Zero-point Vibrational Corrections Research Articles

Determining the CH3SO2→CH3+SO2 barrier from methylsulfonyl chloride photodissociation at 193 nm using velocity map imaging

These imaging experiments study the formation of the methylsulfonyl radical, CH(3)SO(2), from the photodissociation of CH(3)SO(2)Cl at 193 nm and determine the energetic barrier for the radical's subsequent dissociation to CH(3) + SO(2). We first state-selectively detect the angular and recoil velocity distributions of the Cl((2)P(3/2)) and Cl((2)P(1/2)) atoms to further refine the distribution of internal energy partitioned to the momentum-matched CH(3)SO(2) radicals. The internal energy distribution of the radicals is bimodal, indicating that CH(3)SO(2) is formed in both the ground state and low-lying excited electronic states. All electronically excited CH(3)SO(2) radicals dissociate, while those formed in the ground electronic state have an internal energy distribution which spans the dissociation barrier to CH(3) + SO(2). We detect the recoil velocities of the energetically stable methylsulfonyl radicals with 118 nm photoionization. Comparison of the total recoil translational energy distribution for all radicals to the distribution obtained from the detection of stable radicals yields an onset for dissociation at a translational energy of 70+/-2 kcal/mol. This onset allows us to derive a CH(3)SO(2) --> CH(3) + SO(2) barrier height of 14+/-2 kcal/mol; this determination relies on the S-Cl bond dissociation energy, taken here as the CCSD(T) predicted energy of 65.6 kcal/mol. With 118 nm photoionization, we also detect the velocity distribution of the CH(3) radicals produced in this experiment. Using the velocity distributions of the SO(2) products from the dissociation of CH(3)SO(2) to CH(3) + SO(2) presented in the following paper, we show that our fastest detected methyl radicals are not from these radical dissociation channels, but rather from a primary S-CH(3) bond photofission channel in CH(3)SO(2)Cl. We also present critical points on the ground state potential energy surface of CH(3)SO(2) at the //CCSD(T)/aug-cc-pV(Q + d)ZCCSD(T)/6-311++G(2df,p) level. We include harmonic zero-point vibrational corrections as well as core-valence and scalar-relativistic corrections. The CCSD(T) predicted barrier of 14.6 kcal/mol for CH(3)SO(2) --> CH(3) + SO(2) agrees well with our experimental measurement. These results allow us to predict the unimolecular dissociation kinetics of CH(3)SO(2) radicals and critique the analysis of prior time-resolved photoionization studies on this system.

Quantitative prediction of gas-phase O17 nuclear magnetic shielding constants

Benchmark calculations of (17)O NMR chemical shifts for a series of 19 molecules with 22 chemical shifts are presented. This includes calculations at the HF-SCF, DFT (BP86 and B3-LYP), MP2, CCSD(T), and for a special case full CCSDT level of theory using basis sets of quadruple zeta quality and better. The effects of the quality of the geometry, electron correlation, basis set, and the inclusion of zero-point vibrational and temperature corrections are discussed in detail and the results are compared to gas-phase experimental values. Mean and standard deviations are 6 and 24 ppm for HF-SCF, -20 and 14 ppm for BP86, -20 and 13 ppm for B3-LYP, and 26 and 12 ppm for MP2. Results at the CCSD(T)/pz3d2f level of theory using geometries optimized at the CCSD(T)/cc-pVTZ level of theory exhibit a mean deviation of 16 ppm and a standard deviation of 6 ppm. A mean deviation of 6 ppm and a standard deviation of 4 ppm are obtained if these values are corrected for zero-point vibrational and temperature effects.

