An ab initio study of vibrational corrections to the electrical properties of ethylene

Accurate SCF and MP2 quartic property hypersurfaces have been computed for the energy, quadrupole moment and polarizability tensor of ethylene to obtain zero-point vibrational corrections to the properties. Coupled with accurate electrical properties computed at a high level correlated r _e geometry, using a range of correlated methods, especially BD and BD(T), along with a number of purpose-built polarized basis sets, definitive estimates have been made of these properties that incorporate the effects of vibrational averaging. The effect of deuterium substitution on the properties was investigated, and the frequency dependence of the polarizability tensor was studied also. Careful attention has been paid to a critical comparison between these theoretical estimates and experimental measurements, and agreement between the two is shown to be exceptionally good. In particular, it is possible to resolve the disagreement between recent theoretical calculations and experimental measurements of the Cotton–Mouton constant. The results focus attention on both the general utility of the present method, and the necessity to allow for the effects of zero-point vibrational averaging when comparing theory with experiment, or even when comparing different theoretical results with one another using experiment as a benchmark.     

An ab initio study of vibrational corrections to the electrical properties of the fluoromethanes: CH3F,CH2F2, CHF3 and CF4

Accurate SCF and MP2 quartic property hypersurfaces have been computed for the energy, dipole moments, quadrupole moments and polarizability tensors of the fluorinated methanes CF₄, CHF₃, CH₂F₂ and CH₃F, to establish accurate values of zero-point vibrational corrections to the properties. Using a consistent set of r_e geometries from density functional theory, these ZPVCs are coupled with accurate electrical properties computed using a range of correlated methods, especially BD and BD(T), and a number of purpose-built polarized basis sets, to obtain near definitive estimates of these properties that incorporate the effects of vibrational averaging. Careful attention has been paid to a critical comparison between these theoretical estimates and experimental measurements, and agreement between the two is shown to be exceptionally good. In particular, it is clear that in many instances more precise experimental results would be required in order to discriminate between different correlated results, or between the present results and those which may be obtained with larger basis sets. The work highlights the necessity to allow for the effects of zero-point vibrational averaging when comparing theory with experiment, or even when comparing different theoretical results with one another using experiment as a benchmark. It also points to the need for further precise experimental measurements of some of these properties.     

PNO-CI and PNO-CEPA studies of electron correlation effects

Dipole moments and static dipole polarizabilities are calculated for neon and the molecules HF, H₂O, NH₃, CH₄ and CO from SCF and correlated wavefunctions.

The construction of appropriate gaussian-type basis sets is discussed and the convergence of the correlation contributions to the polarizability is analysed. The effect of vibrational averaging is also investigated. The polarizabilities as obtained from the coupled electron pair approximation (CEPA) with the most extended basis sets differ from experimental values by less than 1·5 per cent in all cases. The calculated polarizability anisotropies appear to be correct to about 5–15 per cent. The correlation contributions to the polarizabilities are found to vary from 3 to 12 per cent.     

Calculations of the static polarizability and hyperpolarizability of the LiF molecule including vibrational contributions

The static dipole moment, polarizability and first hyperpolarizability of the LiF molecule have been calculated, including vibrational corrections, using Möller—Plesset perturbation theory and coupled cluster methods. The results show that the vibrational corrections, dominated by the nuclear relaxation term, are as important for the calculations of the polarizability and hyperpolarizability as the electronic contribution, and that the electron correlation effects play an important role in the calculations of both electronic and vibrational contributions for these static properties.     

On the application of the theory of the brownian movement in a periodic potential to the study of inertial effects and dipole coupling

For a series of ten electron molecules (HF, H₂O, NH₃, CH₄) the molecular polarizability tensor and the derivatives with respect to the symmetry coordinates have been calculated from ab initio SCF wavefunctions using the finite field method as well as perturbation theory approaches. Raman intensities and degrees of depolarization derived from the finite field results agree well with the available experimental data.

