Nuclear Motion Corrections Research Articles

Three-body potential and third virial coefficients for helium including relativistic and nuclear-motion effects.

The non-additive three-body interaction potential for helium was computed using the coupled-cluster theory and the full configuration interaction method. The obtained potential comprises an improved nonrelativistic Born-Oppenheimer energy and the leading relativistic and nuclear-motion corrections. The mean absolute uncertainty of our calculations due to the incompleteness of the orbital basis set was determined employing complete-basis-set extrapolation techniques and was found to be 1.2%. For three helium atoms forming an equilateral triangle with the side length of 5.6 bohr - a geometry close to the minimum of the total potential energy surface - our three-body potential amounts to -90.6 mK, with an estimated uncertainty of 0.5 mK. An analytic function, developed to accurately fit the computed three-body interaction energies, was chosen to correctly describe the asymptotic behavior of the three-body potential for trimer configurations corresponding to both the three-atomic and the atom-diatom fragmentation channels. For large triangles with sides r12, r23, and r31, the potential takes correctly into account all angular terms decaying as r-l12 r-m23 r-n21 with l + m + n ≤ 14 for the nonrelativistic Born-Oppenheimer energy and l + m + n ≤ 9 for the post-Born-Oppenheimer corrections. We also developed a short-range analytic function describing the local behavior of the total uncertainty of the computed three-body interaction energies. Using both fits we calculated the third pressure and acoustic virial coefficients for helium and their uncertainties for a wide range of temperatures. The results of these calculations were compared with available experimental data and with previous theoretical determinations. The estimated uncertainties of present calculations are 3-5 times smaller than those reported in the best previous works.

Three-dimensional docking of alcohols to ketones: an experimental benchmark based on acetophenone solvation energy balances.

The two hydrogen bond solvation sites exhibited by the carbonyl group in acetophenone are influenced by alkylation of the methyl group in both the acetophenone and in the prototype solvent methanol, largely due to London dispersion forces. Phenyl docking and alkyl docking preferences can be realized at will by appropriate substitution. In particular, cyclopropylation helps to stabilize the opposite phenyl docking site. In all cases, the energy gap is small enough to allow for a simultaneous detection even under low temperature conditions. This density functional prediction is checked experimentally by jet FTIR spectroscopy and largely confirmed. A spurious out-of-plane solvation preference predicted for cyclopropylphenylketone with tert-butyl alcohol by B3LYP-D3 calculations is not confirmed experimentally. It is unlikely that this discrepancy is due to zero-point energy effects. Instead, the second most stable alkyl-side solvation motif predicted with a more in-plane coordination is found in the jet expansion. Overall, the ability of carbonyl solvation balances to benchmark subtle electronic structure effects for non-covalent interactions without major nuclear motion corrections is supported.

Structure functions for light nuclei

We discuss the nuclear EMC effect with particular emphasis on recent data for light nuclei including $^{2}\mathrm{H}$, $^{3}\mathrm{He}$, $^{4}\mathrm{He}$, $^{9}\mathrm{Be}$, $^{12}\mathrm{C}$, and $^{14}\mathrm{N}$. In order to verify the consistency of available data, we calculate the ${\ensuremath{\chi}}^{2}$ deviation between different data sets. We find a good agreement between the results from the NMC, SLAC E139, and HERMES experiments. However, our analysis indicates an overall normalization offset of about $2%$ in the data from the recent JLab E03-103 experiment with respect to previous data for nuclei heavier than $^{3}\mathrm{He}$. We also discuss the extraction of the neutron/proton structure function ratio ${F}_{2}^{n}/{F}_{2}^{p}$ from the nuclear ratios $^{3}\mathrm{He}$/$^{2}\mathrm{H}$ and $^{2}\mathrm{H}$/$^{1}\mathrm{H}$. Our analysis shows that the E03-103 data on $^{3}\mathrm{He}$/$^{2}\mathrm{H}$ require a renormalization of about $3%$ in order to be consistent with the ${F}_{2}^{n}/{F}_{2}^{p}$ ratio obtained from the NMC experiment. After such a renormalization, the $^{3}\mathrm{He}$ data from the E03-103 and HERMES experiments are in a good agreement. Finally, we present a detailed comparison between data and model calculations, which include a description of the nuclear binding, Fermi motion, and off-shell corrections to the structure functions of bound proton and neutron, as well as the nuclear pion and shadowing corrections. Overall, a good agreement with the available data for all nuclei is obtained.

