Anharmonic force fields from analytic CCSD(T) second derivatives: HOF and F2O

Performance of Vibrational Self-Consistent Field Theory for Accurate Potential Energy Surfaces: Fundamentals, Excited States, and Intensities

The performance of vibrational structure calculations beyond harmonic approximation in the framework of the vibrational self-consistent field method with second-order perturbation corrections (VSCF-PT2) is investigated in conjunction with very accurate potential energy surfaces (PESs) given by various coupled-cluster electronic structure theories. The quality of anharmonic calculations depends on the accuracy of the underlying multidimensional PES obtained from its functional form, which is given by the level of electronic structure theory. Two such highest levels of typical coupled-cluster electronic structure methods, CCSD and the ″gold standard″ CCSD(T), along with their variants such as CCD, CR-CCL (completely renormalized CR-CC(2,3) approach), and CCSD(TQ) are tested for the construction of accurate anharmonic potentials without any fitting or ad hoc scaling and using cc-pVTZ basis sets. The accuracy of VSCF-PT2 theory in comparison to experimental values is tested for a series of 16 molecules with 135 fundamental bands, 64 overtones, and combination bands and also for 39 intensities. It is found that CCD and CCSD bind the potential tighter than CCSD(T) and the computed VSCF-PT2 transitions are more blue-shifted showing higher deviation from the experiment. In general, VSCF-PT2 results computed at the CCSD(T) potential offer a good cost/accuracy ratio, with the mean absolute deviation and the mean absolute percentage error with the experiment being ∼16 cm^-1 and 1.38, respectively, for fundamentals. Additionally, while the CR-CCL and CCSD(TQ) methods offer similar levels of accuracies as compared to CCSD(T), the former offers a better accuracy/cost ratio than the latter and is a suitable alternative to CCSD(T).

How to VPT2: Accurate and Intuitive Simulations of CH Stretching Infrared Spectra Using VPT2+K with Large Effective Hamiltonian Resonance Treatments

This article primarily discusses the utility of vibrational perturbation theory for the prediction of X-H stretching vibrations with particular focus on the specific variant, second-order vibrational perturbation theory with resonances (VPT2+K). It is written as a tutorial, reprinting most important formulas and providing numerous simple examples. It discusses the philosophy and practical considerations behind vibrational simulations with VPT2+K, including but not limited to computational method selection, cost-saving approximations, approaches to evaluating intensity, resonance identification, and effective Hamiltonian structure. Particular attention is given to resonance treatments, beginning with simple Fermi dyads and gradually progressing to arbitrarily large polyads that describe both Fermi and Darling-Dennison resonances. VPT2+K combined with large effective Hamiltonians is shown to be a reliable framework for modeling the complicated CH stretching spectra of alkenes. An error is also corrected in the published analytic formula for the VPT2 transition moment between the vibrational ground state and triply excited states.

tert-Butyl peroxy radical: ground and first excited state energetics and fundamental frequencies

The lowest adiabatic electronic transition origin and fundamental vibrational frequencies are computed, with high accuracy, for the tert-butyl peroxy radical.

Complete analytic anharmonic hyper-Raman scattering spectra

We present the first computational treatment of the complete second-order vibrational perturbation theory applied to hyper-Raman scattering spectroscopy. The required molecular properties are calculated in a fully analytic manner using a recently developed program [Ringholm, Jonsson and Ruud, J. Comp. Chem., 2014, 35, 622] that utilizes recursive routines. For some of the properties, these calculations are the first analytic calculations of their kind at their respective levels of theory. We apply this approach to the calculation of the hyper-Raman spectra of methane, ethane and ethylene and compare these to available experimental data. We show that the anharmonic corrections have a larger effect on the vibrational frequencies than on the spectral intensities, but that the inclusion of combination and overtone bands in the anharmonic treatment can improve the agreement with the experimental data, although the quality of available experimental data limits a detailed comparison.

