Configuration selection as a route towards efficient vibrational configuration interaction calculations

A configuration selective vibrational configuration interaction (CI) approach is presented that efficiently reduces the variational space and thus leads to significant speedups in comparison to standard vibrational CI implementations. Deviations with respect to reference calculations are well below the accuracy of the underlying electronic structure calculations for the potential and hence are essentially negligible. Parallel implementations of the presented configuration selective vibrational CI approaches lead to further significant time savings. Benchmark calculations based on potential energy surfaces of coupled-cluster quality are presented for the fundamental modes of cis- and trans-difluoroethylene. The size-consistency error within the vibrational configuration interaction calculations of the difluoroethylene dimer has been studied in dependence on the excitation level.     

Advances in vibrational configuration interaction theory - part 2: Fast screening of the correlation space

For larger molecules, the computational demands of configuration selective vibrational configuration interaction theory (cs-VCI) are usually dominated by the configuration selection process, which commonly is based on second order vibrational Møller-Plesset perturbation (VMP2) theory. Here we present two techniques, which lead to substantial accelerations of such calculations while retaining the desired high accuracy of the final results. The first one introduces the concept of configuration classes, which allows for a highly efficient exploitation of the analogs of the Slater-Condon rules in vibrational structure calculations with large correlation spaces. The second approach uses a VMP2 like vector for augmenting the targeted vibrational wavefunction within the selection of configurations and thus avoids any intermediate diagonalization steps. The underlying theory is outlined and benchmark calculations are provided for highly correlated vibrational states of several molecules.     

On the number of significant mode-mode anharmonic couplings in vibrational calculations: Correlation-corrected vibrational self-consistent field treatment of di-, tri-, and tetrapeptides

A computational study is made of the number of important anharmonic mode-mode couplings in the context of vibrational calculations for di-, tri-, and tetrapeptides. The method employed is the correlation-corrected vibrational self-consistent field (CC-VSCF) algorithm, which includes correlation effects between different vibrational modes. It is found that results of good accuracy can be obtained in calculations that include only N log N mode-mode coupling terms, where N is the number of modes. This simplification significantly accelerates CC-VSCF calculations for large molecules. A criterion based on the characteristics of the normal-mode displacements is employed to predict a priori unimportant coupling terms. The criterion is tested statistically using Spearman's rank correlation coefficient. The results are illustrated by calculations for several di-, tri-, and tetrapeptides using semiempirical PM3 potential surfaces. These results are analyzed and a statistical model for error estimation is given. The decrease in the number of included coupling from N(2) to N log N opens possibilities of anharmonic vibrational calculations for large peptides.     

A theoretical study on the ionization of H2S with analysis of vibrational structure of the photoelectron spectra

Ab initio calculations were performed to study the molecular structures and the vibrational levels of the low-lying ionic states (²B₁, ²A₁ and ²B₂) of hydrogen sulphide. The equilibrium molecular structure and the vibrational analysis of these states are presented. The normal vibrational calculations at the RHF level and more extensive calculations at the SDCI level using the explicit vibrational Hamiltonians were used for the vibrational analysis. The theoretical ionization intensity curves including the vibrational structures of these ionic states are also presented and compared with the photoelectron spectrum. The results show that the global shape of the potential energy surface has to be taken into consideration in order to analyze the ²A₁ and ²B₂ states. A new assignment of the photoelectron spectra of H₂S is proposed.     

