Effect of secondary basis-set superposition error upon calculated vibrational intensities

The calculated dipole moment and polarizability of a molecule are affected by the position of the ghost orbitais of its partner subunit within a molecular complex. The IR and Raman intensities, evaluated in terms of the derivatives of these properties with respect to an intermolecular motion, are hence subject to a secondary basis-set superposition error (BSSE), here calculated for (HF)₂ with a variety of basis sets. Whereas the IR intensity is only slightly affected, the BSSE introduces enormous errors into the Raman intensities. These errors can be reduced if two sets of polarization functions are included in the basis set.     

Finite-field method calculations. IV. Higher-order moments,dipole moment gradients,polarisability gradients and field-induced shifts in molecular properties: Application to N2, CO,CN−, HCN and HNC

In this paper, theoretical methods developed in III are applied in calculating polarisabilities, polarisability gradients and field-induced shifts, by the finite-field method. Values of dipole moment gradients and higher-order moments, calculated from the unperturbed wavefunctions, are also reported. Results for N₂, CO, CN^?, HCN and HNC have been obtained at the SCF level; some CI results for the N₂ polarisability components and moments and for the dipole moment gradients of HCN are also given. The calculated polarisability gradients and dipole moment gradients have been used to estimate the Raman scattering intensities and depolarisation ratios and the IR absorption intensities. Model calculations of field-induced shifts in bond length, vibrational levels, spectroscopic constants, force constants and dipole moment gradient are reported for N₂ and CO.The discrepancy between the SCF and experimental bond dipole moment gradients for HCN, previously noted in the literature, has been re-examined and resolved by our CI results.     

Calculation of relative Raman intensities: II. Calculations using an extended Hückel valence basis set

Line intensities in Raman spectra are determined by means of a modified extended Hückel [1] method. Perturbation terms are developed which are inserted into the Hamiltonian used in the extended Hückel theory to yield the induced dipole moment as a function of the normal coordinate Q, from which the polarizability change on Q is obtained. The normal coordinate determination is carried out with a programme developed in this laboratory [2]. From a valence basis set within the extended Hückel theory, the Raman intensities of acetylene, formaldehyde, phosgene, thiophosgene, dichloromethane and tetrafluoroethylene calculated from the extended Hückel theory are compared with those obtained by CNDO and INDO calculations and with the measured data. It is found that the Raman intensities calculated from the extended Hückel method are similar to those obtained from the CNDO and INDO calculations.     

Infrared intensities of lattice vibrations in molecular crystals

From the dynamic multipoles model an expression is derived for the dipole moment derivative governing the intensity of infrared absorption by lattice modes in molecular crystals. The result depends on non-local susceptibilities which take proper account of the local electric field in a way consistent with dielectric theory. It is shown that the non-local rsponse follows naturally from microscopic lattice dynamical theory. It arises from dipolar coupling and is intimately connected with the delocalized exciton states produced by the same mechanism. Intensities calculated for the iodine crystal are inproved by including the local field, but a point quadrupole field proves too anisotropic to yield the measured intensity ratio. The treatment shows that infrared intensities can be used to obtain unique effective molecular polarizabilities.     

Dielectric and raman spectroscopic studies on the rotational isomerism of t-butyl formate

Static dielectric constants, refractive indices and densities have been measured for t-butyl formate and acetate in cyclohexane at increasing concentrations and at two temperatures, 20°C and 60°C. The ΔH value for the cis-trans equilibrium of t-butyl formate and the dipole moment of the trans conformation has been calculated from the dielectric measurements taking the ΔS value calculated from the sum-over-states for the cis and trans conformations and assuming the dipole moment of the cis conformation to be equal to 1.94 D as found for t-butyl acetate, which has the cis conformation only.The relative intensities of the Raman bands corresponding to specific vibrations modes of the cis and trans conformations of t-butyl formate are measured in cyclohexane and acetonitrile at various concentrations. The enthalpy difference ΔH is also measured in the liquid state and in acetonitrile by variation of the intensity ratio of the bands with temperature.All thermodynamic quantities obtained from dielectric or Raman intensity measurements are compared with each other and with the theoretical values. The solvation energy difference between cis and trans conformations in cyclohexane and acetonitrile as well as in the liquid state are also compared with theoretical values. The large deviation of solvation energy difference between the experimental value and Onsager's model value are well described by an additional term, which considers dipole-dipole interaction.     

