Rapid anharmonic vibrational corrections derived from partial Hessian analysis

Vibrational analysis within a partial Hessian framework can successfully describe the vibrational properties of a variety of systems where the vibrational modes of interest are localized within a specific region of the system. We have developed a new approach to calculating anharmonic frequencies based on vibrational frequencies and normal modes obtained from a partial Hessian analysis using second-order vibrational perturbation theory and the transition optimized shifted Hermite method. This allows anharmonic frequencies for vibrational modes that are spatially localized to be determined at a significantly reduced computational cost. Several molecular systems are examined in order to demonstrate the effectiveness of this method including organic molecules adsorbed on the Si(100)-2×1 surface, model peptides in solution, and the C-H stretching region of polycyclic aromatic hydrocarbons. Overall, for a range of systems, anharmonic frequencies calculated using the partial Hessian approach are found to be in close agreement with the results obtained using full anharmonic calculations while providing a significant reduction in computational cost.     

The vibrational auto-adjusting perturbation theory

In this work a new method to calculate anharmonic vibrational ground and excited state energies is proposed. The method relies on the auto-adjusting perturbation theory (APT) which has been successfully used to diagonalize square matrices. We use as zeroth order correction the self-consistent vibrational energies, and with the APT approach we calculate the vibrational anharmonic correlation correction to any desired order. In this paper we present the methodology and apply it to a model system and formaldehyde. Vibrational APT approach shows a robust convergent behavior even for the states where the standard (Rayleigh-Schrödinger) vibrational Møller-Plesset perturbation theory is clearly divergent.     

Ab Initio Calculation of Rate Constants for Molecule–Surface Reactions with Chemical Accuracy

The ab initio prediction of reaction rate constants for systems with hundreds of atoms with an accuracy that is comparable to experiment is a challenge for computational quantum chemistry. We present a divide‐and‐conquer strategy that departs from the potential energy surfaces obtained by standard density functional theory with inclusion of dispersion. The energies of the reactant and transition structures are refined by wavefunction‐type calculations for the reaction site. Thermal effects and entropies are calculated from vibrational partition functions, and the anharmonic frequencies are calculated separately for each vibrational mode. This method is applied to a key reaction of an industrially relevant catalytic process, the methylation of small alkenes over zeolites. The calculated reaction rate constants (free energies), pre‐exponential factors (entropies), and enthalpy barriers show that our computational strategy yields results that agree with experiment within chemical accuracy limits (less than one order of magnitude).     

Vibrational quasi-degenerate perturbation theory: applications to fermi resonance in CO2, H2CO, and C6H6

A quasi-degenerate perturbation method with vibrational self-consistent field (VSCF) reference wavefunction is developed. It simultaneously accounts for strong anharmonic mode-mode coupling among a few states (static correlation) by a configuration interaction theory and for weak coupling with a vast number of the other states (dynamic correlation) by a perturbation theory. A general formula is derived based on the van Vleck perturbation theory. An algorithm that selects a compact set of the most important VSCF configurations which contribute to the static correlation is proposed and a scheme to limit the number of configurations considered for dynamic correlation is also implemented. This method reproduces the vibrational frequencies of CO2 and H2CO that are subject to the strongest anharmonic mode-mode coupling within 10 cm(-1) of vibrational configuration interaction results in a computational expense reduced by a factor of one to two orders of magnitude. The method also reproduces the infrared absorption of C6H6 in the CH stretching (nu12) frequency region, in which combination tones nu13nu16 and nu2nu13nu18 appear on account of an intensity borrowing from nu12via the anharmonic coupling.     

A variational approach for calculating Franck-Condon factors including mode-mode anharmonic coupling

We have implemented our new procedure for computing Franck-Condon factors utilizing vibrational configuration interaction based on a vibrational self-consistent field reference. Both Duschinsky rotations and anharmonic three-mode coupling are taken into account. Simulations of the first ionization band of ClO(2) and C(4)H(4)O (furan) using up to quadruple excitations in treating anharmonicity are reported and analyzed. A developer version of the MIDASCPP code was employed to obtain the required anharmonic vibrational integrals and transition frequencies.     

