Vibrational Self-consistent Field Method Research Articles

Ab initio calculations of anharmonic vibrational spectroscopy for hydrogen fluoride (HF) n ( n=3, 4) and mixed hydrogen fluoride/water (HF) n(H 2O) n ( n=1, 2, 4) clusters

Anharmonic vibrational frequencies and intensities are computed for hydrogen fluoride clusters (HF) n with n=3, 4 and mixed clusters of hydrogen fluoride with water (HF) n (H 2O) n where n=1, 2. For the (HF) 4(H 2O) 4 complex, the vibrational spectra are calculated at the harmonic level, and anharmonic effects are estimated. Potential energy surfaces for these systems are obtained at the MP2/TZP level of electronic structure theory. Vibrational states are calculated from the potential surface points using the correlation-corrected vibrational self-consistent field method. The method accounts for the anharmonicities and couplings between all vibrational modes and provides fairly accurate anharmonic vibrational spectra that can be directly compared with experimental results without a need for empirical scaling. For (HF) n , good agreement is found with experimental data. This agreement shows that the Møller–Plesset (MP2) potential surfaces for these systems are reasonably reliable. The accuracy is best for the stiff intramolecular modes, which indicates the validity of MP2 in describing coupling between intramolecular and intermolecular degrees of freedom. For (HF) n (H 2O) n experimental results are unavailable. The computed intramolecular frequencies show a strong dependence on cluster size. Intensity features are predicted for future experiments.

Spectral inhomogeneity induced by vacancies and thermal phonons and associated observables in time- and frequency-domain nonlinear spectroscopy: I2 isolated in matrix argon

The vibrational self-consistent field method is used to analyze the inhomogeneous spectral distribution of transitions caused by vacancies and thermally populated phonons, specializing to molecular iodine isolated in an Ar matrix. At experimentally relevant temperatures, for a vacancy concentration of 1.4%, both defect-induced and phonon-induced spectral shifts contribute to the spectral distribution. Both contributions scale linearly with vibrational overtone number. The predicted widths are consistent with reported resonant Raman spectra. In time-resolved coherent anti-Stokes Raman scattering (TRCARS) measurements, spectral indistinguishability implies that all members of the inhomogeneous ensemble contribute coherently to the detectable homodyne signal. The connection between spectral distribution and the observable in TRCARS is derived. The predicted polarization beats and free induction decay due to the inhomogeneous ensemble are in qualitative agreement with experiments.

Transition from Hydrogen Bonding to Ionization in (HCl)n(NH3)n and (HCl)n(H2O)n Clusters: Consequences for Anharmonic Vibrational Spectroscopy

Anharmonic vibrational frequencies and intensities are calculated for 1:1 and 2:2 (HCl)n(NH3)n and (HCl)n(H2O)n complexes, employing the correlation-corrected vibrational self-consistent field method with ab initio potential surfaces at the MP2/TZP computational level. In this method, the anharmonic coupling between all vibrational modes is included, which is found to be important for the systems studied. For the 4:4 (HCl)n(H2O)n complex, the vibrational spectra are calculated at the harmonic level, and anharmonic effects are estimated. Just as the (HCl)n(NH3)n structure switches from hydrogen-bonded to ionic for n = 2, the (HCl)n(H2O)n switches to ionic structure for n = 4. For (HCl)2(H2O)2, the lowest energy structure corresponds to the hydrogen-bonded form. However, configurations of the ionic form are separated from this minimum by a barrier of less than an O−H stretching quantum. This suggests the possibility of experiments on ionization dynamics using infrared excitation of the hydrogen-bonded form. The strong cooperative effects on the hydrogen bonding, and concomitant transition to ionic bonding, makes an accurate estimate of the large anharmonicity crucial for understanding the infrared spectra of these systems. The anharmonicity is typically of the order of several hundred wavenumbers for the proton stretching motions involved in hydrogen or ionic bonding, and can also be quite large for the intramolecular modes. In addition, the large cooperative effects in the 2:2 and higher order (HCl)n(H2O)n complexes may have interesting implications for solvation of hydrogen halides at ice surfaces.

