Vibrational Averaging Effects Research Articles

Hyperfine coupling constants of dimethyl nitroxide in aqueous solution: Car–Parrinello molecular dynamics and discrete-continuum approaches

Vibrational averaging and solvent effects on the isotropic hyperfine coupling constants of dimethyl nitroxide have been investigated by an integrated computational tool including Car–Parrinello molecular dynamics and discrete-continuum solvent models. The results allow an unbiased judgement of the role of different effects in determining the observed EPR parameters.

Insights into the structure of cyclohexane from femtosecond degenerate four-wave mixing spectroscopy and ab initio calculations.

In this paper, we report the use of femtosecond time-resolved degenerate four-wave mixing rotationally resolved spectroscopy to obtain very accurate structural information on the symmetric top cyclohexane. Apart from highlighting the versatility of this method in determining accurate structures of large and complex molecules without dipole moment, the present study also details the comparison of the experimentally determined rotational constant B(0) with that obtained from high-level ab initio calculations. The theoretical calculations, which were carried out at both the second-order Møller-Plesset (MP2) and coupled-cluster with single, double, and perturbative triple substitutions [CCSD(T)] levels of theory, also take into account vibrational averaging effects. A detailed investigation of the vibrational averaging effects reveals that the corrections emerge from only the six highly symmetric A(1g) modes, a justification of which is provided by an analysis of these modes.

Computation of Spectroscopic Parameters in vacuo and in Condensed Phases by Methods based on the Density Functional Theory

The impact of density functional theory in the computation of reliable spectroscopic parameters is reviewed with special reference to IR, Raman, UV, visible, NMR and EPR techniques. In general terms, the results delivered by the most recent density functionals (especially hybrid ones) are remarkably accurate. Proper treatment of solvent effects by continuum models and of vibrational averaging effects by suitable Hamiltonians governing the nuclear motions, significantly increases the reliability of the results and the fields of application of theoretical computations. Some case examples have been reported to better illustrate the potentialities of this approach also for non specialists.

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 ethane

SCF quartic property hypersurfaces have been computed for the energy, quadrupole moment and polarizability tensor of ethane via finite differences of analytical derivatives to obtain zeropoint vibrational corrections to the properties. Coupled with accurate electrical properties computed at a correlated r e geometry, using a range of correlated methods, especially BD and BD(T), excellent estimates of these properties have been obtained that incorporate the effects of vibrational averaging. The effect of deuterium substitution on the properties has been investigated, including the first known theoretical prediction of the dipole moment of CH3CD3, and the frequency dependence of the polarizability tensor and Rayleigh depolarization ratio have been examined. Careful attention has been paid to a critical comparison between these theoretical estimates and experimental measurements. Although the vibrational corrections are limited to SCF theory, and basis sets not as extensive as used in some studies of this kind, nevertheless the results can be compared quantitatively with experiment, and the agreement is found to be excellent. The results underline the necessity to allow for the effects of zero-point vibrational averaging when comparing theory with experiment, and suggest a viable approach for studies on larger molecules.

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 re 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.

Gas-phase molecular structures of third row transition-metal hexafluorides WF6, ReF6, OsF6, IrF6, and PtF6. An electron-diffraction and ab initio study.

The molecular structures of WF6, ReF6, OsF6, IrF6, and PtF6 have been measured by electron diffraction from the gases, the last from both PtF6 itself and from a vapor assumed to consist of a mixture of O2 and PtF6 obtained by heating the salt O2PtF6. For models of Oh symmetry the bond lengths in the first three members of the series are essentially identical, but the Ir-F and Pt-F bonds are respectively about 0.01 and 0.02 A longer. Models of D4h symmetry were also tested for ReF6, OsF6, and IrF6 in which operation of the Jahn-Teller effect is thought possible. For these models the same trend was seen in the average bond-length values. The effect of three-atom multiple scattering was also investigated, and experimental estimates of the effects of vibrational averaging ("shrinkage") on the distances were obtained. Normal-coordinate analyses based on the observed wavenumbers yielded stretching force constants consistent with the usual inverse bond-length/force-constant relationship. Ab initio molecular orbital optimizations of the molecules constrained to Oh symmetry were carried out at several levels of theory and basis-set size. Less extensive optimizations of ReF6, OsF6, and IrF6 with D4h symmetry were also carried out. The best overall agreement with both the experimental values and the distance trend for Oh symmetry was obtained with the Hay-Wadt (n+1)VDZ basis on the metals and the aug-cc-pVTZ on the fluorines at the MP2 level, but these bases with B3P86 and B3PW91 density functional theory were nearly as good and with B3LYP only slightly worse. The D4h structures for ReF6, OsF6, and IrF6 with the cited bases at the B3P86 level were slightly more stable (respectively 0.8, 2.6, and 1.4 kcal/mol) with the axial bonds shorter by about 0.04 A in ReF6 and 0.07 A in OsF6, but about 0.05 A longer in IrF6. The significance of these values is uncertain. The experimental bond lengths (rg/A) with estimated 2sigma uncertainties for the models of Oh symmetry are W-F = 1.829(2), Re-F = 1.829(2), Os-F = 1.828(2), Ir-F = 1.839(2), and Pt-F = 1.852(2); the Pt-F value from the O2PtF6 sample was 1.851(2) A. Although the experimental data neither confirm nor refute the existence of the Jahn-Teller effect in ReF6, OsF6, and IrF6, they ensure that if present the distortion from Oh symmetry must be small.