The zeroth order bond polarizability model and the atom dipole interaction model have been analysed. Both models can be used to describe the computed static polarizabilities and the derivatives with respect to bond stretching, but fail for the derivatives with respect to the bending coordinates.     

The effects of vibration-rotation on the quadrupole moment,rotational g-factor and spin-rotation parameters of the water molecule

Ab initio SCF surfaces for the quadrupole moment, rotational g-factor and spin-rotation parameters of the water molecule have been obtained from the magnetizability and nuclear shielding surfaces. Values of these properties in low vibration-rotation states of the more important isotopomers are presented.

Vibrational averaging (with an accurate empirical force field) brings calculated values to within 1 per cent of experimental values for the quadrupole moment components and 3 per cent for the g-tensor components. Substantial vibrational effects on the proton, deuteron and ¹⁷O spin-rotation parameters are predicted but the calculated values differ significantly from experiment. This is attributed to inadequacy of the SCF calculation of paramagnetic shielding.     

Trends in the electronic and vibrational contributions to the dipole moment,polarizabilities, and first and second hyperpolarizabilities of the hydrides of Li,Na and K

The dipole moments μ, polarizabilities α, and first and second hyperpolarizabilities, β and γ of LiH, NaH and KH (MeH) have been computed using Hartree-Fock, MP2 and CCSD(T) theories. The static electronic and vibrational contributions to these properties are presented. The vibrational properties have been analysed into contributions due to zero-point vibrational averaging and pure vibrational terms. An alternative dissection of the vibrational properties into nuclear relaxation and curvature terms has also been considered. KH has been selected as a model system to study how the number of electrons, which are correlated (2, 10 and 20) affect both electronic and vibrational properties. The 10 electron approximation gives results that are practically the same as those computed by taking into account all 20 electrons of KH. The double-harmonic approximation has been shown to give satisfactory results for the pure vibrational contributions to the polarizability and the first hyperpolarizability, while this approximation is useful for demonstrating, qualitatively, the significance of the pure vibrational contributions to the second hyperpolarizability. In many cases the vibrational contributions are rather small percentages of the corresponding electronic contribution. However, several exceptions to the above observation have been noted. In all the cases considered the vibrational properties should be computed if reasonably accurate property values are sought. Electron correlation is important for both electronic and vibrational contributions to the electrical properties of the hydrides considered. The results are in satisfactory agreement with most of the best theoretical and experimental data concerning bond lengths, vibrational frequencies and electrical properties.     

Calculation of molecular one-electron properties using coupled Hartree-Fock methods

Various second-order properties for H₂O have been computed using a near Hartree-Fock gaussian wave function and a coupled Hartree-Fock scheme. Satisfactory agreement with experimental data is obtained for vibrational frequencies and for magnetic properties. The calculated electric polarizability only accounts for 64 per cent of the experimental value.     

Calculations of ozone line shifting induced by N2 and O2 pressure

Ozone line shifts by nitrogen and oxygen pressure are computed for the ν₁ + ν₃, 2ν₁ and 2ν₃ bands of the 5 μm spectral region by a semiempirical approach. The calculated values agree with measurements better than 0.001 cm^?1 atm^?1 for 98% of O₃–N₂ lines and 87% of O₃–O₂ lines. In contrast with the water molecule case, the polarization components of the interaction potential are shown to contribute to the line shift more efficiently than the electrostatic interactions. As intermediate results, the mean dipole polarizability and the components of the polarizability tensor for the vibrational states (101), (200), and (002) of ozone molecule are determined by least-squares fitting of theoretical shifts to some experimental values. The temperature exponents for the ν₁ + ν₃ band lines are also estimated.     

Ab initio nonadiabatic vibrational energies of the hydrogen molecule ion

Nonadiabatic corrections to the four lowest vibrational energy levels of H₂⁺ and HD⁺ are computed by a variational-perturbational method. The results increase the disagreement with experiment of the theoretical 2-1 and 3-2 vibrational transitions and improve the theoretical energy of the 1-0 transition.     