Vibrational frequencies and infrared intensities of the hydrogen-bonded complexes of nitrous acid with ethers: ab initio and DFT studies

The vibrational spectra of the binary complexes formed by HONO-trans and HONO-cis with dimethyl and diethyl ethers have been investigated using ab initio calculations at the SCF and MP2 levels with 6-311++G(d,p) basis set and B3LYP calculations with 6-31G(d,p) and 6-31+G(d,p) basis sets. Full geometry optimisation was made for the complexes studied. The accuracy of the ab initio calculations have been estimated by comparison between the predicted values of the vibrational characteristics (vibrational frequencies and infrared intensities) and the available experimental data. It was established, that the methods, used in this study are well adapted to the problem under examination. The predicted values with the B3LYP calculations are very near to the results, obtained with 6-311++G(d,p)/MP2. The ab initio and DFT calculations show that the changes in the vibrational characteristics (vibrational frequencies and infrared intensities) upon hydrogen bonding for the hydrogen-bonded complex (CH3)2O...HONO-trans are larger than for the complex (CH3)2O...HONO-cis.     

Modeling carbon nanostructures with the self-consistent charge density-functional tight-binding method: vibrational spectra and electronic structure of C(28), C(60), and C(70)

The self-consistent charge density-functional tight-binding (SCC-DFTB) method is employed for studying various molecular properties of small fullerenes: C(28), C(60), and C(70). The computed bond distances, vibrational infrared and Raman spectra, vibrational densities of states, and electronic densities of states are compared with experiment (where available) and density-functional theory (DFT) calculations using various basis sets. The presented DFT benchmark calculations using the correlation-consistent polarized valence triple zeta basis set are at present the most extensive calculations on harmonic frequencies of these species. Possible limitations of the SCC-DFTB method for the prediction of molecular vibrational and optical properties are discussed. The presented results suggest that SCC-DFTB is a computationally feasible and reliable method for predicting vibrational and electronic properties of such carbon nanostructures comparable in accuracy with small to medium size basis set DFT calculations at the computational cost of standard semiempirical methods.     

An efficient molecular orbital approach for a simultaneous evaluation of the vibrational circular dichroism and absorption intensities

We present a procedure for evaluating vibrational circular dichroism and absorption intensities simultaneously, using finite electric field perturbation theory. In this procedure seven SCF calculations are sufficient to obtain all vibrational intensities. Preliminary calculations using CNDO wavefnctions are used to test the soundness of this procedure.     

The emergence of collective vibrations in cluster models: quantum chemical study of the methyl-terminated Si(111) surface

In this paper we present structures and harmonic vibrational frequencies for the methylated silicon (111) surface from quantum chemical calculations using both cluster models and periodic boundary conditions. The results from both calculations are in very good agreement with experimentally determined frequencies. We demonstrate that relatively small cluster models already show the emergence of collective vibrational modes and provide a general method for the assignment of vibrational frequencies for extended surfaces from cluster models. Finally, we discuss a vibrational mode that results from the coupling between near-surface phonons and the silicon-carbon bending modes.     

Vibrational excitation following the Sls core ionization of CS

Ab initio non-relativistic spin-unrestricted Hartree-Fock calculations are performed on CS and its Sls core-ionized state. Geometrical relaxation is investigated. As in the corresponding first-row CO, relaxation greatly influences the vibrational band profile. The one-particle vibrational picture leads to bond-length shortening whereas relaxation and direct calculations indicate a slight bond-length increase, leading to a predicted small vibrational broadening.     

A theoretical study on the ionization of OCS with an analysis of vibrational structures of the photoelectron spectrum

 Ab initio calculations have been performed to study the molecular structures and vibrational levels of the four low-lying ionic states (1, 2²Π, and 1, 2²Σ⁺) of carbonyl sulfide. The global regions of the potential-energy surfaces have been obtained by multireference single and double excitation configuration interaction calculations. Vibrational calculations using explicit vibrational Hamiltonians have been used for vibrational analysis. The equilibrium molecular structures and a vibrational analysis of the four ionic states are presented. The theoretical ionization intensity curves including the vibrational structures of the ionic states are also presented and are compared with the photoelectron spectrum. Received: 20 January 2001 / Accepted: 22 August 2001 / Published online: 30 October 2001     

Raman spectra of long chain hydrocarbons: anharmonic calculations, experiment and implications for imaging of biomembranes