Structure and magnetic properties of benzyl, anilino, and phenoxyl radicals by density functional computations

A recently developed quantum mechanical approach devoted to the study of structural and magnetic properties of open-shell species was applied to the isoelectronic series formed by benzyl, anilino, and phenoxyl radicals. Hybrid Hartree–Fock/density functional models (here B3LYP) confirm their reliability, whereas, contrary to other cases, vibrational averaging and solvent effects play only a negligible role. The spin dependent properties are interpreted in terms of a new model including first and second order spin polarization effects.

An ab initio study of vibrational corrections to the electrical properties of the second-row hydrides

Accurate ab initio calculations of the dipole and quadrupole moments, polarizabilities and polarizability anisotropies are reported for the second-row hydrides, silane (SiH4), phosphine (PH3), hydrogen sulphide (H2S) and hydrogen chloride (HCl). The Brueckner orbital variant of coupled cluster theory, namely Brueckner doubles (BD) with perturbatively linked triples (BD(T)) has been combined with large augmented triple-zeta basis sets to provide high-quality estimates that include vibrational averaging effects. Fourth-order energy and property derivatives have been calculated via a numerical least-squares procedure and used to calculate property zero-point vibrational corrections and pure vibrational polarizabilities from perturbation theory expressions. The effects of deuterium substitution on the properties is investigated and the frequency dependence of the polarizability and the polarizability anisotropy also studied. For those properties for which experimental data are available, a detailed comparison is made between theory and experiment. Vibrationally averaged BD(T) predictions of the dipole and quadrupole moments underestimate experiment by between 1 and 3% ; however, vibrationally averaged BD(T) mean polarizabilities typically lie within 0·5% of experiment. Calculated polarizability anisotropies are also shown to agree well with available experimental estimates, with the study demonstrating the importance of including vibrational corrections with accurate theoretical predictions of electrical properties.

Electronic, vibrational and environmental effects on the hyperfine coupling constants of nitroside radicals. H2NO as a case study

The effect of polar solvents on the structure and EPR parameters of dihydronitrosyl radical H2NO have been investigated by a hybrid density functional/Hartree-Fock approach coupled to a proper description of vibrational averaging effects from the out of plane vibration and different polarizable continuum models for the description of the solvent. The adequacy of the electronic computations and averaging procedure are confirmed by the reliable results obtained for the isolated molecule. The shift in hyperfine couplings induced by the solvent is quantitatively reproduced, although the standard Onsager model saturates too quickly as a function of the dielectric constant. Introduction of the Block-Walker model rectifies matters and provides satisfactory results for polar solvents without hydrogen bonding capacity.

Structures, hyperfine parameters, and inversion barriers of cyclopropyl and oxiranyl radicals

A comparative post-Hartree–Fock study has been performed on cyclopropyl and oxiranyl radicals in order to ascertain the role of the oxygen atom in modifying the hyperfine structure and height of the barrier governing inversion at the radical center. The structural parameters and harmonic force fields obtained for the parent molecules using second-order many-body perturbation theory with a large basis set are in good agreement with experiment. The same approach points out significant distortions upon breaking of a CH bond and a larger pyramidality for the radical center in oxiranyl with respect to cyclopropyl. Also inversion barriers of both radicals are in remarkable agreement with experimental estimates. Isotropic hyperfine parameters in good agreement with those obtained from electron spin resonance spectra can be computed only when using purposely tailored basis sets in the framework of a coupled cluster approach and taking into account vibrational averaging effects induced by the inversion motion. Interpretation of the results in terms of direct and spin polarization effects points out a number of general trends for germinal and vicinal atoms. Furthermore, it is well evidenced that replacement of a methylenic group by an oxygen atom modifies the hyperfine parameters through geometric rather than direct electronic effects.