Thermal averaging of the indirect nuclear spin-spin coupling constants of ammonia: The importance of the large amplitude inversion mode

Analytic internal-coordinate representations are reported for two accurate ab initio spin-spin coupling surfaces of the ammonia molecule, (1)J ((15)N,H) and (2)J(H,H). Calculations were carried out at the level of the second-order polarization propagator approximation involving coupled-cluster singles and doubles amplitudes (CCSD) and using a large specialized basis set, for a total of 841 different geometries corresponding to 2523 distinct points on the (1)J ((15)N,H) and (2)J(H,H) surfaces. The results were fitted to power series expansions truncated after the fourth-order terms. While the one-bond nitrogen-hydrogen coupling depends more on the internuclear distance, the geminal hydrogen-hydrogen coupling exhibits a pronounced dependence on the bond angle. The spin-spin parameters are first vibrationally averaged, using vibrational wave functions obtained variationally from the TROVE computer program with a CCSD(T) based potential energy surface, for ammonia and its various deuterated isotopologues. The vibrationally averaged quantities are then thermally averaged to give values of the couplings at absolute temperatures of 300 and 600 K. We find that the nuclear-motion corrections are rather small. The computed one-bond couplings and their minute isotope effects are in excellent agreement with the experimental values.

Electron affinity of Li7 calculated with the inclusion of nuclear motion and relativistic corrections

Explicitly correlated Gaussian functions have been used to perform very accurate variational calculations for the ground states of (7)Li and (7)Li(-). The nuclear motion has been explicitly included in the calculations (i.e., they have been done without assuming the Born-Oppenheimer (BO) approximation). An approach based on the analytical energy gradient calculated with respect to the Gaussian exponential parameters was employed. This led to a noticeable improvement of the previously determined variational upper bound to the nonrelativistic energy of Li(-). The Li energy obtained in the calculations matches those of the most accurate results obtained with Hylleraas functions. The finite-mass (non-BO) wave functions were used to calculate the alpha(2) relativistic corrections (alpha=1c). With those corrections and the alpha(3) and alpha(4) corrections taken from Pachucki and Komasa [J. Chem. Phys. 125, 204304 (2006)], the electron affinity (EA) of (7)Li was determined. It agrees very well with the most recent experimental EA.

Theoretical studies of high-harmonic generation based on the Keldysh–Faisal–Reiss theory

We use the Keldysh–Faisal–Reiss (KFR) approach to study the process of high-harmonic generation (HHG) for hydrogen and helium atoms and a hydrogen molecule where the helium atom and hydrogen molecule wavefunctions are described by a 1s single Slater determinant. In this model we directly use the photoionization amplitude calculated by the KFR approach and relate it to the HHG spectra. We plot HHG from hydrogen and helium atoms, and a hydrogen molecule in the presence of a linearly and circularly polarized laser field, and also discuss the nuclear motion corrections for the hydrogen molecule, which are calculated under the Frank–Condon (FC) approximation by using both displaced-distorted harmonic oscillators and Morse wavefunctions. Contributions from each vibrational state are also discussed.