Vibrational self-consistent field approach to anharmonic spectroscopy of molecules in solids: Application to iodine in argon matrix

An extension of the vibrational self-consistent field (VSCF) method is developed for quantitative calculations of molecular vibrational spectroscopy in a crystalline solid environment. The approach is applicable to fields such as matrix-isolation spectroscopy and spectroscopy of molecular crystals. Advantages of the method are that extended solid vibrations and their coupling to intramolecular modes are incorporated, and that the treatment includes anharmonic effects, both due to the intrinsic property of individual modes and due to coupling between modes. Suitable boundary conditions are adopted in treating the solid environment. In applications, e.g., molecules in rare-gas crystals, hundreds of coupled molecular and matrix modes can be handled computationally. The method is applied to the vibrational matrix-shift of iodine in an argon matrix, and the calculated overtone frequencies are compared to experimental values obtained from both time-domain coherent Raman and frequency-domain Resonance Raman measurements. The physical origin of the shifts is interpreted in detail, and the properties of the iodine–argon interactions essential to obtain the correct sign and magnitude of the shift are elucidated. An I2–Ar potential, based on anisotropic atom–atom interactions and fitted to ab initio calculations, gives the best agreement with experiment. The results show that the VSCF solid-state approach is a powerful tool for matrix spectroscopy.

Anharmonic vibrational spectroscopy of the glycine–water complex: Calculations for ab initio, empirical, and hybrid quantum mechanics/molecular mechanics potentials

Effects of intermolecular hydrogen bonding between glycine and one water molecule on the vibrational spectrum are investigated, using ab initio (at the level of second order Møller–Plesset perturbation theory), empirical (OPLS-AA), and mixed ab initio/empirical quantum mechanics/molecular mechanics (QM/MM) potentials. Vibrational spectroscopy is calculated using the correlation corrected vibrational self-consistent field method that accounts for anharmonicities and couplings between different vibrational normal modes. The intermolecular hydrogen bonding interactions are found to be very strong and to affect vibrational frequencies and infrared intensities of both the glycine and the water molecule to a very large extent. The predicted ab initio anharmonic spectra can be used to identify amino acids in complexes with water in experimental studies. The OPLS-AA potential is found to describe hydrogen bonding between glycine and water incorrectly, and to predict erroneous vibrational spectra. Hybrid (QM/MM) techniques can, however, be used to calculate more reliable vibrational spectra, in agreement with full ab initio treatment of the whole system, provided that the regions that contain hydrogen bonds are described by ab initio potentials.

Torsional analyses of trans-2-butene and propene cations: A comparative investigation of two prototypical ions with different degrees of symmetry

The mass analyzed threshold ionization spectra of trans-2-butene and propene have been obtained using single-step vacuum ultraviolet excitation. The ionization potential for trans-2-butene is 73 605±4 cm−1, while for propene it is 78 587±4 cm−1. Both species have progressions of the low frequency, torsional, normal modes. Using the torsional normal mode and first overtone from a trans-2-butene cation the torsional barrier is determined to be approximately 453 cm−1, assuming a sinusoidal potential. Normal mode analysis indicates that all low frequency normal modes of the propene cation involve substantial internal motion of the vinyl component, and the spectrum shows a very anharmonic torsional mode progression. These factors complicate direct torsional barrier analysis from the experimental lines, but through the use of various ab initio methods the propene torsional barrier is determined to be approximately 429 cm−1. Due to the anharmonicity found in propene, the correlation corrected vibrational self-consistent field method in GAMESS was used to verify the assignments of the experimental lines. The torsional barriers for both cations are found to lie approximately 275–300 cm−1 below the barrier heights of the neutral species.

Anharmonic Vibrational Spectroscopy of Glycine: Testing of ab Initio and Empirical Potentials

The second-order Møller−Plesset ab initio electronic structure method is used to compute points on the potential energy surface of glycine. Some 50 000 points are computed, covering the spectroscopically relevant regions, in the vicinity of the equilibrium structures of the three lowest-lying conformers of glycine. The vibrational states and spectroscopy are computed directly from the potential surface points using the correlation corrected vibrational self-consistent field (CC-VSCF) method, and the results are compared with experiment. Anharmonic effects and couplings between different vibrational modes that are included in the treatment are essential for satisfactory accuracy. The following are found: (1) The spectroscopic predictions from the ab initio potential are in very good accord with matrix experiments. (2) Theory agrees even more closely with spectroscopic data for glycine in He droplets, where environmental effects are much weaker than in the matrix. This suggests that errors in the ab initio potential are smaller than rare-gas matrix effects. (3) The accuracy of the ab initio potential is, by this spectroscopic test, much superior to that of OPLS-AA, a state-of-the-art empirical potential. The relative failure of the empirical potential is due to its inability to describe details of the hydrogen-bonded interactions, and is most critical in one of the glycine conformers where such interactions play an especially important role.