Vibrational effects in the parity-violating contributions to the isotropic nuclear magnetic resonance chemical shift

Abstract We investigate the effect of vibrational corrections to the parity-violating (PV) contributions to the nuclear magnetic resonance shielding constant for the CHFClBr molecule using a non-relativistic framework. Density-functional theory is used for the electronic structure part and vibrational configuration interaction for the vibrational part. Zero-point vibrational corrections are found to be of the order of a less than 10% with respect to the PV contributions calculated at the equilibrium geometry in relevant cases. Vibrational corrections are evaluated also for the fundamental vibrations and are found to be up to 42% of the total PV contribution in the heavy elements.

Special issue “Advances in Chiroptical Methods”

Special issue “Advances in Chiroptical Methods”

Gas phase optical rotation calculated from coupled cluster theory with zero‐point vibrational corrections from density functional theory

Molecular vibrations can have a significant influence on gas phase specific optical rotations. Mainly due to the large number of nuclear degrees of freedom in most chiral molecules, theoretical predictions of vibrational corrections quickly become prohibitively expensive. Here, we investigate an approach in which the purely electronic contribution is calculated at the coupled cluster singles and doubles level, while the zero-point vibrational correction is computed using the less demanding density functional theory (B3LYP functional). By comparing to experimental gas phase results for seven molecules and two wavelengths, we find that the mixed coupled cluster/B3LYP approach performs significantly better than pure B3LYP predictions. In fact, we find that it is more important to use high-level electron correlation for the electronic contribution than to include zero-point vibrational corrections.

Muoniated radical states in the group 16 elements: Computational studies

Recent experimental studies on positive muon implantation in silicon, selenium, and tellurium have been interpreted on the basis that the primary paramagnetic species observed is XMu ( X = S , Se, or Te), the muonium-substituted analog of the appropriate diatomic chalcogen monohydride radical. However, temperature-dependent signal visibility, broadening, and hyperfine shift effects remain puzzling. The interplay of degeneracy, spin–orbit coupling, and vibrational averaging in these species makes them computationally challenging despite their small size. In this work computational studies are carried out on all hydrogen isotopomers of the series OH, SH, SeH, and TeH. Several different methodological approaches are compared, and the effects of wavefunction symmetry, spin–orbit coupling, and zero-point vibrational corrections on the isotropic and anisotropic components of the hyperfine interaction are examined. Additionally, some models of the Mu site in rhombic sulfur are briefly considered.

High-level ab-initio calculation of gas-phase NMR chemical shifts and secondary isotope effects of methanol

In this contribution high-level ab-initio calculations of the chemical shifts of methanol including zero-point vibrational and temperature corrections are presented. For the first time, secondary isotope effects have been calculated via second order vibrational perturbation theory. In comparison with recent experimental gas-phase data and in contrast to other quantum-chemical methods the results are consistent and in very good agreement with the experimental 13C, 17O and 1H chemical shifts reported by Makulski [W. Makulski, J. Mol. Struct. 872 (2008) 81]. Secondary isotope effects can be calculated with remarkable accuracy of a few hundredths of a ppm in comparison to experiment.

Influence of Systematic Variations of Molecular Geometries of Small Hydrocarbons on ab initio HF/6-31G* and 6-311G* GIAO Calculated 1H and 13C NMR Chemical Shifts

GIAO HF calculations with symmetry retaining variations of selected CH or CC distances in a large range but constant retention of other geometric parameters have been performed for 10 molecules using the 6-31G* basis set (set A) and for a larger set of 18 molecules 1 to 18 in the 6-311G* basis set (set B). The graphical representations for calculated 1 H NMR shifts in dependence on CH or CC bond lengths variations are mostly linear or slightly curved and show no ex- treme values in the range studied. The slopes are generally positive, i. e. an elongation of distances leads to low field shifts because of reduction of the density of shielding electrons in the varied bonds. The slopes of regression lines may be classi- fied for CH bonds according to hybridization and with the kind of substitution. Calculated 13 C NMR chemical shifts are dependent for connected C atoms on variations of CC as well as on CH bond distances. The graphs are mostly curved, also positive and in magnitude dependent on the types of bonds. Two dimensional plots of simultaneous variations of CH and CC bonds show for 1 H NMR independent behavior of these parameters. The effect of variations of angles on 1 H and 13 C shifts was studied only for a few molecules and shows curved graphs with rather small slopes. The determined slopes of linear regressions may be used to estimate zero-point vibrational corrections in close agreement to directly calculated values.