Nuclear motion effects on the [formula omitted], [formula omitted] and [formula omitted] shielding in methyl fluoride

The 19 F , 13 C and 1 H shielding in methyl fluoride and its deuterated isotopomers has been calculated from ab initio shielding surfaces for selected temperatures. In each case it is the stretching which contributes most to the nuclear motion corrections which total −9.425 ppm for the 19 F shielding, −4.558 ppm for the 13 C shielding and −0.601 ppm for the proton shielding. However, some second-order stretching and bending contributions are significant. The deuterium induced isotope shifts are substantial and should be easily measurable. There is a predicted nonadditivity in the 19 F and 13 C isotope shifts which can be traced to two of the bending contributions.

Calculated nuclear shielding surfaces in the water molecule; prediction and analysis of sigma(O), sigma(H) and sigma(D) in water isotopomers

Ab initio, internal valence coordinate oxygen and hydrogen nuclear shielding surfaces for the water molecule are presented. Calculations have been performed at theMCSCF level of theory using gauge-including atomic orbitals and a large basis set. The shielding at each of 37 points on the oxygen surface and 49 points on the hydrogen surface was calculated. The results were ® tted to Taylor series expansions and are reported to second order in the coordinates. The correlated proton surface is little di€ erent from a coupled Hartree± Fock surface calculated some time ago but the oxygen surface is changed considerably by the inclusion of electron correlation. The surfaces have been averaged over the nuclear motion using a very recent, highly accurate force ® eld to give values of s (O), s (H) and s (D) for selected isotopomers over a range of temperature. For the oxygen shielding the dominant nuclear motion contribution comes from the ® rst order stretching term which is deshielding as is normally the case. Important contributions are also made by the second order stretching term (also deshielding) and the second order bending term (which gives greater shielding). For low density H2 O vapour at 300K the calculated oxygen shielding of 333.723ppm is in good agreement with an experimental value of 344 ( 17) ppm. The O-isotope shifts of HDOand D2 Orelative to H2 O are calculated to be 1.356ppm and 2.697ppm which are in excellent agreement with recently observed liquid-phase values of 1.4203(1) ppm and 2.8324(1) ppm. The very slight non-additivity in these ® gures comes predominantly from the second order bending contribution. Expressions for the temperature dependence of the absolute oxygen and proton shielding in low density water vapour are proposed in the absence of experimentally determined ones. The calculated proton shielding at 300K is 30.232ppm which is in very good agreement with the experimental value of 30.052(15) ppm. The negative nuclear motion corrections to the proton shielding are almost entirely governed by the stretching of the OH bond containing the proton with the second order term partially cancelling the ® rst order term. The proton isotope shift of HDOwith respect to H2 O is calculated to be 0.039ppm at 300K; this is close to the value of 0.0304(1) ppm observed in solution. A recent experimental value for the temperature dependence of the H2 O/H2 O proton isotope shift occurring in the sixth signi® cant ® gure of shielding is too small to be calculated with the present level of accuracy.

Calculated nuclear shielding surfaces in the water molecule; prediction and analysis of σ(O), σ(H) and σ(D) in water isotopomers

