How Reliable Are Modern Density Functional Approximations to Simulate Vibrational Spectroscopies?

One- and two-photon absorption spectra of organoboron complexes: vibronic and environmental effects

We synthesized a series of four parent aza-β-ketoiminate organoboron complexes and performed spectroscopic studies using both experimental and computational techniques. We studied how benzannulation influences the vibronic structure of the UV/Vis absorption bands with a focus on the bright lowest-energy π → π* electronic excitation. Theoretical simulations, accounting for inhomogeneous broadening effects using different embedding schemes, allowed gaining in-depth insights into the observed differences in band shapes induced by structural modifications. We observed huge variations in the distributions of vibronic transitions depending on the position of benzannulation. By and large, the harmonic approximation combined with the adiabatic hessian model delivers qualitatively correct band shapes for the one-photon absorption spectra, except in one case. We also assessed the importance of non-Condon effects (accounted for by the linear term in Herzberg-Teller expansion of the dipole moment) for S0 → S1 band shapes. It turned out that non-Condon contributions have no effect on the band shape in one-photon absorption spectra. In contrast, these effects significantly change the Franck-Condon band shapes of the two-photon absorption spectra. For one of the studied organoboron complexes we also performed a preliminary exploration of mechanical anharmonicity, resulting in an increase of the intensity of the 0-0 transition, which improves the agreement with the experimental data compared to the harmonic model.

Spurious Oscillations Caused by Density Functional Approximations: Who is to Blame? Exchange or Correlation?

We analyze the varying susceptibilities of different density functional approximations (DFAs) to present spurious oscillations on the profiles of several vibrational properties. Among other problems, these spurious oscillations cause significant errors in harmonic and anharmonic IR and Raman frequencies and intensities. This work hinges on a judicious strategy to dissect the exchange and correlation components of DFAs and pinpoint the origins of these oscillations. We identify spurious oscillations in derivatives of all energy components with respect to nuclear displacements, including those energy terms that do not involve numerical integrations. These indirect spurious oscillations are attributed to suboptimal electron densities resulting from a self-consistent field procedure using a DFA that exhibits direct spurious oscillations. Direct oscillations stem from inaccurate numerical integration of the exchange and correlation energy density functionals. A thorough analysis of direct spurious oscillations reveals that only a handful of exchange and correlation components are insensitive to spurious oscillations, giving rise to three families of functionals, BH&H, LSDA, and BLYP. Among the functionals in these families, we encounter four widespread DFAs: BLYP, B3LYP, LC-BLYP, and CAM-B3LYP. Certain DFAs like PBE appear less sensitive to spurious oscillations due to compensatory cancellations between their energy components. Additionally, we found non-negligible but small oscillations in PBE and TPSS, which could be safely employed provided a sufficiently large integration grid is used in the calculations. These findings hint at the key components of current approximations to be improved and emphasize the necessity to develop accurate DFAs suitable for studying molecular spectroscopies.

The Pseudo Jahn-Teller effect and NBO analysis for untangling the symmetry breaking in the planar configurations of M2X4+ (M = Si, Ge and X = Cl, Br, I): effect on electronic structure and chemical properties

CONTEXT

The Pseudo Jahn- Teller effect is a significant tool for evaluating molecular distortion and symmetry breaking. The PJT effect associated with NBO analysis can be a powerful method for studying the structural properties variations arising from D2h → C2h distortions. The theoretical studies on Si2X4+ and Ge2X4+ radical cations have been rare. The calculations have shown that C2h non-planar structures are more stable than planar structures with D2h symmetry. The [Formula: see text] PJTE problem of M2X4+ compounds is a result of the coupling between the ground B3u state and the exited B1u state in the Qb2g direction causes. Also, the difference in M and X atoms can affect the PJT instability of compounds. The findings of this work show that the energy gap between the ground and excited states that have D2h symmetry decreases from M2Cl4+ to M2I4+ and increases from Si2X4+ to Ge2X4+. In fact, there is a significant relationship between instability of high-symmetry configurations, geometric parameters, electron delocalization, chemical hardness, electronegativity, electrophilicity index, and PJT stabilization energies. These results may serve to evaluate the distortion of similar systems.