Anharmonic vibrational spectroscopy and investigation of intramolecular mode couplings in adenine

Vibrational frequencies for the nucleobase adenine are calculated by the vibrational self-consistent field (VSCF) and correlation corrected vibrational self-consistent field (CC-VSCF) methods using Hartree-Fock (HF), density functional theory (DFT) and second order Møller-Plesset (MP2) theories. A large number of potential energy surface (PES) points were computed in the anharmonic calculations corresponding to each method. The quartic force field (QFF) approximation was used to generate the full grid of points for the VSCF solver. We have implemented our new procedure for computing the mode-mode coupling integrals in the 2-mode coupling representations of the quartic force field (2MR-QFF) for prediction of coupling magnitudes. Calculations were performed using the 6-31G(d,p) basis set. Comparison of the calculated ab initio anharmonic spectra with Ar matrix experimental data of adenine reported in the literature reveals that, the CC-VSCF (DFT) wavenumbers show the best agreement. The experimental geometric parameters of adenine are compared with the theoretically optimized molecular structural parameters. These are found to be in good agreement. Vibrational assignments are based on the calculated potential energy distribution (PED) values.     

Hydrogen bonding in the urea dimers and adenine–thymine DNA base pair: anharmonic effects in the intermolecular H-bond and intramolecular H-stretching vibrations

The equilibrium structures, binding energies, vibrational harmonic frequencies, and the anharmonic corrections for two different (cyclic and asymmetric) urea dimers and for the adenine–thymine DNA base pair system have been studied using the second-order Møller–Plesset perturbation theory (MP2) method and different density functional theory (DFT) exchange–correlation (XC) functionals (BLYP, B3LYP, PBE, HCTH407, KMLYP, and BH and HLYP) with the D95V, D95V**, and D95V++** basis sets. The widely used a posteriori Boys–Bernardi or counterpoise correction scheme for basis set superposition error (BSSE) has been included in the calculations to take into account the BSSE effects during geometry optimization (on structure), on binding energies and on the different levels of approximation used for calculating the vibrational frequencies. The results obtained with the ab initio MP2 method are compared with those calculated with different DFT XC functionals; and finally the suitability of these DFT XC functionals to describe intermolecular hydrogen bonds as well as harmonic frequencies and the anharmonic corrections is assessed and discussed.     

Strong correlation treated via effective hamiltonians and perturbation theory

We propose a new approach to determine a suitable zeroth-order wavefunction for multiconfigurational perturbation theory. The same ansatz as in complete active space (CAS) wavefunction optimization is used but it is split in two parts, a principal space (A) and a much larger extended space (B). Lo?wdin's partitioning technique is employed to map the initial eigenvalue problem to a dimensionality equal to that of (A) only. Combined with a simplified expression for the (B) portion of the wavefunction, we are able to drastically reduce the storage and computational demands of the wavefunction optimization. This scheme is used to produce reference wavefunctions and energies for subsequent second-order perturbation theory (PT2) corrections. Releasing the constraint of computing the exact CAS energy and wavefunction prior to the PT2 treatment introduces a nonstandard paradigm for multiconfigurational methods. Based on the results of test calculations, we argue that principal parts with only few percents of the total number of CAS configurations could provide final multiconfigurational PT2 energies of the same accuracy as in the standard paradigm. In the future, algorithmic improvements for this scheme will bring into reach active spaces much beyond the present limit of CAS-based methods, therefore allowing for accurate studies of systems featuring strong correlation.     

The infrared spectrum of Au-.CO2

The Au-.CO2 ion-molecule complex has been studied by gas phase infrared photodissociation spectroscopy. Several sharp transitions can be identified as combination bands involving the asymmetric stretch vibrational mode of the CO2 ligand. Their frequencies are redshifted by several hundred cm(-1) from the frequencies of free CO2. We discuss our findings in the framework of ab initio and density-functional theory calculations, using anharmonic corrections to predict vibrational transition energies. The infrared spectrum is consistent with the formation of an aurylcarboxylate anion with a strongly bent CO2 subunit.     