Anharmonic Vibrational Spectroscopy Calculations for Novel Rare-Gas-Containing Compounds: HXeH, HXeCl, HXeBr, and HXeOH

A first-principles calculation of vibrational spectroscopy of HXeH, HXeCl, HXeBr, and HXeOH molecules is performed by combining ab initio codes with the vibrational self-consistent field (VSCF) method, and with its extension by perturbation theory (CC-VSCF). The MP2/CC-VSCF method is anharmonic, and it is able to reproduce the experimentally observed spectral features of HXeH, HXeCl, HXeBr, and HXeOH. The most intense bands of the HXeY molecules, the Xe−H stretching modes, are found to be highly anharmonic. In general, the other fundamental modes presented anharmonic effects to a lesser extent. New predictions of overtone and combination vibrations are made to help experimental investigations of these molecules. It is shown that vibrational spectroscopy calculations are reliable and useful for analyzing the spectral features of rare-gas-containing molecules. While the results of the MP2/CC-VSCF calculations are in much better agreement with experiments than the corresponding harmonic frequencies, substant...

Direct vibrational self-consistent field method: Applications to H2O and H2CO

The vibrational self-consistent field (VSCF) and virtual configuration interaction (VCI) methods are directly combined with ab initio electronic structure calculations for evaluations of the potential energy at VSCF quadrature points. Referred to as direct VSCF and direct VCI, respectively, these methods have been applied to evaluations of anharmonic vibrational energy levels of H2O and H2CO at the second-order Mo/ller–Plesset MP2/aug-cc-pVTZ and MP2/cc-pVTZ computational levels, respectively. The purpose of the present study is to develop a direct methodology for vibrational state calculations by examining the accuracy of the results, as well as their computational costs. In addition, the accuracy and applicability of two approximate potential energy surfaces (PES), a quartic force field (QFF), and the PES determined by the modified-Shepard interpolation method (Int-PES), are investigated via comparisons of calculated energy levels of vibrational states with those derived by the direct methods. The results are analyzed in terms of three considerations: (i) truncations of higher-order intercoordinate couplings in the PES; (ii) mode–mode coupling effects; (iii) approximations in ab initio electronic structure methods. In the direct VCI calculations, the average absolute deviations in fundamental frequencies relative to the experimental values are 9.3 cm−1(H2O) and 34.7 cm−1(H2CO). The corresponding values evaluated with approximate PESs relative to those derived by the direct method are 35.0 cm−1 (QFF) and 15.3 cm−1 (Int-PES) for H2O, and 6.3 cm−1 (QFF) and 10.3 cm−1 (Int-PES) for H2CO.

Anharmonic Vibrational Spectroscopy of Hydrogen-Bonded Systems Directly Computed from ab Initio Potential Surfaces: (H2O)n, n = 2, 3; Cl-(H2O)n, n = 1, 2; H+(H2O)n, n = 1, 2; H2O−CH3OH

Vibrational energy levels and infrared absorption intensities of several neutral and ionic hydrogen-bonded clusters are computed directly from ab initio potential energy surfaces, and the results are compared with experiment. The electronic structure method used to compute the potential surfaces is MP2, with Dunning's triple-ζ + polarization basis set. The calculation of the vibrational states from the potential surface points is carried out using the correlation corrected vibrational self-consistent field (CC-VSCF) method. This method includes anharmonicity and the coupling between different vibrational modes. The combined electronic structure/vibrational algorithm thus provides first-principles calculations of vibrational spectroscopy at a fairly accurate anharmonic level and can be useful for testing the accuracy of electronic structure methods by comparing with experimental vibrational spectroscopy. Systems treated here are (H2O)n, n = 2, 3; Cl-(H2O)n, n = 1, 2; H+(H2O)n, n = 1, 2; and H2O−CH3OH. In the cases of (H2O)3 and H2O−CH3OH, over 13 000 potential surface points are computed. For each system treated, all the fundamental transitions are computed, but the experimental data for comparison is mostly available for the OH stretches or other stiff modes only. The results show very good agreement between the calculated and experimental frequencies for all systems. The typical deviation for OH stretching modes is on the order of 50 cm-1, indicating that the ab initio potential surfaces are of good accuracy. This is very encouraging for further pursuing MP2 calculations of potential energy surfaces of hydrogen-bonded systems.