METHODS

The structures of Si2X4+ and Ge2X4+ are optimized by LC-BLYP, M06-2X, and B3LYP methods with def2-TZVPP basis set in GAMESS software. The details of the excited states of compounds are studied by the TD-DFT method. NBO analysis for planar and non-planar structures is carried out at B3LYP/def2-TZVPP level by the NBO 5. G program that demonstrates HOMO, LUMO, ED, bonding and antibonding orbital occupancies, bond order, and E2.

Pitfall in simulations of vibronic TD-DFT spectra: diagnosis and assessment

In this Communication, we study the effect of spurious oscillations in the profiles of energy derivatives with respect to nuclear coordinates calculated with density functional approximations (DFAs) for formaldehyde, pyridine, and furan in their ground and electronic excited states. These spurious oscillations, which can only be removed using extensive integration grids that increase enormously the CPU cost of DFA calculations, are significant in the case of third- and fourth-order energy derivatives of the ground and excited states computed by M06-2X and ωB97X functionals. The errors in question propagate to anharmonic vibronic spectra computed under the Franck-Condon approximation, i.e., positions and intensities of vibronic transitions are affected to a large extent (shifts as significant as hundreds of cm-1 were observed). On the other hand, the LC-BLYP and CAM-B3LYP functionals show a much less pronounced effect due to spurious oscillations. Based on the results presented herein, we recommend either LC-BLYP or CAM-B3LYP with integration grids (250, 974) (or larger) for numerically stable simulations of vibronic spectra including anharmonic effects.

Artificial Neural Network-Based Density Functional Approach for Adiabatic Energy Differences in Transition Metal Complexes

During the past decades, approximate Kohn-Sham density functional theory schemes have garnered many successes in computational chemistry and physics, yet the performance in the prediction of spin state energetics is often unsatisfactory. By means of a machine learning approach, an enhanced exchange and correlation functional is developed to describe adiabatic energy differences in transition metal complexes. The functional is based on the computationally efficient revision of the regularized, strongly constrained, and appropriately normed functional and improved by an artificial neural network correction trained over a small data set of electronic densities, atomization energies, and/or spin state energetics. The training process, performed using a bioinspired nongradient-based approach adapted for this work from the particle swarm optimization, is analyzed and discussed extensively. The resulting machine learned meta-generalized gradient approximation functional is shown to outperform most known density functionals in the prediction of adiabatic energy differences for a diverse set of transition metal complexes with varying local coordinations and metal choices.

Investigating the accuracy of density functional methods for molecules in electric fields

The use of oriented external electric fields (OEEFs) as a potential tool for catalyzing chemical reactions has gained traction in recent years. Electronic structure calculations using OEEFs are commonly done using methods based on density functional theory (DFT), but until now, the performance of DFT methods for calculating molecules in OEEFs had not been assessed in a more general scope. Looking at the accuracy of molecular geometries, electronic energies, and electric dipole moments compared to accurate coupled-cluster with perturbative triples data, we have investigated a wide variety of density functionals using different basis sets to determine how well the individual functionals perform on various types of chemical bonds. We found that most functionals accurately calculate geometries in OEEFs and that small basis sets are sufficient in many cases. Calculations of electronic energies show a significant error introduced by the OEEF, which the use of a larger basis set helps mitigate. Our findings show that DFT methods can be used for accurate calculations in OEEFs, allowing researchers to make full use of the advantages that they bring.

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. This study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).

Are Accelerated and Enhanced Wave Function Methods Accurate to Compute Static Linear and Nonlinear Optical Properties?

