Anharmonic Frequency Calculations Research Articles

Infrared Spectrum of the Protonated Water Dimer in the Gas Phase

The frequency-dependent gas-phase infrared multiple photon dissociation (IRMPD) spectrum for the proton-bound dimer of water is reported. The present spectrum is shown to be only in fair agreement with a spectrum reported in an earlier communication but is in agreement with spectra predicted by theoretical means. Two different possible assignments of the observed infrared bands are provided. The first is based on the harmonic oscillator approximation from density functional theory calculations, and a second is based on a quantum four-dimensional model calculation of anharmonic frequencies and intensities. Both calculated spectra agree fairly well, but the density functional calculation assignments are in better agreement. This is expected despite the anharmonic nature of the asymmetric stretch due to the flat potential energy surface associated with this mode.

Vibrational coupled cluster theory.

The theory and first implementation of a vibrational coupled cluster (VCC) method for calculations of the vibrational structure of molecules is presented. Different methods for introducing approximate VCC methods are discussed including truncation according to a maximum number of simultaneous mode excitations as well as an interaction space order concept is introduced. The theory is tested on calculation of anharmonic frequencies for a three-mode model system and a formaldehyde quartic force field. The VCC method is compared to vibrational self-consistent-field, vibrational Møller-Plesset perturbation theory, and vibrational configuration interaction (VCI). A VCC calculation typically gives higher accuracy than a corresponding VCI calculation with the same number of parameters and the same formal operation count.

Explicitly correlated SCF study of anharmonic vibrations in (H2O)2

AbstractModeling solvation in high‐pressure liquid chromatography (HPLC) requires calculation of anharmonic vibrational frequencies of solvent clusters for a statistical partition function. An efficient computational method that includes electron correlation is highly desirable for large clusters. A modified version of the “soft Coulomb hole” method of Chakravorty and Clementi has recently been implemented in a Gaussian‐lobe‐orbital (GLO) program (PCLOBE) to include explicit electron–electron correlation in molecules. The soft Coulomb hole is based on a modified form of Coulomb's law: An algorithm has been developed to obtain the parameter “w” from a polynomial in the effective scaling of each primitive Gaussian orbital relative to the best single Gaussian of the H1s orbital. This method yields over 90% of the correlation energy for molecules of low symmetry for which the original formula of Chakravorty and Clementi does not apply. In this work, all the vibrations of the water dimer are treated anharmonically. A quartic perturbation of the harmonic vibrational modes is constrained to be equal to the exact Morse potential eigenvalue based on a three‐point fit. This work evaluates the usefulness of fitting a Morse potential to a hydrogen bond vibrational mode and finds it to be slightly better than using MP2 vibrational analysis for this important dimer. A three‐point estimate of the depth, De, of a Morse potential leads to a correction formula for anharmonicity in terms of the perturbed harmonic frequency: When scaled by 0.9141, the harmonic Morse method leads to essentially the same results as scaling the BPW91 local density method by 0.9827. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

The infrared spectrum of the O⋯H⋯O fragment of H5O2+: Ab initio classical molecular dynamics and quantum 4D model calculations

The gas phase IR spectrum of the O⋯H⋯O fragment of H5O2+ and its deuterated analogue are calculated using ab initio classical molecular dynamics based on a MP2 potential energy surface. The assignment of the bands is made in terms of the quantum four-dimensional model calculations of anharmonic frequencies and intensities. Comparing low and high kinetic temperature simulations the importance of anharmonicities of the potential energy surface for understanding the vibrational band structure is highlighted. It is shown that any reasonable simulation of IR spectra of systems with very strong hydrogen bonds has to account for the dipole moment function beyond the linear approximation.

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.