Direct calculation of anharmonic vibrational states of polyatomic molecules using potential energy surfaces calculated from density functional theory

Potential energy surface points computed from variants of density functional theory (DFT) are used to calculate directly the anharmonic vibrational frequencies of H2O, Cl−H2O, and (H2O)2. The method is an adaptation to DFT of a recent algorithm for direct calculations of anharmonic vibrational frequencies using ab initio electronic structure codes. The DFT calculations are performed using the BLYP and the B3LYP functionals and the results are compared with experiment, and also with those calculated directly from a potential energy surface obtained using ab initio Möller-Plesset second–order perturbation theory (MP2). The direct calculation of the vibrational states from the potential energy points is performed using the correlation-corrected vibrational self-consistent field (CC-VSCF) method. This method includes anharmonicity and correlations between different vibrational modes. The accuracy of this method is examined and it is shown that for the experimentally measured transitions the errors in the CC-VSCF calculations are much less than the errors due to the potential energy surface. By comparison with the experimentally measured frequencies the CC-VSCF method thus provides a test for the quality of the potential energy surfaces. The results obtained with the B3LYP functional, in contrast to those of the BLYP functional, are of comparable quality to those obtained with MP2. The B3LYP anharmonic frequencies are in good agreement with experiment, showing this DFT method describes well the anharmonic part of the potential energy surface. The BLYP results systematically underestimate both the harmonic and anharmonic frequencies and indicate that using this functional for the description of hydrogen-bonded systems may cause significant errors.

Ab initio calculation of anharmonic vibrational states of polyatomic systems: Electronic structure combined with vibrational self-consistent field

An algorithm for first-principles calculation of vibrational spectroscopy of polyatomic molecules is proposed, which combines electronic ab initio codes with the vibrational self-consistent field (VSCF) method, and with a perturbation-theoretic extension of VSCF. The integrated method directly uses points on the potential energy surface, computed from the electronic ab initio code, in the VSCF part. No fitting of an analytic potential function is involved. A key element in the approach is the approximation that only interactions between pairs of normal modes are important, while interactions of triples or more can be neglected. This assumption was found to hold well in applications. The new algorithm was applied to the fundamental vibrational excitations of H2O, Cl−(H2O), and (H2O)2, using the Möller–Plesset method for the electronic structure. The vibrational frequencies found are in very good accord with experiments. Estimates suggest that this electronic ab initio/VSCF approach should be feasible, with reasonable computational resources, for all-mode calculations of vibrational energies and wave functions for systems of up to 10–15 atoms. The new method can be also very useful for testing the accuracy of electronic structure codes by comparing with experimental vibrational spectroscopy.

Classical and quantum mechanical studies of the CO vibrations in CO/Cu(100)

We report classical and quantum mechanical calculations of the vibrational energies of the CO/Cu(100) focusing on the CO–CO intermolecular coupling and the anharmonic coupling between the six CO–Cu modes. The normal mode analysis is used for the classical calculation, and the vibrational self-consistent field method is used to solve the vibrational eigenvalue problem for the quantum mechanical calculation. The vibrational frequencies of the six CO–Cu modes are obtained. A significant vibrational frequency change has been found in frustrated translational mode due to CO–CO intermolecular coupling. The agreement with recent experiments is generally quite good. Details of vibrational dynamics will be discussed with respect to the CO–CO coupling and the anharmonic coupling.