Analytic calculations of anharmonic infrared and Raman vibrational spectra

Using a recently developed recursive scheme for the calculation of high-order geometric derivatives of frequency-dependent molecular properties [Ringholm et al., J. Comp. Chem., 2014, 35, 622], we present the first analytic calculations of anharmonic infrared (IR) and Raman spectra including anharmonicity both in the vibrational frequencies and in the IR and Raman intensities. In the case of anharmonic corrections to the Raman intensities, this involves the calculation of fifth-order energy derivatives-that is, the third-order geometric derivatives of the frequency-dependent polarizability. The approach is applicable to both Hartree-Fock and Kohn-Sham density functional theory. Using generalized vibrational perturbation theory to second order, we have calculated the anharmonic infrared and Raman spectra of the non- and partially deuterated isotopomers of nitromethane, where the inclusion of anharmonic effects introduces combination and overtone bands that are observed in the experimental spectra. For the major features of the spectra, the inclusion of anharmonicities in the calculation of the vibrational frequencies is more important than anharmonic effects in the calculated infrared and Raman intensities. Using methanimine as a trial system, we demonstrate that the analytic approach avoids errors in the calculated spectra that may arise if numerical differentiation schemes are used.

Predicting the structure and vibrational frequencies of ethylene using harmonic and anharmonic approaches at the Kohn-Sham complete basis set limit

In this work, regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limit are demonstrated for the first time. The performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with two Pople basis sets (6-311++G** and 6-311++G(3df,2pd)), the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, 6) was tested.

The BLYP-calculated harmonic frequencies were found to be markedly closer than the B3LYP-calculated harmonic frequencies to the experimentally derived values, while the calculated anharmonic frequencies consistently underestimated the observed wavenumbers. The different basis set families gave very similar estimated values for the CBS parameters. The anharmonic frequencies calculated with B3LYP/aug-pc-3 were consistently significantly higher than those obtained with the pc-3 basis set; applying the aug-pcseg-n basis set family alleviated this problem. Utilization of B3LYP/aug-pcseg-n basis sets instead of B3LYP/aug-cc-pVXZ, which is computationally less expensive, is suggested for medium-sized molecules. Harmonic BLYP/pc-2 calculations produced fairly accurate ethylene frequencies.

Graphical Abstract

DENSITY FUNCTIONAL THEORY STUDIES OF SPECTROSCOPIC CONSTANTS AND ANHARMONIC FORCE FIELD OF O35ClO

The equilibrium structure, spectroscopy constants and anharmonic force field of O35ClO have been calculated at B3PW91 and B3LYP levels of theory with two basis sets 6-311++G(2df,2pd) and 6-311++G(3df,3pd) , respectively. The computed geometries, dipole moment, rotational constants, vibration–rotation interaction constants, vibrational band origins, anharmonic constants, quartic, and sextic centrifugal distortion constants are compared with the available experimental data. The cubic and quartic force constants are predicted. The calculated results show that the B3PW91 results are in excellent agreement with experiment and represent a substantial improvement over the results obtained from B3LYP.

AB INITIOSTUDY OF SPECTROSCOPIC CONSTANTS AND ANHARMONIC FORCE FIELD OFAsH2RADICAL

The equilibrium structure, spectroscopic constants and anharmonic force field of AsH2have been investigated at B3LYP, B3PW91 and MP2 methods employing the basis sets of cc-pVNZ and aug-cc-pVNZ (N ∈ { T , Q }), respectively. The computed geometries, rotational constants, part of vibrational frequencies, quartic and sextic centrifugal distortion constants are compared with the available experimental data or theoretical results. The other vibrational frequencies, equilibrium rotational constants, anharmonic constants, vibration–rotation interaction constants, cubic and quartic force constants of AsH2are also predicted for the first time. Furthermore, the calculated results show that the DFT method is superior to MP2 at the calculations of geometries, spectroscopic constants and force constants. The B3PW91/aug-cc-pVQZ results are more reliable. Our predictions can provide useful data for the experimental studies of the corresponding spectroscopic constants of AsH2.