Ab initio, internal valence coordinate oxygen and hydrogen nuclear shielding surfaces for the water molecule are presented. Calculations have been performed at the MCSCF level of theory using gauge-including atomic orbitals and a large basis set. The shielding at each of 37 points on the oxygen surface and 49 points on the hydrogen surface was calculated. The results were fitted to Taylor series expansions and are reported to second order in the coordinates. The correlated proton surface is little different from a coupled Hartree-Fock surface calculated some time ago but the oxygen surface is changed considerably by the inclusion of electron correlation. The surfaces have been averaged over the nuclear motion using a very recent, highly accurate force field to give values of σ(O), σ(H) and σ(D) for selected isotopomers over a range of temperature. For the oxygen shielding the dominant nuclear motion contribution comes from the first order stretching term which is deshielding as is normally the case. Important contributions are also made by the second order stretching term (also deshielding) and the second order bending term (which gives greater shielding). For low density H2 17O vapour at 300 K the calculated oxygen shielding of 333.723 ppm is in good agreement with an experimental value of 344 (±17) ppm. The 17O-isotope shifts of HD17O and D2 17O relative to H2 17O are calculated to be 1.356 ppm and 2.697 ppm which are in excellent agreement with recently observed liquid-phase values of 1.4203(1) ppm and 2.8324(1) ppm. The very slight non-additivity in these figures comes predominantly from the second order bending contribution. Expressions for the temperature dependence of the absolute oxygen and proton shielding in low density water vapour are proposed in the absence of experimentally determined ones. The calculated proton shielding at 300 K is 30.232 ppm which is in very good agreement with the experimental value of 30.052(15) ppm. The negative nuclear motion corrections to the proton shielding are almost entirely governed by the stretching of the OH bond containing the proton with the second order term partially cancelling the first order term. The proton isotope shift of HD16O with respect to H2 16O is calculated to be 0.039 ppm at 300 K; this is close to the value of 0.0304(1) ppm observed in solution. A recent experimental value for the temperature dependence of the H2 16O/H2 18O proton isotope shift occurring in the sixth significant figure of shielding is too small to be calculated with the present level of accuracy.

Spin dependent parton distributions in a bound nucleon

The determination of the spin distribution functions for the neutron requires an understanding of the changes induced by a nuclear medium. We present the first estimates of the changes induced in the spin-dependent, valence parton distributions of the proton and neutron bound in 3 He and 6 Li. For 3 He the result is quite reassuring, in that the off-shell correction to g 1 n is very small. On the other hand, in 6 Li the corrections to the spin distributions in the bound proton are sufficiently large that they should be taken into account if one aims for a precision of better than 10%. We provide a simple parametrization of the off-shell changes in the valence spin distributions of 3 He and 6 Li, which can be used with any conventional estimate of nuclear binding and Fermi motion corrections.

Calculated spin-spin coupling surfaces in the water molecule; prediction and analysis of J (O,H), J (O,D) and J (H,D) in water isotopomers

Ab initio symmetry and internal valence coordinate oxygen–proton and proton–proton spin–spin coupling surfaces for the water molecule have been computed for the first time. Calculations have been performed at the SOPPA (CCSD) level using a large basis set and a grid of forty-nine geometries on the two surfaces. Equilibrium values differ significantly from some other calculated values especially for the Fermi contact terms. The bond length dependence of J(O, H) is ‘normal’ i.e. J(O, H1) is much more sensitive to stretching the O–H1 bond than the O–H2 bond. This contrasts greatly with the corresponding situation in methane. The surfaces have been averaged over the nuclear motion using a recent highly accurate force field to give values of J (O, H) and J (O, D) for H2 17O, HD17O and D2 17O and J(H, D) for HD16O, HD17O and HD18O over a range of temperatures. For J (O, H) and J (O, D) bond stretching at first order is the dominant part of the nuclear motion correction with second order bending making an important contribution. For J (H, D) the second order bending is by far the largest contribution to the nuclear motion corrections although the other terms partially cancel this contribution. Non-additivity can be largely attributed to the bending term for J (O, H). As expected, the bending terms also contribute relatively more to the temperature dependence of the couplings for J (O, H), J (O, D) and J (H, D). Our calculated J (O, H) in H2 17O of -77.22Hz at 293K is in very good agreement with Wasylishen and Friedrich's observed value of -78.70 (±0.02) Hz in cyclohexane at this temperature. Our calculated J(H, D) in HD 16O at 323K of -1.233Hz is close to a recent experimental value of -1.114 (±0.003) Hz in nitromethane-d 3 observed by Sergeyev et al. at that temperature.