Structure and hyperfine parameters of cyclopropyl and bicyclobutyl radicals from post-Hartree–Fock computations

Extensive post-Hartree–Fock calculations are reported for the geometrical structures and hyperfine parameters of cyclopropyl and bicyclobutyl radicals. Computations for the parent molecules, whose structures are experimentally well characterized, show that reliable geometrical parameters are obtained, especially for bicyclobutane, only when using sufficiently flexible basis sets including f functions on carbon. Isotropic hyperfine splittings obtained by purposely tailored basis sets, proper treatment of correlation, and inclusion of vibrational averaging effects are in remarkable agreement with experiment. Our results suggest a revision of the accepted assignment for bicyclobtyl radical and suggest that long-range couplings are not governed by the well-known W rule but rather by a syn rule.

Calculation of nuclear shielding constants and magnetizabilities of the hydrogen fluoride molecule

Nuclear shielding constants and magnetizabilities of the hydrogen fluoride molecule have been calculated adopting the multiconfigurational self-consistent field method. Effects of vibrational averaging are calculated by adopting a Gaussian function with variable width and position to describe the vibrational part of the wave function. The rovibrationally averaged 19F shielding constant is calculated to 407.4 ppm and its anisotropy to 111.2 ppm, both in good agreement with experimental results. Also the isotope effect, 〈σF(DF)〉−〈σF(HF)〉, which is calculated to 3.0 ppm agrees well with the available NMR experiment. The effective geometry, dipole moment, vibrational frequencies, and rotational constants are also calculated and discussed.

ESR features of the bicyclobutyl radical revisited. A counterintuitive ordering of short- and long-range isotropic hyperfine coupling constants

A quantum mechanical protocol for the study of flexible open-shell systems has been applied in a reinvestigation of the isotropic hyperfine coupling constants of the bicyclobutyl radical. Our computations indicate that the most stable structure of the radical corresponds to the exo-form and is characterized by a strongly pyramidal radical center. The hyperfine coupling constants computed for this form are in good agreement with experiment, but indicate that the accepted assignment of H α and H γ endo protons should be reversed. The energy difference between the exo and endo form is sufficiently large to avoid thermal averaging of observables at reasonable temperatures. Vibrational averaging effects in the potential well corresponding to the exo minimum are significant for the C α atom, but do not alter results for H atoms. A striking outcome of this study is the demonstration that stereo-electronic can lead to the counterintuitive results that long range couplings are larger than α ones.

Structure and ESR features of glycine radical in its zwitterionic form

Extensive post Hartree-Fock calculations are reported for the geometrical structure and hyperfine parameters of the carbon-centered glycine radical in its zwitterionic form. Vibrational averaging effects connected to inversion at the radical center are significant for C α and H α atoms. The good agreement between computed and experimental hyperfine splittings confirms the nature of one of the radicals obtained from irradiation of glycine crystals. On the other hand, the ESR spectrum obtained in aqueous solution cannot be due to the zwitterionic form.

Potential functions for carbon dioxide–hydrogen halide and hydrogen halide dimer van der Waals complexes

A potential function model containing distributed repulsion, dispersion, and electrostatic interactions is applied to hydrogen halide dimers and carbon dioxide–hydrogen halide complexes. The (HX)2 functions are compatible with all experimental data and are compared with both empirical and large scale ab initio potential surfaces. The main focus of this paper is the CO2–HX group. We obtain excellent results for CO2–HF and CO2–HCl, describing essentially linear molecules undergoing large amplitude vibrations that closely resemble rigid bender behavior. The calculated CO2–HBr equilibrium structure is not in agreement with vibrationally averaged experimental results. This may arise from vibrational averaging effects. It is shown that different views of the same potential function can give very different impressions of structure and internal motions.