One‐bond 29Si‐1H spin‐spin coupling constants in the series of halosilanes: benchmark SOPPA and DFT calculations,relativistic effects,and vibrational corrections

A number of most representative second order polarization propagator approach (SOPPA) based wavefunction methods, SOPPA, SOPPA(CC2) and SOPPA(CCSD), and density functional theory (DFT) based methods, B3LYP, PBE0, KT2, and KT3, have been benchmarked in the calculation of the one‐bond ²⁹Si‐¹H spin‐spin coupling constants in the series of halosilanes SiH_nX_4?n (X = F, Cl, Br, I), both at the non‐relativistic and full four‐parameter Dirac's relativistic levels taking into account vibrational corrections. At the non‐relativistic level, the wavefunction methods showed much better results as compared with those of DFT. At the DFT level, out of four tested functionals, the Perdew, Burke, and Ernzerhof's PBE0 showed best performance. Taking into account, relativistic effects and vibrational corrections noticeably improves wavefunction methods results, but generally worsens DFT results. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical-analytic implementation of the higher-order canonical Van Vleck perturbation theory for the interpretation of medium-sized molecule vibrational spectra

Anharmonic vibrational states of semirigid polyatomic molecules are often studied using the second-order vibrational perturbation theory (VPT2). For efficient higher-order analysis, an approach based on the canonical Van Vleck perturbation theory (CVPT), the Watson Hamiltonian and operators of creation and annihilation of vibrational quanta is employed. This method allows analysis of the convergence of perturbation theory and solves a number of theoretical problems of VPT2, e.g., yields anharmonic constants y(ijk), z(ijkl), and allows the reliable evaluation of vibrational IR and Raman anharmonic intensities in the presence of resonances. Darling-Dennison and higher-order resonance coupling coefficients can be reliably evaluated as well. The method is illustrated on classic molecules: water and formaldehyde. A number of theoretical conclusions results, including the necessity of using sextic force field in the fourth order (CVPT4) and the nearly vanishing CVPT4 contributions for bending and wagging modes. The coefficients of perturbative Dunham-type Hamiltonians in high-orders of CVPT are found to conform to the rules of equality at different orders as earlier proven analytically for diatomic molecules. The method can serve as a good substitution of the more traditional VPT2.     

Exploring the rich energy landscape of sulfate-water clusters SO4(2-) (H2O)(n=3-7): an electronic structure approach

We present a reinvestigation of sulfate-water clusters SO4(2-) (H2O)(n=3-7), which involves several new aspects. Using a joint molecular mechanics/first principles approach, we perform exhaustive searches for stable cluster geometries, showing that the sulfate-water landscape is much richer than anticipated previously. We check the compatibility of the new structures with experiment by comparing vertical detachment energies (VDEs) calculated at the B3LYP/6-311++G** level of theory and determine the energetic ordering of the isomers at the RI-MP2/aug-cc-pVTZ level. Our results are bench-marked carefully against reference energies of estimated CCSD(T)/aug-cc-VTZ quality and VDEs of CCSD(T)/aug-cc-pVDZ quality. Furthermore, we calculate anharmonic vibrational corrections for up to the n = 6 clusters, which are shown to be significant for isomer energy ordering. We use energy decomposition analysis (EDA) based on the absolutely localized fragment (ALMO) expansion to gain chemical insight into the binding motifs.     

Calculation of Franck-Condon factors including anharmonicity: simulation of the C2H4+X2B3u<--C2H4X1A(g) band in the photoelectron spectrum of ethylene

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B3u<--C2H4X1A(g) band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2D4 results to be not as good as those for C2H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested.     