Calculation of13C shielding of the isotopomers CH3Cl, CH2DCl, CHD2Cl, and CD3Cl

The {sup 13}C shielding of the isotopomers CH{sub 3}Cl, CH{sub 2}DCl, CHD{sub 2}Cl, and CD{sub 3}Cl has been calculated for a range of temperatures from an self-consistent field (SCF) shielding surface computed by Buckingham and Olegario. It is found that each successive deuterium substitution increases the shielding by about 0.19 ppm and that a very slight nonadditivity occurs. The principal factor which governs the nuclear motion correction for each isotopomer is the stretching of the bonds with both first- and second-order terms being significant. Angle bending contributions are very small at first order but quite substantial at second order. Not only should the {sup 13}C-isotope shifts in this experimentally uninvestigated series be easily measured but the temperature dependence of the shielding in any one isotopomer should be observable provided that careful measurements are made. The {sup 13}C-shielding difference between CH{sub 3} {sup 35}Cl and CH{sub 3} {sup 37}Cl has also been calculated and is found to agree well with experiments. 28 refs., 4 tabs.

Ab initiocalculation of nuclear motion corrections to the geometries of water, methanol and silanol

Complete sets of harmonic and cubic force constants of water, methanol and silanol are calculated by the ab initio SCF method using double zeta plus polarization type basis sets. Nuclear motion corrections to equilibrium geometries are derived. The OH bonds become longer by about 1·7 pm and the XOH angles wider by about 0·15°. Vibrationally averaged r α and r g structures are calculated which agree with observed data within experimental limits of uncertainty.

Gas phase acidities and molecular geometries of H3SiOH, H3COH, and H2O

Theoretical predictions are made by the coupled pair functional method employing large basis sets, [6s,5p,2d,1f/5s,3p,2d,1f/3s,2p] for geometries and [6s,5p,2d,1f/8s,5p,3d,1f/4s,2p] for deprotonation energies. The geometries obtained for H2O and CH3OH agree with the observed ones within the experimental uncertainty limits. The predicted equilibrium geometry (picometers, degrees) for silanol is r(SiO)=165.0, r(OH)=95.76, r(SiH)=146.8 (in plane), r(SiH)=147.6 (out of plane), angle (SiOH)=117.7. Nuclear motion corrections to geometries and vibrational contributions to deprotonation energies are considered. The predicted gas phase acidities (ΔH0298) are 392.3 (H2O), 384.5 (CH3OH), and 359.3 (SiH3OH) kcal/mol. The differences are discussed in terms of the potential on the acidic proton as well as of contributions from rearrangement of electrons and relaxation of nuclei. The remaining basis set error is assessed on calculations for H2O which employ a [10s,8p,4d,2f,1g/7s,3p,1d] basis set. The best theoretical estimate of ΔH0298 for H2O is 391.0±2.5 kcal/mol.

Temperature dependent carbon-13 and proton isotope shifts of some isotopomers of methane

The carbon-13 and proton isotope shifts of 13CH 3D, 13CHD 3 and 13CD 4 with respect to 13CH 4 have been measured over the temperature range 200–370 K. The isotope shifts increase with temperature in all cases, with the increase being more marked for the more heavily deuterated isotopomers. The variations are attributable entirely to intramolecular effects and the data have been fitted by weighted least-squares regression analyses to defined carbon-13 and proton shielding surfaces to obtain derivatives of the shielding with respect to internal coordinates. At the first-order level it is found for the carbon-13 shielding that σ r , the derivative with respect to the stretching of a single bond, is − 71.0 (±0.6) ppm Å −1; for the proton shielding σ r , the derivative with respect to the length of the bond involving the proton, is − 23.5 (±1.5) ppm Å −1 whilst σ s , the derivative with respect to the length of one of the other bonds is − 2.1(±0.5) ppm Å −1. The derivatives are used to predict the values of the nuclear motion corrections for 13CH 4 and to predict isotope shifts for 13CH 2D 2 which was not studied experimentally in this work.