Harmonic and Anharmonic Vibrational Frequency Calculations with the Double-Hybrid B2PLYP Method: Analytic Second Derivatives and Benchmark Studies

This work aims to provide reliable benchmark data on the accuracy of harmonic and anharmonic vibrational frequencies computed with the B2PLYP double-hybrid density functional method. The exchange-correlation contributions required for the B2PLYP analytical second derivatives are presented here, which allow for the effective calculation of harmonic frequency as well as cubic and semidiagonal quartic force fields. The latter, in turn, are necessary to compute the anharmonic vibrational frequencies with the perturbative approach (VPT2). The quality of harmonic vibrational frequencies computed in conjunction with basis sets of double- to quadruple-ζ quality has been checked against reference data from the F38 benchmark set. Then, for an additional set of small closed- and open-shell systems, both harmonic frequencies and anharmonic contributions computed at the B2PLYP/N07D and the B2PLYP/aug-cc-pVTZ levels have been compared to their CCSD(T) counterparts. Moreover, for selected medium-size molecules (furan, pyrrole, thiophene, uracil, anisole, phenol, and pyridine), anharmonic frequencies have been compared to well established experimental results. Such benchmark studies have shown that the B2PLYP/N07D model provides good quality harmonic frequencies and describes correctly anharmonic contributions, the latter being of similar accuracy to their B3LYP/N07D counterparts, but obtained at significantly larger computational cost. Additionally, increased accuracy can be obtained by adopting hybrid models where the B2PLYP/N07D anharmonic contributions are combined with harmonic frequencies computed with more accurate quantum mechanical (QM) approaches or by B2PLYP with larger basis sets. This work confirmed also that most of the recently developed density functionals are significantly less suited for vibrational computations, while the B2PLYP method can be recommended for spectroscopic studies where a good accuracy of vibrational properties is required.

H2O, H2, HF, F2 and F2O nuclear magnetic shielding constants and indirect nuclear spin-spin coupling constants (SSCCs) in the BHandH/pcJ-n and BHandH/XZP Kohn-Sham limits

Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H(2)O, H(2), HF, F(2) and F(2)O nuclear isotropic shielding constants in the BHandH Kohn-Sham basis set limit was shown. The results of two- and three-parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization-consistent basis sets pcS-n and pcJ-n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were more sensitive to the XZP basis set size and generally less accurate than those estimated using pcJ-n basis set family. The BHandH density functional markedly outperforms B3LYP method in predicting heavy atom shieldings and SSCCs values in the studied systems.

Competition of hydrogen bonds and halogen bonds in complexes of hypohalous acids with nitrogenated bases

A theoretical study of the complexes formed by hypohalous acids (HOX, X = F, Cl, Br, I, and At) with three nitrogenated bases (NH 3, N 2, and NCH) has been carried out by means of ab initio methods, up to MP2/aug-cc-pVTZ computational method. In general, two minima complexes are found, one with an OH...N hydrogen bond and the other one with a X...N halogen bond. While the first one is more stable for the smallest halogen derivatives, the two complexes present similar stabilities for the iodine case and the halogen-bonded structure is the most stable one for the hypoastatous acid complexes.

Ab initio study of spectroscopic constants and anharmonic force field of 74GeCl2

The equilibrium structure, spectroscopy constants, and anharmonic force field of germanium dichloride have been calculated at MP2, B3LYP, and CCSD(T) levels of theory employing two basis sets, cc-pVDZ and cc-pVTZ, respectively. The computed geometries, rotational constants, and vibration-rotation interaction constants, and quartic centrifugal distortion constants are compared with the available experimental data. The harmonic frequencies, anharmonic constants, and cubic and quartic force constants are predicted. The calculated results show that the MP2 results are in excellent agreement with experiment and represent a substantial improvement over the results obtained from B3LYP. The CCSD(T) method is also an advisable choice to study anharmonic force field of molecules.