Anharmonic Vibrational Self-Consistent Field Calculations as an Approach to Improving Force Fields for Monosaccharides

An Amber-type of force field, based on experimental vibrational frequencies which is suitable for monosaccharides, is presented. In the present force field, the atomic partial charges and some torsional parameters are derived from a fit of calculated vibrational energy levels to known experimental spectra for α-d-glucose. The vibrational spectra were calculated using the vibrational self-consistent field (VSCF) method, which includes contributions from both anharmonic and mode-coupled terms. We find that with a reparametrization of the force field the agreement between the experimental and calculated vibrational spectra is ±3.3 cm-l for α-glucose and ±5.1 cm-l for β-glucose. Using the VSCF method, we are also able to lend support to the idea that the COH bending motion is strongly coupled to the methylene and methine modes, as well as the other internal modes. We then test our spectroscopically derived force field by calculating the anomeric effect for α → β glucose. Molecular dynamics simulations are per...

Computation of the Electronic and Spectroscopic Properties of Carbohydrates Using Novel Density Functional and Vibrational Self-Consistent Field Methods

ABSTRACT A novel density functional method is presented for the calculation of electronic and thermodynamical properties of oligosaccharides. This method, termed K2-BVWN, offers two advantages; it scales as N 3, where N is the number of basis functions, and there are only two adjustable parameters. The current density functional method is tested in terms of reproducing high level gas phase ab initio calculations in eleven low energy conformers of D-glucopyranose including exo-anomeric and different hydroxymethyl orientations (G −, G +, and T). The K2-BVWN method is also tested in terms of reproducing the spectroscopic features of D-glucopyranose and D-mannopyranose (α/β) as compared with both a vibrational self-consistent field calculation (VSCF) as well as experimental infrared spectroscopy. The VSCF calculations offer the advantage that it is possible to include higher order mode coupling and anharmonic effects directly into the calculation of the vibrational frequencies. In general, the K2-BVWN method reproduces the ab initio energetic trends of the different conformers of D-glucose. While the absolute energies are not the same between the ab initio and the K2-BVWN method, both methods do predict a preference for the α-anomer in the gas phase (0.4 kcal/mol ab initio, 0.0 – 0.5 kcal/mol K2-BVWN). The K2-BVWN method was able to reproduce the experimental and VSCF calculated spectrum of both D-glucopyranose and D-mannopyranose in the frequency range between 1500 – 800 cm−1. Because the current density functional method is both relatively quick and accurate, it represents a significant advancement in the development of oligosaccharide force fields.

Combined diffusion quantum Monte Carlo–vibrational self-consistent field (DQMC–VSCF) method for excited vibrational states of large polyatomic systems

Diffusion quantum Monte Carlo (DQMC) is a powerful method for calculating the vibrational ground state of large systems but is inapplicable in general for excited states. We propose a general method for excited states, based on combining DQMC with the approximate vibrational self-consistent field (VSCF) approach; the latter is used to obtain the nodes of the excited state wavefunctions. The combined DQMC–VSCF is approximate but found high accuracy in test calculations of Ar 3. DQMC–VSCF is also applied to collective mode excitations of Ar 13. The method provides full spectroscopic assignment for the computed excited states through VSCF.

Extensions and tests of "multimode": a code to obtain accurate vibration/rotation energies of many-mode molecules

We describe extensions and tests of the code “multimode” which does vibrational self-consistent field method (VSCF) and two types of state-mixing (denoted VSCF-CI and V-CI) for rovibrational energies of many-mode systems. The extensions include an exact treatment of rotation, flexible approaches to perform the CI calculations, and the inclusion of a Davidson diagonalization routine to find low-lying eigenvalues of large matrices. The code is tested against previous exact variational calculations for non-rotating H2CN, and J=0 and J=1 rovibrational states of H2CS. The code represents the full potential by a hierarchical n-mode representation, where n is the number of normal coordinates that are coupled together. Tests are presented for the convergence and accuracy of this representation for n equal to 3 and 4, where 4 is the current maximum value. These tests are done at the VSCF and V-CI level, with very encouraging results.