Key components of organic-based electro-optic devices are challenging to design or optimize because they exhibit nonlinear optical responses, which are difficult to model or rationalize. Computational chemistry furnishes the tools to investigate extensive collections of molecules in the quest for target compounds. Among the electronic structure methods that provide static nonlinear optical properties (SNLOPs), density functional approximations (DFAs) are often preferred because of their low cost/accuracy ratio. However, the accuracy of the SNLOPs critically depends on the amount of exact exchange and electron correlation included in the DFA, precluding the reliable calculation of many molecular systems. In this scenario, wave function methods such as MP2, CCSD, and CCSD(T) constitute a reliable alternative to compute SNLOPs. Unfortunately, the computational cost of these methods significantly restricts the size of molecules to study, a limitation that hampers the identification of molecules with significant nonlinear optical responses. This paper analyzes various flavors and alternatives to MP2, CCSD, and CCSD(T) methods that either drastically reduce the computational cost or improve their performance but were scarcely and unsystematically employed to compute SNLOPs. In particular, we have tested RI-MP2, RIJK-MP2, RIJCOSX-MP2 (with GridX2 and GridX4 setups), LMP2, SCS-MP2, SOS-MP2, DLPNO-MP2, LNO-CCSD, LNO-CCSD(T), DLPNO-CCSD, DLPNO-CCSD(T0), and DLPNO-CCSD(T1). Our results indicate that all these methods can be safely employed to calculate the dipole moment and the polarizability with average relative errors below 5% with respect to CCSD(T). On the other hand, the calculation of higher-order properties represents a challenge for LNO and DLPNO methods, which present severe numerical instabilities in computing the single-point field-dependent energies. RI-MP2, RIJK-MP2, or RIJCOSX-MP2 are cost-effective methods to compute first and second hyperpolarizabilities with a marginal average error with respect to canonical MP2 (up to 5% for β and up to 11% for γ). More accurate hyperpolarizabilities can be obtained with DLPNO-CCSD(T1); however, this method cannot be employed to obtain reliable second hyperpolarizabilities. These results open the way to obtain accurate nonlinear optical properties at a computational cost that can compete with current DFAs.

Surrogate Based Genetic Algorithm Method for Efficient Identification of Low-Energy Peptide Structures

Identification of the most stable structure(s) of a system is a prerequisite for the calculation of any of its properties from first-principles. However, even for relatively small molecules, exhaustive explorations of the potential energy surface (PES) are severely hampered by the dimensionality bottleneck. In this work, we address the challenging task of efficiently sampling realistic low-lying peptide coordinates by resorting to a surrogate based genetic algorithm (GA)/density functional theory (DFT) approach (sGADFT) in which promising candidates provided by the GA are ultimately optimized with DFT. We provide a benchmark of several computational methods (GAFF, AMOEBApro13, PM6, PM7, DFTB3-D3(BJ)) as possible prescanning surrogates and apply sGADFT to two test case systems that are (i) two isomer families of the protonated Gly-Pro-Gly-Gly tetrapeptide (Masson, A.; J. Am. Soc. Mass Spectrom.2015, 26, 1444-1454) and (ii) the doubly protonated cyclic decapeptide gramicidin S (Nagornova, N. S.; J. Am. Chem. Soc.2010, 132, 4040-4041). We show that our GA procedure can correctly identify low-energy minima in as little as a few hours. Subsequent refinement of surrogate low-energy structures within a given energy threshold (≤10 kcal/mol (i), ≤5 kcal/mol (ii)) via DFT relaxation invariably led to the identification of the most stable structures as determined from high-resolution infrared (IR) spectroscopy at low temperature. The sGADFT method therefore constitutes a highly efficient route for the screening of realistic low-lying peptide structures in the gas phase as needed for instance for the interpretation and assignment of experimental IR spectra.

Infrared intensities of [Formula: see text]: a true challenge for DFT methods

Absolute infrared intensities of [Formula: see text] were evaluated with a great variety of DFT and ab initio methods and basis sets. It is shown that the intensities calculated by different levels of theory may not agree with each other even in the qualitative (weak/strong) sense. Geometrical parameters, as well as net atomic charges evaluated from multiple partition schemes, did not vary as much as the intensities and thus cannot explain the tremendous differences found for the latter. As there are no experimental estimates for the intensities to guide the theoretical evaluation, deciding on the best level of theory is reduced to comparisons between the different DFT methods and QCISD or CCSD, believed to be the best theoretical estimates in the set. The differences found among the various DFT methods suggest the development of new methods, instead of converging to a focal point, is rather diverging.