Vibration-rotation effects on the polarizabilities of CH4and CD4calculated from anab initiopolarizability surface

A polarizability surface has been calculated for the methane molecule using a Hartree-Fock wavefunction. Coefficients of the surface are given to second order in terms of both symmetry coordinates and internal coordinates. The polarizability is sensitive to bond stretching and angle bending. The effects of nuclear motion on the polarizabilitles of 12CH4 and 12CD4 have been calculated from the coefficients of the surface. Some of the second order coefficients are found to be significant in contributing to the nuclear motion corrections. The ν3 mode is the dominant contributor to the corrections. The temperature dependences of the mean molecular polarizabilities of 12CH4 and 12CD4 are also calculated. The results suggest that modern methods of measurement could distinguish between the isotopomers CH4-n D n (n=0–4) thereby enabling an experimental surface to be obtained.

The effects of rotation and vibration on the carbon-13 shielding, magnetizabilities and geometrical parameters of some methane isotopomers

An ab initio carbon-13 shielding surface to quadratic terms in displacement coordinates has been used to calculate the effects of temperature on the shielding in 13CH4 and its four deuterated isotopomers. Some of the second order terms are significant. For 3CH4 the total nuclear motion correction at 300 K is −3·695 ppm (−2%). The isotope effects observed by Alei and Wageman along the series 13CHnD4-n, are explained quantitatively to a high degree and the predictions of the temperature dependence of the shielding are in agreement with the meagre experimental data available. A similar calculation is reported for the temperature dependence of the molar magnetizabilities of 12CH4 and 12CD4 using an ab initio magnetizability surface to second order. Again some quadratic terms are important and the nuclear motion correction at 300 K is this time +2%. Modern SQUID magnetometers should be able to measure the variations predicted. Results are also given for the effects of vibration and rotation on the bond lengths...

Further contributions to the energy levels of a perturbed anharmonic oscillator: Application to adiabatic corrections

The investigation of further contributions to the energy levels of a perturbed anharmonic oscillator is continued. It is shown that, by using a Taylor series for several variables, the contributions to the energy levels due to an additional perturbing interaction can be directly derived from the Yun Dunham-type coefficients by means of analytic relations involving products of differential operators. Consequently, the analytic expressions for the whole set of these contributions are generated from the Yu0 coefficients alone and are easily calculated by using a computer algebraic manipulation language. As an illustrative application, the case of the adiabatic corrections for nuclear motion to the potential energy curves of diatomic molecules in 1Σ+ states, such as lithium hydrides and hydrogen chlorides, is considered.

Ab initio calculation of the isotope shift in the fine structure of C II and N II.

The nuclear-motion fine-structure isotope shifts in the ground states of C ii and N ii are computed by use of many-body perturbation theory. There are three different kinds of nuclear motion corrections to the atomic fine structure: normal mass effects on the spin-orbit and spin-spin interactions, electron-nucleus relativistic interactions, and higher-order cross terms between the specific-mass-shift operator and spin-dependent interactions. All three types of corrections have been considered and computed to third order in the many-body perturbation expansion. The computed results are in excellent agreement with recent accurate experimental values.

Nuclear-motion corrections to Born–Oppenheimer barrier heights for chemical reactions

We use diatomics-in-molecules theory to estimate the nuclear-motion contributions to atom–diatom potential energy surfaces for reactive systems, with special emphasis on the saddle point region. We examine the reactions of H, O, F, and Cl with H2 and H with Cl2. Nuclear-motion corrections at the saddle point are in the range 0.007–0.07 kcal/mol for cases with one or two hydrogens and classical barrier heights in the range 0.7–3 kcal/mol and are about 0.2 kcal/mol for cases with two hydrogens and classical barrier heights in the range 8–12 kcal/mol. For F+H2 with parameters such that the predicted nuclear-motion correction is 0.03 kcal/mol at the saddle point, the correction is as large as 0.2 kcal/mol elsewhere on the surface. Isotopic substitution of D for H changes the classical barrier height by 0.003–0.1 kcal/mol for the cases studied.