Nonadiabatic corrections to the rotational energies of the hydrogen molecule

Nonadiabatic corrections to the rotational energies and rotational constants B_ν have been computed by a variational perturbation method for several vibrational levels of the H₂, HD, and D₂ molecules. It is believed that the convergence error in the computed corrections to the energy is less than 10^?3 cm^?1. The corrections improve the agreement of theoretical and experimental rotational quanta, but there are still discrepancies that amount in some cases to a few hundredths of a cm^?1. These discrepancies are irregular and it is argued that they are at least partly due to experimental inaccuracies.     

Equilibrium structure of protonated cyanogen, HNCCN

The cubic force field of protonated cyanogen, HNCCN⁺, has been calculated at the CCSD(T) level of theory employing correlation consistent bases of quadruple-zeta quality. Semi-experimental equilibrium structures have then been derived from the experimental ground-state rotational constants available for various isotopologues and the corresponding vibrational corrections calculated from the theoretical force fields. While a good agreement has been found with the pure theoretical best estimate of equilibrium geometry, computed at the CCSD(T) level of theory accounting for basis set truncation as well as including core correlation corrections, large discrepancies have been noted with the experimental substitution, r_s, as well as effective, r₀, structures.     

Finite-field calculations of molecular polarizabilities using field-induced polarization functions: second- and third-order perturbation correlation corrections to the coupled Hartree-Fock polarizability of H2O

Ordinary Rayleigh-Schrödinger perturbation theory with Møller-Plesset (RSMP) partitioning is used to calculate second- and third-order correlation corrections to the CHF polarizability and dipole moment of the water molecule by a finite-field procedure. [2/1] Padé approximants are found to be useful in accelerating the convergence of the property perturbation expansions. Field-induced polarization functions suitable for polarizability calculations are determined. The average polarizability calculated, neglecting vibrational averaging, with Dunning's (9s5p/4s-4s2p/2s) contracted GTO basis set augmented by field-induced 1s1p2d/1p polarization functions is within 3 per cent of the experimental result. Correlation corrections to the dipole moment and polarizability of the water molecule calculated by the finite-field RSMP and single + double excitation CI(SDCI) methods for the same basis set are found to be in close agreement. The RSMP approach has the advantages of being size-consistent and of being capable of greater efficiency than the SCDI method. Comparative calculations carried out using Epstein-Nesbet partitioning show that through third order RSEN correlation perturbation expansions for the dipole moment and polarizability are less rapidly convergent than RSMP expansions. However, reasonable accord with RSMP results can be achieved by using [2/1] Padé approximants to accelerate the convergence of RSEN energy perturbation expansions. The convergence of RSMP property correlation expansions based on the zeroth-order uncoupled-Hartree-Fock (UCHF) and coupled-Hartree-Fock (CHF) approximations are compared through third order. Whereas the CHF + RSMP expansions are for practical purposes fully converged, the UCHF + RSMP expansions are not adequately converged.     

Rotational-vibrational polarizability operator for nonlinear X<Subscript>2</Subscript>Y molecules: Application to the calculation of the Raman spectrum of the H<Subscript>2</Subscript>O molecule

For nonlinear X₂Y molecules, an expression for the transformed polarizability operator is obtained with an accuracy of up to the second order of the theory of perturbation. This operator is applied to the calculation of the intensities of Raman lines of the H₂O molecule. The corrections to the polarizability of the molecule associated with the vibrational-rotational interaction are shown to considerably change the integral intensity of a pure rotational band. The dependence of the average polarizability of the molecule on the vibrational quantum number V ₂, describing deformation vibrations, is estimated.     