Vibrational spectroscopy of the hydrogen bond: An ab initio quantum-chemical perspective

The hydrogen bond has long been recognized as an important type of intermolecular interaction. Its infrared (IR) spectroscopic signature is the shift to lower frequency and the increase in intensity of the A-H stretching band upon formation of the A-H…B hydrogen bond. Ab initio calculations carried out with an appropriate wavefunction model and basis set, and using the harmonic approximation, can reasonably reproduce the shift of the A-H stretching band upon hydrogen bonding, if the equilibrium structure exists in a relatively deep potential well on the surface, so that both the V=0 and the V=1 vibrational states of the proton-stretching mode are confined within this well. However, if the equilibrium structure is found in a region of the surface which is broad and relatively flat, or if a second region of the surface can be accessed in either the V=0 or the V=1 vibrational state of the proton-stretching mode, then the harmonic approximation fails to describe the anharmonicity inherent in the surface. For such complexes, experimental gas-phase structures and experimental IR spectra obtained in low-temperature rare-gas matrices may give conflicting descriptions of the hydrogen bond, and discrepancies will exist between experimental and computed harmonic IR spectra. Anharmonic frequencies for both fundamental and combination bands are needed to understand and reproduce qualitatively the most important features of the experimental spectra. In this article, an overview of the calculation of anharmonic frequencies is presented, and results of one- and two-dimensional anharmonic treatments of vibration are reported for a variety of hydrogen-bonded complexes. Computed frequencies are compared with experimental gas-phase frequencies when these are available, and with experimental frequencies obtained in low-temperature rare-gas matrices.

Application of the generalized-gradient approximation to rare-gas dimers

By performing numerically precise calculations on the ${\mathrm{He}}_{2},$ ${\mathrm{Ne}}_{2},$ ${\mathrm{Ar}}_{2},$ ${\mathrm{Kr}}_{2},$ HeNe, HeAr, HeKr, NeAr, NeKr, and ArKr diatomic molecules we have determined the capacity of three popular approximations to density-functional theory to accurately describe bonding in these rare-gas systems. The local-density approximation, the Perdew-Wang 1991 generalized-gradient approximation, and the Perdew-Burke-Ernzerhof generalized-gradient approximation are utilized in the calculation of equilibrium bond lengths, atomization energies, and anharmonic and harmonic vibrational frequencies. We also use the density-functional-based determination of atomic polarizabilities and ionization potentials to obtain the coefficients for the long-range ${(1/r}^{6})$ attraction. Our calculations suggest that the interaction from the overlap of atomic densities is the primary binding mechanism in these systems at short range but that the long-range ${1/r}^{6}$ attraction could also contribute to the total binding energy.

Water molecules in different crystal surroundings: Vibrational O–H frequencies from a b i n i t i o calculations

A b initio quantum-mechanical calculations of anharmonic frequencies for the water O–H vibrations have been performed for a series of crystalline hydrates. In each case, the potential-energy curve for the uncoupled water O–H stretch was derived at the Mo/ller–Plesset MP2 level. Nearest neighbors of the water molecule were explicitly included in the supermolecule and the rest of the surroundings were mimicked by point charges to reproduce the crystal field out to infinity. The time-independent Schrödinger equation for the motion of the proton in this potential well was solved variationally and the frequency was obtained from the energy difference between the 0 and 1 eigenstates. Computed frequencies can be directly compared with existing infrared data for isotope-isolated water molecules in these hydrates. The compounds selected (LiClO4⋅3H2O, LiHCOO⋅H2O, LiOH⋅H2O ) exhibit experimental O–H frequency shifts in a wide range, from −150 down to −930 cm−1. Good agreement is found between experimental and theoretical frequencies (experimental values in parentheses): 3596 (3556) for LiClO4⋅3H2O, 3129 (3112) and 3488 (3390) for LiHCOO⋅H2O, and 2817 (2775) cm−1 for LiOH⋅H2O. Correlation curves of typical H-bond parameters such as ν(O–H) vs R(H⋅⋅⋅O), re (O–H) and νOH/νOD have been computed and compared with experiment. The vibrational intensities are also discussed.