On the calculation of dipole moment and polarizability derivatives by the analytical energy gradient method: Application to the formaldehyde molecule

Following the suggestion of Komornicki and McIver we have implemented an efficient computational scheme for the evaluation of dipole moment and polarizability derivatives at the Hartree-Fock SCF level. The derivatives are obtained by utilizing the analytical gradients of the molecular energy, calculated in the presence of an external electric field, with respect to the atomic cartesian coordinates, which are differentiated numerically with respect to the field. The implementation of the method within the framework of the MOLECULE program is discussed, concentrating on such aspects as numerical accuracy, utilization of molecular symmetry and computational efficiency. As an application, the dipole moment and polarizability derivatives of the formaldehyde molecule have been calculated, yielding infrared intensities and Raman scattering activities in the double harmonic approximation. The theoretical results are compared with the available experimental data; the agreement is satisfactory given the inherent restrictions of the SCF model.     

A comparison of Hartree—Fock,MP2, and DFT results for the HCN dimer and crystal

A number of hydrogen-bond related quantities—geometries, interaction energies, dipole moments, dipole moment derivatives, and harmonic vibrational frequencies—were calculated at the Hartree—Fock, MP2, and different DFT levels for the HCN dimer and the periodic HCN crystal. The crystal calculations were performed with the Hartree—Fock program CRYSTAL92, which routinely allows an a posteriori electron-correlation correction of the Hartree—Fock obtained lattice energy using different correlation-only functionals. Here, we have gone beyond this procedure by also calculating the electron-correlation energy correction during the structure optimization, i.e., after each CRYSTAL92 Hartree—Fock energy evaluation, the a posteriori density functional scheme was applied. In a similar manner, we optimized the crystal structure at the MP2 level, i.e., for each Hartree—Fock CRYSTAL92 energy evaluation, an MP2 correction was performed by summing the MP2 pair contributions from all HCN molecules within a specified cutoff distance. The crystal cell parameters are best reproduced at the Hartree—Fock and the nongradient-corrected HF + LDA and HF + VWN levels. The BSSE-corrected MP2 method and the HF + P91, HF + LDA, and HF + VWN methods give lattice energies in close agreement with the ZPE-corrected experimental lattice energy. The (HCN)₂ dimer properties are best reproduced at the MP2 level, at the gradient-corrected DFT levels, and with the B3LYP and BHHLYP methods. © 1996 John Wiley & Sons, Inc.     

Energy of charged states in the acetanilide crystal: trapping of charge-transfer states at vacancies as a possible mechanism for optical damage

Calculations for the acetanilide crystal yield the effective polarizability (16.6 A(3)), local electric field tensor, effective dipole moment (5.41 D), and dipole-dipole energy (-12.8 kJ/mol). Fourier-transform techniques are used to calculate the polarization energy P for a single charge in the perfect crystal (-1.16 eV); the charge-dipole energy W(D) is zero if the crystal carries no bulk dipole moment. Polarization energies for charge-transfer (CT) pairs combine with the Coulomb energy E(C) to give the screened Coulomb energy E(scr); screening is nearly isotropic, with E(scr) approximately E(C)/2.7. For CT pairs W(D) reduces to a term deltaW(D) arising from the interaction of the charge on each ion with the change in dipole moment on the other ion relative to the neutral molecule. The dipole moments calculated by density-functional theory methods with the B3LYP functional at the 6-311++G(**) level are 3.62 D for the neutral molecule, changing to 7.13 D and 4.38 D for the anion and cation, relative to the center of mass. Because of the large change in the anion, deltaW(D) reaches -0.9 eV and modifies the sequence of CT energies markedly from that of E(scr), giving the lowest two CT pairs at -1.98 eV and -1.41 eV. The changes in P and W(D) near a vacancy are calculated; W(D) changes for the individual charges because the vacancy removes a dipole moment and modifies the crystal dielectric response, but deltaW(D) and E(C) do not change. A vacancy yields a positive change DeltaP that scatters a charge or CT pair, but the change DeltaW(D) can be negative and large enough to outweigh DeltaP, yielding traps with depths that can exceed 150 meV for single charges and for CT pairs. Divacancies yield traps with depths nearly equal to the sum of those produced by the separate vacancies and so they can exceed 300 meV. These results are consistent with a mechanism of optical damage in which vacancies trap optically generated CT pairs that recombine and release energy; this can disrupt the lattice around the vacancy, thereby favoring trapping and recombination of CT pairs generated by subsequent photon absorption, leading to further lattice disruption. Revisions to previous calculations on trapping of CT pairs in anthracene are reported.     