First-principles anharmonic vibrational calculations are carried out for the Raman spectrum of the C-H stretching bands in dodecane, and for the C-D bands in the deuterated molecule. The calculations use the Vibrational Self-Consistent Field (VSCF) algorithm. The results are compared with liquid-state experiments, after smoothing the isolated-molecule sharp-line computed spectra. Very good agreement between the computed and experimental results is found for the two systems. The combined theoretical and experimental results provide insights into the spectrum, elucidating the roles of symmetric and asymmetric CH(3) and CH(2) hydrogenic stretches. This is expected to be very useful for the interpretation of spectra of long-chain hydrocarbons. The results show that anharmonic effects on the spectrum are large. On the other hand, vibrational degeneracy effects seem to be rather modest at the resolution of the experiments. The degeneracy effects may have more pronounced manifestations in higher-resolution experiments. The results show that first-principles anharmonic vibrational calculations for hydrocarbons are feasible, in good agreement with experiment, opening the way for applications to many similar systems. The results may be useful for the analysis of CARS imaging of lipids, for which dodecane is a representative molecule. It is suggested that first-principles vibrational calculations may be useful also for CARS imaging of other systems.     

Conformational and vibrational analysis with the aid of normal coordinate calculations

Many organic compounds exist as equilibrium mixtures of two or more molecular conformations, and vibrational spectroscopy can be used to obtain information about the structure of those conformations. Normal coordinate calculations are often an aid to those conformational studies and to making vibrational assignments for the different conformers. However, sometimes those calculations are partially inconclusive, and a few results are briefly discussed in which both conclusive and inconclusive results were obtained from calculations. Calculations are then applied to some 1,2-dichloro- and 1,2-dibromo-alkanes. Previous calculations on 1,2-dichloropropane and 1,2-dichlorobutane are revised, and calculations are reported for 1,2-dibromopropane, 1,2-dibromopropane-d₆, and 1,2-dibromobutane. Spectra are given for the last two of these compounds. A modified valence force field was determined for each family of 1,2-dihaloalkane that should be transferable to other members of the family.     

Quantitative prediction of gas-phase 19F nuclear magnetic shielding constants

Benchmark calculations of (19)F nuclear magnetic shielding constants are presented for a set of 28 molecules. Near-quantitative accuracy (ca. 2 ppm deviation from experiment) is achieved if (1) electron correlation is adequately treated by employing the coupled-cluster singles and doubles (CCSD) model augmented by a perturbative correction for triple excitations [CCSD(T)], (2) large (uncontracted) basis sets are used, (3) gauge-including atomic orbitals are used to ensure gauge-origin independence, (4) calculations are performed at accurate equilibrium geometries [obtained from CCSD(T)/cc-pVTZ calculations correlating all electrons], and (5) vibrational averaging and temperature corrections via second-order vibrational perturbation theory (VPT2) are included. For the CCSD(T)/13s9p4d3f calculations corrected for vibrational effects, mean and standard deviation from experiment are -1.9 and 1.6 ppm, respectively. Less elaborate theoretical treatments result in larger errors. Consideration of relative shifts can reduce the mean deviation (through an appropriately chosen reference compound), but does not change the standard deviation. Density-functional theory calculations of absolute and relative (19)F nuclear magnetic shielding constants are found to be, at best, as accurate as the corresponding Hartree-Fock self-consistent-field calculations and are not improved by consideration of vibrational effects. Molecular systems containing fluorine-oxygen, fluorine-nitrogen, and fluorine-fluorine bonds are found to be more challenging than the other investigated molecules for the considered theoretical methods.     