The adiabatic rotation approximation for rovibrational energies of many-mode systems: Description and tests of the method

We extend the vibrational self-consistent field method (VSCF), and two types of state mixing [denoted VSCF-CI and V-CI (configuration interaction)], to include an approximate, adiabatic treatment of overall rotation. In this approach, the asymmetric-top rotational Hamiltonian is diagonalized in an “instantaneous” principal axis system, and the resulting coordinate-dependent rotational energy is added to the exact Hamiltonian of the nonrotating system to form an effective Hamiltonian for the rotation/vibrational energies. The energy eigenvalues of that Hamiltonian are then obtained by the VSCF approach and/or variational, state-mixing methods. In this present formulation for many-mode systems, we use the general Watson Hamiltonian, and also a hierarchical representation of the many-mode potential described previously [S. Carter, S. Culik, and J. M. Bowman, J. Chem. Phys. 107, 10458 (1997)]. This approach, at the VSCF, and VSCF-CI and V-CI levels is tested against recent exact calculations of vibrational/rotation energies of HO2 and H2O. HO2 is an approximate prolate symmetric top, which is a favorable case for the approximate treatment of rotation, whereas H2O is a highly asymmetric top with large rotation constants, and represents an unfavorable case for the method.

Vibrational self-consistent field method for many-mode systems: A new approach and application to the vibrations of CO adsorbed on Cu(100)

We report calculations of the vibrational energies of CO–Cu(100) using a new code to perform vibrational self-consistent field (VSCF) and state-mixing calculations for many-mode systems. The major new feature of the code is the representation of the potential. Unlike recent implementations of the VSCF method, the potential is not expanded in terms of normal coordinates as a multinomial series about a minimum. The full potential, in normal coordinates, is used in the Watson Hamiltonian. This approach, while rigorous, can lead to prohibitively large numerical quadratures, and so we suggest a novel representation of the potential as an expansion in all two-mode, or all three-mode, or all four-mode coupling terms. The new code is tested against previous exact calculations of vibrational states of HCO, and also against previous VSCF calculations that used a fourth-order, normal coordinate force field representation of the global HCO potential. The new code is applied to calculations of the vibrations of CO adsorbed to Cu(100). We explicitly treat nine modes corresponding to the motion of the C and O atoms and the Cu atom that is bonded to C. The potential used is a semi-empirical one developed by Tully and co-workers [J. C. Tully, M. Gomez, and M. Head-Gordon, J. Vac. Sci. Technol. A 11, 1914 (1993)], and is used fully, i.e., without recourse to multinomial expansion in displacement coordinates. We test the convergence of the results with respect to the number of modes coupled and find that the errors in the two-mode coupling representation vary from 0.6 to 6 cm−1 for the fundamentals but grow to 30 cm−1 for overtone and combination states. The errors in the three-mode representation of the potential are less than 0.2 cm−1 for the fundamentals and no larger than 2.5 cm−1 for high overtone/combination states with as much as 9 quanta of excitation. We calculate the thermally broadened spectra of the CO-stretch fundamental, the CO–Cu frustrated rotation and the CO–Cu frustrated translation over the temperature range 50–350 K. We compare the temperature dependence of the average frequency and standard deviation of these modes with experiment, and find semiquantitative agreement.

Vibrational Spectroscopy of Peptides and Peptide−Water Complexes: Anharmonic Coupled-Mode Calculations

Quantum calculations are reported for vibrational states and energy levels of several peptide and peptide−water complexes, to provide insight into the spectroscopic properties of such systems and their dependency on presently available anharmonic force fields. A blocked di-l-serine−H2O complex and trialanine in an antiparallel β sheet configuration are the main systems treated. The calculations are for variants of the Amber force field and use the vibrational self-consistent field (VSCF) method, which includes effects of anharmonicity as well as interactions between modes. The main findings are as follows: (1) Distinct isomers of a single peptide−H2O complex corresponding to different hydrogen binding sites of the H2O are observed. (2). The H2O induces shifts of up to 50 cm-1 in the frequencies of fundamental transitions associated with the peptide modes. (3). Some of the “intermolecular” modes of the peptide−H2O cluster are of frequencies and geometry that suggest effective peptide-to-water energy transfer. (5). Changing the TIP3 water potential in the Amber force field into the Coker−Watts potential produces significant spectroscopic changes. (5). The peptide−H2O cluster is found to have several tunneling states, which are assigned in detail. At least some of these states should be spectroscopically observable by the magnitude of the splitting. (6) The trialanine calculations are compared with experimental data available for part of the transitions. For many of the “stiff” transitions good agreement is found, but the remaining differences suggest that the force field should be revised. It is argued on the basis of these results that high-resolution spectroscopy in jets should be an excellent tool for improving and developing biomolecular force fields.