Anharmonic analysis of the vibrational spectrum of ketene by density functional theory using second-order perturbative approach

The paper reports main results of a comprehensive study of the vibrational spectrum of ketene computed using second-order perturbation theory treatment based on quartic, cubic and semidiagonal quartic force constants. Two different models--a homogeneous model using the same density functionals and basis functions for the harmonic calculations and anharmonic corrections, and a hybrid model in which the two parts of the calculation are conducted using different density functionals and basis sets--have been employed in the present calculations. Different DFT and CCSD methods and DZ and TZ extended basis sets involving diffuse and polarization functions have been used to calculate optimized and vibrationally averaged geometrical parameters, the harmonic and anharmonic vibrational frequencies and the spectroscopic constants such as anharmonicity constants, rotational constants, rotation-vibration coupling constants, Nielsen's centrifugal distortion constants and Coriolis coupling constants. Homogeneous model is found to be superior to the hybrid model in several respects. Difficulties in the hybrid model may arise due to one of the following reasons: (a) the basic requirement that the geometry optimization and frequency calculations must be done at the same level of theory to have valid frequencies is not met in the hybrid model; (b) the molecular structure gets reoptimized at the low level for anharmonic corrections; (c) in addition, the perturbation could also diverge for the above reasons, particularly for the very low, very anharmonic terms where the harmonic approximation is not close enough to make the perturbation work.     

Variational method for calculating the anharmonic vibrations of polyatomic molecules using a combined morse-anharmonic basis taking into account the fragmentary structure of molecules

A method of variational solution of anharmonic vibration problems using a mixed Morse—anharmonic basis is proposed. The basis functions are the products of the Morse oscillator eigenfunctions for vibrations of peripheral bonds, the harmonic oscillator eigenfunctions for almost harmonic skeletal and deformation vibrations, and the anharmonic basis functions for essentially anharmonic skeletal and deformation vibrations. The anharmonic basis wave functions are taken as a linear combination of the Morse and harmonic oscillator eigenfunctions. The introduction of the combined Morse—anharmonic functions allows one to factorize the solution of a problem into a series of individual blocks according to the fragmentary structure of molecules. Volgograd Pedagogical University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 231–238, March–April, 1995. Translated by I. Izvekova     

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 kJ mol^?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 kJ mol^?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.     

Acceleration of Correlation-corrected Vibrational Self-consistent Field Calculation Times for Large Polyatomic Molecules

Acceleration of the correlation-corrected Vibrational self-consistent field (CC-VSCF) method for anharmonic calculations of vibrational states of polyatomic molecules is described. The acceleration assumes pairwise additive interactions between different normal modes, and employs orthogonality of the single-mode vibrational wavefunctions. This greatly reduces the effort in computing correlation effects between different vibrational modes, which is treated by second order perturbation theory in CC-VSCF. The acceleration can improve the scaling of the overall computational effort from N ⁶ to N ⁴, where N is the number of vibrational modes. Sample calculation times, using semi-empirical potential surfaces (PM3), are given for a series of glycine peptides. Large computational acceleration, and significant reduction of the scaling of the effort with system size, is found and discussed.     

Application of dynamical Lie algebraic method to atom–diatomic molecule scattering

The dynamical Lie algebraic approach developed by Alhassid and Levine combined with intermediate picture is applied to the study of translational–vibrational energy transfer in the collinear collision between an atom and an anharmonic oscillator. We find that the presence of the anharmonic terms indeed has an effect on the vibrational probabilities of the oscillator. The computed probabilities are in good agreement with those obtained using exact quantum method. It is shown that the approach of dynamical Lie algebra combining with intermediate picture is reasonable in the treating of atom–anharmonic oscillator scattering.     

Novel methods for calculating the fine vibronic spectra of polyatomic molecules

Novel approximate methods for calculating the vibrational structure of the electronic spectra of polyatomic molecules—a method for the direct calculation of the overlap integrals of vibrational wave functions for the electronic states involved in a transition and a variational method for the solution of the vibrational problem for the excited states—are discussed. The methods are based on the consideration of the displacement and entanglement of normal coordinates, the quasiorthogonality of the Dushinsky transformation, and the classification of the states by total vibrational quantum numbers. Matrix perturbation theory is employed. It is shown that the accuracy of these methods compares well with the accuracy of the available “exact” techniques (the errors are ∼1 cm⁻¹ for frequency and 10% for relative intensity). At the same time, calculations by the new methods are performed more than two orders of magnitude faster than by the previously known methods. K. A. Timiryazev Agricultural Academy, Moscow. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 217–230, March–April, 1995. Translated by I. Izvekova