Comment on a sum rule for vibrational raman optical activity

The expressions for the sum of vibrational Raman optical activity (ROA) intensities indicate that the ROA intensity sum for chiral molecules is non-zero for those with an anisotropic electric dipole polarizability. The non-zero sum depends upon the electric dipole, magnetic dipole and electric quadrupole polarizability components and moments of inertia at equilibrium geometry.     

Calculation of raman intensities by a modified cndo/2/indo method

Line intensities in Raman spectra determined by means of a modified CNDO/2 and a modified INDO method [1,2] give perturbation terms which are inserted into the Hartree—Fock operator used in the CNDO/2 and INDO theory [3, 4] to yield the induced dipole moment as a function of the normal co-ordinate Q, from which the polarizability change upon Q is obtained. The results for ethylene, tetrafluoroethylene, tetrachloroethylene, dichloromethane and phosgene are discussed. Calculated intensities agree well with experimental intensities obtained from Raman spectra.     

The frequency-dependent dipole polarizability of the mercury dimer from four-component relativistic density-functional theory

The frequency-dependent dipole polarizability of Hg(2) is calculated using response theory within four-component relativistic density-functional theory [using the local-density approximation (LDA) and the hybrid functional B3LYP] including corrections for the basis-set superposition error. The anisotropic component of the polarizability tensor agrees well with the values obtained from collision-induced Raman spectroscopy carried out at a wavelength of 488 nm. The values obtained from the two density functionals agree closely with the experimentally derived anisotropy component of the dipole polarizability, despite their rather large differences in the dimer potential-energy curves (LDA is strongly overbinding while B3LYP is purely repulsive). The first two refractivity virial coefficients for the generalized Clausius-Mossotti function are derived.     

Polarizable model of water with field-dependent polarization

The polarizable charge-on-spring model of water with three Gaussian charges developed by the present authors [A. Baranyai and P. T. Kiss, J. Chem. Phys. 133, 144109 (2010)] was studied. We introduced an analytic function for the polarizability in terms of the local electric field. Following theoretical suggestions, the polarizability decreases from its experimental gas-phase value, in our approach, toward a high-field threshold. Using this modified polarizability, we reparameterized the model by calculating its dielectric constant and obtained good estimates of density and internal energy for ambient water, hexagonal ice, and water cluster properties. Mimicked by the new model, we studied liquid water under the impact of homogeneous static electric field in the rage of 0-2.5 V/?. Both the density and the average dipole moment increase with the strength of the electric field. However, the internal energy shows a minimum at ~0.35 V/?. At this field strength, the model starts ordering into a crystal structure. At higher fields the liquid forms a crystalline structure which is a special version of cubic ice.     

Static-lattice theory of crystalline HCN: I. Effective dipole potential

An intermolecular potential is constructed for HCN in its two crystalline modifications. The long-range part is treated as the electrostatic interaction of point effective dipoles obtained using dielectric data, lattice summations and molecular-orbital calculation. The short-range part is represented by a symmetrical dumb-bell model with 6:12 potentials, a simple form chosen to clarify the role of the effective dipoles. It is parametrized to yield the correct static-lattice energy at the observed tetragonal structure while being consistent with gas-phase second virial coefficients. A generally satisfactory understanding of both crystal structures is obtained, although no stable orthorhombic structure is found. The potential is readily used for calculating piezoelectric properties, as in the following paper.     

Polarizabilities and dipole moments of benzaldehyde, benzoic acid and oxalic acid in polar and nonpolar solvents

The purpose of this report is to calculate the orientation polarizability of benzaldehyde, benzoic acid and oxalic acid in polar and nonpolar solvents. The calculations are based on the knowledge of permanent dipole moment of the solutions. Other important physical quantities such as refractive index, density, specific volume, dielectric constant, molar polarization and molar refractivity are also calculated. Dipole moments of the solutions are calculated by using measured dielectric constants of the solutions. The dielectric constant measurements were made at 100 kHz. Relationships between the polarizability and concentration, specific volume, dielectric constant and dipole moment of the solutions are suggested.     