The accuracy of rotational constants predicted by high-level quantum-chemical calculations. I. molecules containing first-row atoms

A statistical analysis of the accuracy of theoretically predicted rotational constants is presented based on the data for a total of 16 molecules and 97 isotopologues. Special focus is given on the treatment of electron correlation by using coupled-cluster methods up to quadruple excitations, core correlation, basis-set effects, zero-point vibrational corrections, and the electronic contribution to the rotational constants. The high accuracy achieved in the present investigation is demonstrated by the fact that at our best theoretical level, termed as CCSD(T)cc-pV infinity Z+Delta core+DeltaT+DeltaQ+DeltaB vib+DeltaB el, the mean absolute error is 0.04% and the standard deviation is 0.07% in comparison with the available experimental data. The importance of higher excitations, core correlation, and zero-point vibrational effects is emphasized, while the electronic contribution is found to be less important.

The empirical equilibrium structure of diacetylene

High-level quantum-chemical calculations are reported at the MP2 and CCSD(T) levels of theory for the equilibrium structure and the harmonic and anharmonic force fields of diacetylene, H C C C C H. The calculations were performed employing Dunning’s hierarchy of correlation-consistent basis sets cc-pV XZ, cc-pCV XZ, and cc-pwCV XZ, as well as the ANO2 basis set of Almlöf and Taylor. An empirical equilibrium structure based on experimental rotational constants for 13 isotopic species of diacetylene and computed zero-point vibrational corrections is determined ( r e emp : r C H = 1.0615 Å , r C C = 1.2085 Å , r C C = 1.3727 Å ) and in good agreement with the best theoretical structure (CCSD(T)/cc-pCV5Z: r C H = 1.0617 Å , r C C = 1.2083 Å , r C C = 1.3737 Å ). In addition, the computed fundamental vibrational frequencies are compared with the available experimental data and found in satisfactory agreement.

Solvent effects on zero-point vibrational corrections to optical rotations and nuclear magnetic resonance shielding constants

We present a study of solvent effects on the zero-point vibrational corrections (ZPVC) to optical rotations and nuclear magnetic resonance shielding constants of solvated molecules. The model used to calculate vibrational corrections rely on an expansion of the potential and property surfaces around an effective molecular geometry and includes both harmonic and anharmonic corrections. Numerical examples are presented for ( S)-propylene oxide in various solvents as well as for acetone and the three diazene molecules. We find that solvent effects on the ZPVCs may be significant and in some cases crucial to accurately predict solvent shifts on molecular properties.

Correlated Linear Response Calculations of the C6 Dispersion Coefficients of Hydrogen Halides

Three correlated linear response theory methods - the second order polarization propagator approximation (SOPPA), the second order polarization propagator approxima- tion with coupled cluster singles and doubles amplitudes, SOPPA(CCSD), and multiconfig- urational self-consistent field (MCSCF) linear response theory - were used to determine the electric dipole polarizabilities at imaginary frequencies of the hydrogen halides HX (with X = F, Cl, Br and I). The dynamic polarizabilities were subsequently used to calculate the C6 dispersion coefficient for a pair of interacting HX molecules via numerical integra- tion of the Casimir-Polder formula. The dependence of the polarizabilities, their frequency dependence and C6 coefficients on the one-electron basis set, the level of correlation and zero-point vibrational corrections was studied. Furthermore it was investigated whether relativistic effective core potentials (RECP) could be employed in such calculations. It was found that SOPPA(CCSD) and MCSCF calculations with large active spaces using basis sets of at least double augmented quadruple zeta quality give comparable results which in particular for SOPPA(CCSD) are in close agreement with the available experimental values. Furthermore it could be shown that the results of the RECP calculations are in close agreement with the all electron calculations.