Rozen's Epoxidation Reagent, CH3CN·HOF: A Theoretical Study of Its Structure, Vibrational Spectroscopy, and Reaction Mechanism

Rozen's epoxidation reagent, CH(3)CN.HOF, and a prototype epoxidation reaction employing it, have been subjected to an extensive ab initio and density functional study. Its anharmonic force field reveals a very strong red shift for the OH stretch and a strong blue shift for the HOF bend, in semiquantitative agreement with experiment. The very strong hydrogen bond (8.20 kcal/mol at the W1 level) not only serves to stabilize the reactant but also considerably lowers the barrier height for epoxidation of ethylene. Moreover, the reaction byproduct HF is found to act autocatalytically. The OH moiety acquires HO(+) character in the transition state. Our W1 benchmark data for the reaction profile allow the performance of various DFT functionals to be assessed. In general, "kinetics" functionals overestimate barrier heights, the BMK functional less so than the others. The B1B95 and TPSS33B95 meta-GGA functionals both perform very well, whereas general-purpose hybrid GGAs underestimate barrier heights. The simple PBE0 functional does reasonably well.

Vibrational zero-point energies and thermodynamic functions beyond the harmonic approximation

This paper compares harmonic and anharmonic zero-point energies and thermodynamic functions for a number of molecules of small and medium size. Anharmonic corrections cannot be neglected for quantitative studies, but can be obtained quite effectively by a perturbative treatment including cubic force constants to the second order and semidiagonal quartic constants to the first order. Simple finite difference equations provide all the necessary terms by at most 6N-11 Hessian evaluations, where N is the number of atoms in the system. Accurate values are obtained by this method using the Becke three parameter Lee-Yang-Parr functional, medium size basis sets, and, when needed, proper treatment of internal rotations. The whole model has been completely automated in the Gaussian package.

Accurate quantum-chemical prediction of enthalpies of formation of small molecules in the gas phase

The coupled-cluster approach, including single and double excitations and perturbative corrections for triple excitations, is capable of predicting molecular electronic energies and enthalpies of formation of small molecules in the gas phase with very high accuracy (specifically, with error bars less than 5 kJmol-1), provided that the electronic wavefunction is dominated by the Hartree-Fock configuration. This capability is illustrated by calculations on molecules containing O-H and O-F bonds, namely OH, FO, H2O, HOF, and F2O. To achieve this very high accuracy, it is imperative to account for electron-correlation effects in a quantitative manner, either by using explicitly correlated two-particle basis functions (R12 functions) or by extrapolating to the limit of a complete basis. Besides taking into account harmonic zero-point vibrational energies, it is also necessary to account for anharmonic corrections to the zero-point vibrational energies, to include the core orbitals into the coupled-cluster calculations, and to account for spin-orbit corrections and scalar relativistic effects. These additional corrections constitute small but significant contributions in the range of 1-4 kJmol-1 to the enthalpies of formation of the aforementioned molecules. The highly accurate coupled-cluster results, obtained by employing R12 functions and by including various corrections, are compared with standard Kohn-Sham density-functional calculations as well as with the Gaussian-2 and complete-basis-set model chemistries.

Equilibrium Structure and Spectroscopic Constants of Difluorovinylidene: An ab Initio Study

Highly correlated ab initio calculations with large basis sets are reported for difluorovinylidene, F(2)CC. Based on CCSD(T)/aug-cc-pVQZ results and taking core correlation effects properly into account, a reliable theoretical equilibrium geometry is derived: r(e)(CC) = 134.74(10) pm, r(e)(CF) = 131.00(10) pm, and angle(e)(FCC) = 123.23(10) degrees. The error bars are estimated from analogous comparative calculations on the equilibrium structures of the CF(2), C(2), and C(3) species. Correlated harmonic [CCSD(T)/aug-cc-pVQZ] and anharmonic [CCSD(T)/TZ2Pf] force fields provide theoretical values for the fundamental vibrational wavenumbers which are in excellent agreement with those measured previously in an argon matrix. Many spectroscopic constants of F(2)CC are predicted. In addition, the energy of F(2)CC relative to difluoroethyne (FCCF) and the barrier to isomerization from F(2)CC to FCCF have been reinvestigated by means of the present high-level ab initio calculations. Copyright 2001 Academic Press.