE is notably reduced compared to other (m)GGAs, as is demonstrated for several examples. After all, this remarkably efficient and robust method is chosen as our new group default, replacing previous low-level DFT and partially even expensive high-level methods in most standard applications for systems with up to several hundreds of atoms.

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