Geometries of Second-Row Transition-Metal Complexes from Density-Functional Theory.

A data set of 19 second-row transition-metal complexes has been collated from sufficiently precise gas-phase electron-diffraction experiments and used for evaluating errors in DFT optimized geometries. Equilibrium geometries have been computed using 15 different combinations of exchange-correlation functionals in conjunction with up to three different effective core potentials. Most DFT levels beyond the local density approximation can reproduce the 29 metal-ligand bond distances selected in this set with reasonable accuracy and precision, as assessed by the mean and standard deviations of optimized vs experimentally observed bond lengths. The pure GGAs tested in this study all have larger standard deviations than their corresponding hybrid variants. In contrast to previous findings for first-row transition-metal complexes, the TPSSh hybrid meta-GGA is slightly inferior to the best hybrid GGAs. The ranking of some popular density functionals, for second-row transition-metal complexes, ordered according to decreasing standard deviation, is VSXC ≈ LSDA > BLYP > BP86 > B3LYP ≈ TPSSh > PBE hybrid ≈ B3PW91 ≈ B3P86. When zero-point vibrational corrections, computed at the BP86/SDD level, are added to equilibrium bond distances obtained from a number of density-functional/basis-set combinations, the overall performance in terms of mean and standard deviations from experiment is not improved. For a combined data set comprised of the first- and second-row transition-metal complexes the hybrid functionals B3P86, B3PW91, and the meta-GGA hybrid TPSSh afford the lowest standard deviations.

Vibrational corrections to geometries of transition metal complexes from density functional theory

Zero-point vibrational corrections are computed at the BP86/AE1 level for the set of 50 transition-metal/ligand bonds that have recently been proposed as testing ground for DFT methods, because of the availability of precise experimental gas-phase geometries (Bühl and Kabrede, J Chem Theory Comput 2006, 2, 1282). These corrections are indicated to be transferable to a large extent between various density-functional/basis-set combinations, so that they can be used to estimate zero-point averaged r0g distances from re values optimized at other theoretical levels. Applying this approach to a number of popular DFT levels does not, in general, improve their overall accuracy in terms of mean and standard deviations from experiment. The hybrid variant of the meta-functional TPSS is confirmed as promising choice for computing structures of transition-metal complexes.

Zero-Point Corrections and Temperature Dependence of HD Spin−Spin Coupling Constants of Heavy Metal Hydride and Dihydrogen Complexes Calculated by Vibrational Averaging

Vibrational corrections (zero-point and temperature dependent) of the H-D spin-spin coupling constant J(HD) for six transition metal hydride and dihydrogen complexes have been computed from a vibrational average of J(HD) as a function of temperature. Effective (vibrationally averaged) H-D distances have also been determined. The very strong temperature dependence of J(HD) for one of the complexes, [Ir(dmpm)Cp*H2]2 + (dmpm = bis(dimethylphosphino)methane) can be modeled simply by the Boltzmann average of the zero-point vibrationally averaged JHD of two isomers. For this complex and four others, the vibrational corrections to JHD are shown to be highly significant and lead to improved agreement between theory and experiment in most cases. The zero-point vibrational correction is important for all complexes. Depending on the shape of the potential energy and J-coupling surfaces, for some of the complexes higher vibrationally excited states can also contribute to the vibrational corrections at temperatures above 0 K and lead to a temperature dependence. We identify different classes of complexes where a significant temperature dependence of J(HD) may or may not occur for different reasons. A method is outlined by which the temperature dependence of the HD spin-spin coupling constant can be determined with standard quantum chemistry software. Comparisons are made with experimental data and previously calculated values where applicable. We also discuss an example where a low-order expansion around the minimum of a complicated potential energy surface appears not to be sufficient for reproducing the experimentally observed temperature dependence.