The experimental studies on the determination of the ground and excited state dipole moments of some hemicyanine dyes

The ground state (mu(g)) and excited state (mu(e)) dipole moments of 15 hemicyanine dyes were studied at room temperature. They were estimated from solvatochromic shifts of the absorption and the fluorescence spectra as function of the solvent dielectric constant (varepsilon) and refractive index (n). In this paper we applied the Stokes shift phenomena not only for the determination of the difference in the dipole moment of excited state and ground state, but to determine the value of polarizability alpha as well. The obtained results show that excited state dipole moments of hemicyanine dyes are in the range from 5 to 15 Debye, and the difference between the excited and ground state dipole moments vary from 1 to 7 Debye. The excited and ground state dipole moments difference (mu(e)-mu(g)) obtained for selected dyes are positive. It means that the excited states of the dyes under the study are more polar than the ground state ones. Additionally, the value of both polarizability (alpha) and the Onsager radius (a) of each investigated hemicyanine dye molecule are determined, and the ratio of alpha/a(3) for each dye were calculated, which oscillate from 0.29 to 5.21. The increase in dipole moment has been explained in terms of the nature of excited state and its resonance structure.     

Quasi‐classical fluctuation–dissipation description of dielectric loss in oxides with implications for quantum information processing

One of the most important problems in developing devices for quantum computation is the coupling and dissipation of states by thermal noise. We present a study of a two‐state electric dipole in a crystal coupling to noise from a reservoir. As a realization of such an energy‐dissipating dipole, we report and analyze dielectric loss measurements in single crystal and polycrystalline Al₂O₃ over the temperature range 70–300 K. We are able to model the dielectric loss in terms of a quasi‐classical model that uses the fluctuation–dissipation theorem. Two key parameters in this model are the crystal oscillator energy and reservoir–lattice coupling constant. In polycrystalline samples, it is assumed that the main effect of structural disorder is a modification of the spectrum of the thermal phonons, so that acoustical vibrations acquire some optical mode character. The temperature dependence of the linewidth of the high dielectric strength infrared (IR) mode at 438 cm^?1 and the quasi‐degenerate Raman mode of the k = 0 (418 cm^?1) transition are also investigated and are shown to be related simply to the dielectric loss. The model reproduces the unusual temperature dependence of the dielectric loss observed experimentally. The implications for the coupling of quantum mechanical objects to noise and quantum information processing are discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Infrared intensities of liquids XXII: Optical and dielectric constants, molar polarizabilities, and integrated intensities of liquid benzene-d6 at 25 °C between 5000 and 450 cm–1

This paper presents accurate infrared absorption intensities of liquid benzene-d₆ at 25?°C, between 5000 and 450 cm^–1. The results are presented as graphs and tables of the real, n, and imaginary, k, refractive index spectra, which are also called the optical constant spectra. The real refractive index is shown between 8000 and 450 cm^–1. The absolute errors in the k values are estimated to be ～3% below, and up to 60%, above, 4700 cm^–1, with those in the n values ～0.25% throughout. The Beer-Lambert molar absorption coefficient spectra, E _m(?ν), and the complex dielectric constant spectra, ?′(?ν) and ?″(?ν), were calculated from the optical constant spectra. To correct for macroscopic dielectric effects, the complex molar polarizability spectra, α′_m(?ν) and α″_m(?ν), were calculated from the dielectric constant spectra under the Lorentz local field. The properties of bands in these different spectra are compared. The imaginary molar polarizability spectra were fitted convincingly to 208 Classical Damped Harmonic Oscillator bands, and the areas under the corresponding ?να″_m bands gave the integrated intensities C _j . These were assigned as far as possible and are tabulated. The transition dipole moments of well assigned transitions, and for the infrared-active fundamentals, under the double harmonic approximation, the dipole moment derivatives with respect to the normal coordinates, were calculated from the values of C _j , and are presented. This appears to be the first extensive measurement of the infrared absorption intensities of liquid benzene-d₆. The results are compared with literature data for liquid and gaseous benzene-d₆.