General Perturbative Approach for Spectroscopy, Thermodynamics, and Kinetics: Methodological Background and Benchmark Studies

Abstract

A general second-order perturbative approach based on resonance- and threshold-free computations of vibrational properties is introduced and validated. It starts from the evaluation of accurate anharmonic zero-point vibrational energies for semirigid molecular systems, in a way that avoids any singularity. Next, the degeneracy corrected second-order perturbation theory (DCPT2) is extended to a hybrid version (HDCPT2), allowing for reliable computations even in cases where the original formulation faces against severe problems, including also an automatic treatment of internal rotations through the hindered-rotor model. These approaches, in conjunction with the so-called simple perturbation theory (SPT) reformulated to treat consistently both energy minima and transition states, allow one to evaluate degeneracy-corrected partition functions further used to obtain vibrational contributions to properties like enthalpy, entropy, or specific heat. The spectroscopic accuracy of the HDCPT2 model has been also validated by computing anharmonic vibrational frequencies for a number of small-to-medium size, closed- and open-shell, molecular systems, within an accuracy close to that of well established but threshold-dependent perturbative-variational models. The reliability of the B3LYP/aug-N07D model for anharmonic computations is also highlighted, with possible improvements provided by the B2PLYP/aug-cc-pVTZ models or by hybrid schemes. On a general grounds, the overall approach proposed in the present work is able to provide the proper accuracy to support experimental investigations even for large molecular systems of biotechnological interest in a fully automated manner, without any ad hoc scaling procedure. This means a fully ab initio evaluation of thermodynamic and spectroscopic properties with an overall accuracy of about, or better than, 1 kJ mol(-1), 1 J mol(-1) K(-1) and 10 cm(-1) for enthalpies, entropies, and vibrational frequencies, respectively.

Dispersion corrected DFT approaches for anharmonic vibrational frequency calculations: nucleobases and their dimers

“…On the contrary, in the case of the adenine stacked dimer B3LYP-D3 yields similar values of harmonic and anharmonic ΔZPVEs while for B3LYP-DCP both values differ by about 0.25 kcal mol −1 . Considering the similar performances of B3LYP and B3LYP-D3, for the latter an accuracy of anharmonic corrections to ZPVE of about 0.05 kcal mol −1 can be expected 86 . By comparison with B3LYP-D3 we can estimate for anharmonic ΔZPVEs computed with B3LYP-DCP an average error of about 0.2 kcal mol −1 , with maximum discrepancies of up to 0.5 kcal mol −1 .…”

“…Vibrational wavenumbers have been computed within the generalized VPT2 model (GVPT2), where nearly-resonant contributions are removed from the perturbative treatment (leading to the deperturbed model, DVPT2) and treated in a second step variationally 61,66,68 . This model, as implemented in the GAUSSIAN package 86 , provided accurate vibrational wavenumbers for several semi-rigid systems 31,32,90,[97][98][99]103,104,117,129,130,132,134,135 . Such an approach relies on semi-empirical thresholds for Fermi and Darling-Denninson resonances.…”

“…Recently, exact solutions for the treatment of few active modes to the vibrational problem for a generic system has been proposed 55 and effective schemes to compute vibrational frequencies within the second order vibrational perturbative (VPT2) [56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75] or vibrational self-consistent field (VSCF) based [76][77][78][79][80][81][82][83][84][85] approaches have been developed and implemented. In particular, a general VPT2 framework to compute thermodynamic properties, vibrational energies and transition intensities from the vibrational ground state to fundamentals, overtones and combination bands 66,67,[86][87][88] has been developed in our group. It should be noted that information about the intensities of overtones and combination transitions, not available from any computations based on the double-harmonic approximation, is required to reproduce the overall band pattern, and might be necessary to correctly analyze experimental outcomes, for example to distinguish lowintensity features related to non-fundamental transitions of the most populated species present in experimental mixtures from fundamental transitions of the less abundant species 89,90 .…”

A theoretical study on the spectroscopy, structure, and stability of C2H3NS molecules

“…aug-cc-pVTZ-derived anharmonic vibrational frequencies [56] and were carried out using the Gaussian 09 package [49].…”

Computational Study of the Thermochemistry of N2O5 and the Kinetics of the Reaction N2O5 + H2O → 2 HNO3

“…The former of these is known to be 0.982 for M06-2X/ MG3S. 26 To obtain the scale factor for the latter effect, we follow the prescription of Zheng et al, 54 whereby we compute the anharmonic ZPE for the species of interest using hybrid degeneracy-corrected second-order vibrational perturbation theory 27 and take the ratio of this ZPE to the harmonic ZPE (i.e., the half sum of the computed harmonic frequencies).…”