Valence electron momentum distributions of ethylene; comparison of EMS measurements with near Hartree-Fock limit, configuration interaction and density functional theory calculations

Abstract The valence binding energy spectra and orbital electron momentum profiles of C 2 H 4 have been measured by energy dispersive, multichannel, symmetric non-coplanar electron momentum spectroscopy at an impact energy of 1200 eV + binding energy. The effects of final state correlation on the valence binding energy spectrum are investigated using multi-reference singles and doubles configuration interaction calculations and the results are compared with calculations from the literature and with experiment. The measured momentum profiles are compared with cross sections calculated using a range of wavefunctions from minimal basis to essentially Hartree-Fock limit in quality. In addition, the effects of correlation and relaxation on the calculated momentum profiles are investigated using multi-reference singles and doubles configuration interaction calculations of the full ion-neutral overlap distributions. Several different configuration interaction results are investigated in the case of the 1b 3u HOMO momentum profile. Electron correlation effects in the ground state are also examined using several density functional approaches for all the momentum profiles. The experimental momentum resolution is accounted for in all of the calculated momentum profiles by using the Gaussian-weighted planar grid procedure. The effects of vibrational averaging are investigated in the case of the 1b 3u orbital of ethylene.

Structure, internal mobility, and spectrum of the ammonia dimer: Calculation of the vibration–rotation-tunneling states

We have obtained a potential for (NH3)2 by calculating the six-dimensional vibra- tion–rotation-tunneling (VRT) states from a model potential with some variable parameters, and adjusting some calculated transition frequencies to the observed far-infrared spectrum. The equilibrium geometry is strongly bent away from a linear hydrogen bonded structure. Equivalent minima with the proton donor and acceptor interchanged are separated by a barrier of only 7 cm−1. The barriers to rotation of the monomers about their C3 axes are much higher. The VRT levels from this potential agree to about 0.25 cm−1 with all far-infrared frequencies of (NH3)2 observed for K=0, ‖K‖=1, and ‖K‖=2 and for all the symmetry species: Ai=ortho–ortho, Ei=para–para, and G=ortho–para. Moreover, the dipole moments and the nuclear quadrupole splittings agree well with the values that are observed for the G states. The potential has been explicitly transformed to the center-of-mass coordinates of (ND3)2 and used to study the effects of the deuteration on the VRT states. The observed decrease of the dipole moment and the (small) changes in the nuclear quadrupole splittings are well reproduced. It follows from our calculations that the ammonia dimer is highly nonrigid and that vibrational averaging effects are essential. Seemingly contradictory effects of this averaging on its properties are the consequence of the different hindered rotor behavior of ortho and para monomers.

Computational exploration of the six-dimensional vibration–rotation–tunneling dynamics of (NH3)2

In order to address the well-known problem that the nearly cyclic structure of (NH3)2 deduced from microwave spectra differs greatly from the hydrogen-bonded equilibrium structure obtained from ab initio calculations, we have calculated the vibration–rotation–tunneling (VRT) states of this complex, and explicitly studied the effects of vibrational averaging. The potential used is a spherical expansion of a site–site potential which was extracted from ab initio data. The six-dimensional VRT wave functions for all the lowest states with J=0 and J=1 were expanded in products of radial (van der Waals stretch) functions and free-rotor states for the internal and overall rotations, which were first adapted to the complete nuclear permutation inversion group G36. Although the (expanded) potential is too approximate to expect quantitative agreement with the observed microwave and far-infrared spectra, we do find several interesting features: The 14N quadrupole splittings and the dipole moment of the complex, which are indicative of the orientational distributions of the NH3 monomers, are substantially affected by vibrational averaging. The interchange tunneling of the two monomers is not quenched. In the ortho–ortho and para–para states, of A and E symmetry, this tunneling manifests itself in a very different manner than in the ortho–para states of G symmetry. In contrast with the interpretation of Nelson et al. [J. Chem. Phys. 87, 6364 (1987)], we believe that the Gα and Gβ states observed by these authors correspond to a single VRT state which is split by (hindered) NH3 monomer inversion.

Correlated calculations of the rotationalg-tensor and origin independent magnetizability surface of BH

Polarization propagator calculations of the magnetizability and the rotational g-tensor surface of BH are presented and we show that it is essential to include correlation through the level of the coupled cluster polarization propagator (CCPPA) theory. The effects of basis set choice and of vibrational averaging on the properties are studied. The results show that it is necessary to use rather large basis sets, especially at the correlated level, but that the effect of vibrational averaging is relatively small. We have analysed the gauge origin dependence of previous calculations of magnetizabilities of BH.