New theoretical and experimental infrared results on formaldehyde in solution

An extension of our combined procedure to determine a complete quartic force field and to resolve a vibrational problem thanks to a variational treatment is proposed for quantitative calculations of vibrational spectra in solution. Energies and gradients are obtained through a polarizable continuum model (PCM), the so-called self-consistent isodensity (SCI)-PCM. We present in this paper new experimental results dealing with formaldehyde in solution in cyclohexane, chloroform, THF, acetonitrile, DMSO and water; the obtained vibrational spectra are then compared with CCSD(T)/cc-pVQZ calculations. In addition, density functional theory (DFT) calculations have been carried out with the aim of both anticipating and positioning these approaches for larger sized molecules.     

Vibrational contributions to indirect spin-spin coupling constants calculated via variational anharmonic approaches

Zero-point vibrational contributions to indirect spin-spin coupling constants for N2, CO, HF, H2O, C2H2, and CH4 are calculated via explicitly anharmonic approaches. Thermal averages of indirect spin-spin coupling constants are calculated for the same set of molecules and for C2X4, X = H, F, Cl. Potential energy surfaces have been calculated on a grid of points and analytic representations have been obtained by a linear least-squares fit in a direct product polynomial basis. Property surfaces have been represented by a fourth-order Taylor expansion around the equilibrium geometry. The electronic structure calculations employ density functional theory, and vibrational contributions to indirect spin-spin coupling constants are calculated employing vibrational self-consistent-field and vibrational configuration-interaction methods. The performance of vibrational perturbation theory and various approximate variational calculations are discussed. Thermal averages are computed by state-specific and virtual vibrational self-consistent-field methods.     

A comparison of experimental and calculated spectra of HNO3 in the near-infrared using Fourier transform infrared spectroscopy and vibrational perturbation theory

This work combines new laboratory studies of the near-infrared vibrational spectra of HNO3 with theoretical predictions of these spectra as a means to understand the properties of this molecule at energies well above the fundamental region. Trends in overtone and combination band energy levels and intensities are compiled and examined. The theoretical calculations are in excellent agreement with the observed frequencies and intensities of the transitions in this spectral region. The calculations also serve as a valuable aid for assigning many of the transitions. This work validates the ab initio generated potential energy surface for HNO3 by comparing vibrational perturbation theory calculations to experimental spectra focused on combination band and overtone absorptions.     

Molecular dynamic structure and dimerization of polyacetylene

The vibrational self-consistent-field approximation is used to calculate excited vibrational energy levels of the water molecule in hyperspherical coordinates. The calculations are made for a global realistic Sorbie–Murrell-type potential surface for which exactum quantum variational results are known for comparison. The coupled SCF equations are solved using the discrete variable representation (DVR ) method, which allows computation of the coupled multidimensional integrals in a very simple and efficient way. The results are in good agreement with exactum quantum calculations and are more accurate than SCF energy eigenvalues obtained using normal mode coordinates.     

Distorted wave calculations of the vibrational relaxation of CO in collision with He atoms

Cross sections are calculated for vibrational relaxation of the CO/He system. The calculations use the exponential distorted wave, the distorted wave and close-coupling techniques for the vibrational motion. Rotational motion is treated with the infinite-order sudden approximation. Good agreement is shown between the distorted wave methods and the close-coupled calculations. Vibrational relaxation rate constants are calculated and compared with experimentally determined values. The distorted wave approximation is shown to provide results of useful accuracy.     

Non-Born-Oppenheimer calculations of the pure vibrational spectrum of HeH+

Very accurate calculations of the pure vibrational spectrum of the HeH(+) ion are reported. The method used does not assume the Born-Oppenheimer approximation, and the motion of both the electrons and the nuclei are treated on equal footing. In such an approach the vibrational motion cannot be decoupled from the motion of electrons, and thus the pure vibrational states are calculated as the states of the system with zero total angular momentum. The wave functions of the states are expanded in terms of explicitly correlated Gaussian basis functions multipled by even powers of the internuclear distance. The calculations yielded twelve bound states and corresponding eleven transition energies. Those are compared with the pure vibrational transition energies extracted from the experimental rovibrational spectrum.