Vibrational corrections to electric properties of weakly bound systems

The pure electronic and vibrational contributions to electric dipole moments, dipole polarizabilities, and first hyperpolarizabilities have been evaluated for the HF and H₂O dimers. The zero-point vibrational average corrections to dipole moments and dipole polarizabilities turn out to be relatively small. However, the corresponding contributions to the first hyperpolarizability are found to be of the same magnitude as the pure electronic values. The so-called pure vibrational corrections to the dipole polarizability and first hyperpolarizability of hydrogen bonded dimers are exceptionally large and indicate that the perturbation theory method used for their evaluation fails to account properly for the high mechanical and electric anharmonicities present in these systems. The analysis of different harmonic and anharmonic contributions to the pure vibrational correction to the first hyperpolarizability shows explicitly the importance of the low frequency intermolecular modes.     

Electron spin resonance detection of acrylic acid radical anions and related species in low temperature glasses

A contracted gaussian basis set in double-zeta form (plus polarization functions) has been used to calculate the vibrational characteristics of CH₃F by means of an ab-initio SCF finite-difference method. The diagonal force constants, with an error of about 10 per cent, are an upper limit to experiment. The off-diagonal interaction constants give a correct picture of the molecular force field, unlike the Hybrid Orbital Force Field model. With the derivatives of a dipole moment corresponding to a good theoretical evaluation (about 2D), it is possible to discuss the problem of signs in infra-red intensity analysis.     

An ab initio calculation of the vibrational energies and transition moments of HSOH

We report new ab initio potential energy and dipole moment surfaces for the electronic ground state of HSOH, calculated by the CCSD(T) method (coupled cluster theory with single and double substitutions and a perturbative treatment of connected triple excitations) with augmented correlation-consistent basis sets up to quadruple-zeta quality, aug-cc-pV(Q+d)Z. The energy range covered extends up to 20 000 cm⁻¹ above equilibrium. Parameterized analytical functions have been fitted through the ab initio points. Based on the analytical potential energy and dipole moment surfaces obtained, vibrational term values and transition moments have been calculated by means of the variational program TROVE. The theoretical term values for the fundamental levels ν_SH (SH-stretch) and ν_OH (OH-stretch), the intensity ratio of the corresponding fundamental bands, and the torsional splitting in the vibrational ground state are in good agreement with experiment. This is evidence for the high quality of the potential energy surface. The theoretical results underline the importance of vibrational averaging, and they allow us to explain extensive perturbations recently found experimentally in the SH-stretch fundamental band of HSOH.     

Electro-optical parameters and Raman intensities of CH4, CH3D,CH2D2, CHD3 and CD4

The absolute Raman intensities and the depolarization ratios of the vibrational bands of gaseous CH₄, CH₃D, CH₂D₂, CHD₃ and CD₄ have been computed here using a compact formulation of the bond polarizability theory, in its zero and first-order approximations. The agreement with experimental values taken from the literature is very good for the first-order approximation, although the difference between both approximations is not very large for these molecules. The derivatives of the polarizability with respect to the symmetry coordinates of methane are given with signs that are physically meaningful.     

The puzzling infrared spectra of the nitric oxide dimer radical cation: a systematic application of Brueckner methods

Since symmetry breaking occurs in the ONNO⁺ cation with the self-consistent field (SCF) method and inverse symmetry breaking occurs when density functional theory (DFT) methods are used, Brueckner double excitation coupled cluster methods (BD) and BD plus perturbative triple-excitation contributions [BD(T)]have been used to study the geometries and vibrational frequencies for the trans and cis structures of the ONNO⁺ cation. Double-ζ plus polarization (DZP) basis sets and triple-ζ plus double polarization with f functions (TZ2Pf) basis sets were utilized. The ground state of the trans-ONNO cation is of ²A_g symmetry, which has a slightly (0.36 kcalmol^-1) lower energy than the cis conformer (²A₁). The controversial vibrational frequency corresponding to the asymmetric N–O stretching mode for both trans and cis structures is predicted as about 1600cm^-1. This value is discussed in the context of the many (sometimes variant) experimental assignments.