Magnitude of Zero-Point Vibrational Corrections to Optical Rotation in Rigid Organic Molecules: A Time-Dependent Density Functional Study

The zero-point vibrational corrections (ZPVCs) to the optical rotation of 22 rigid organic molecules have been calculated using time-dependent density functional theory with the B3LYP hybrid functional. We outline an implementation for calculating ZPVCs that can be applied with a variety of quantum chemistry programs and methods. It is shown that the ZPVCs to optical rotation have a wide range of values and can be quite significant depending on the molecule. On average, it has been determined that vibrational corrections can account for about 20% of the optical rotation for the equilibrium value. It is also concluded that vibrational effects alone cannot be the only factor in improving the calculated values of optical rotation with respect to experimental data measured in solution.

The second hyperpolarizability of the N 2 molecule calculated using the approximate coupled cluster triples model CC3

The static and frequency-dependent hyperpolarizabilities of the N 2 molecule have been calculated using the coupled cluster approximate triples model CC3. The CC3 basis-set limit of the hyperpolarizability has been estimated. Considering the zero-point vibrational correction and neglecting the relativistic contributions (which are found to be small) the best estimate of the static hyperpolarizability is 912.9 ± 4.3 a.u. (the uncertainty of 4.3 a.u. does not account for correlation effects beyond CC3). The effect of triples is important and increases with frequency. The hyperpolarizabilities calculated at the CC3 level agree well with experiment, the discrepancies being of 0.1–2.2%. The largest CC3 calculations employed 326 basis functions.

The Importance of Molecular Vibrations: The Sign Change of the Optical Rotation of Methyloxirane

Sign language: The experimentally observed sign change of the optical rotation of (S)-methyloxirane when varying the wavelength of incident light from 589 to 355 nm is a result of zero-point vibrational corrections. Agreement between theory and experiment is obtained when coupled-cluster (CC3) equilibrium optical rotations are combined with the reported zero-point vibrational (ZPV) contributions (see picture).

Calculation of binary magnetic properties and potential energy curve in xenon dimer: Second virial coefficient of Xe129 nuclear shielding

Quantum chemical calculations of the nuclear shielding tensor, the nuclear quadrupole coupling tensor, and the spin-rotation tensor are reported for the Xe dimer using ab initio quantum chemical methods. The binary chemical shift delta, the anisotropy of the shielding tensor Delta sigma, the nuclear quadrupole coupling tensor component along the internuclear axis chi( parallel ), and the spin-rotation constant C( perpendicular ) are presented as a function of internuclear distance. The basis set superposition error is approximately corrected for by using the counterpoise correction (CP) method. Electron correlation effects are systematically studied via the Hartree-Fock, complete active space self-consistent field, second-order Møller-Plesset many-body perturbation, and coupled-cluster singles and doubles (CCSD) theories, the last one without and with noniterative triples, at the nonrelativistic all-electron level. We also report a high-quality theoretical interatomic potential for the Xe dimer, gained using the relativistic effective potential/core polarization potential scheme. These calculations used valence basis set of cc-pVQZ quality supplemented with a set of midbond functions. The second virial coefficient of Xe nuclear shielding, which is probably the experimentally best-characterized intermolecular interaction effect in nuclear magnetic resonance spectroscopy, is computed as a function of temperature, and compared to experiment and earlier theoretical results. The best results for the second virial coefficient, obtained using the CCSD(CP) binary chemical shift curve and either our best theoretical potential or the empirical potentials from the literature, are in good agreement with experiment. Zero-point vibrational corrections of delta, Delta sigma, chi (parallel), and C (perpendicular) in the nu=0, J=0 rovibrational ground state of the xenon dimer are also reported.

The energetics of the isomeric anthrols

We report the results of geometry optimized MP2(FULL)/6-31G(d) quantum chemical calculations with zero-point vibrational energies and thermal corrections of the isomeric 1-, 2- and 9-anthrols and the tautomeric anthrone. We find that 1- and 2-anthrols have nearly the same enthalpy of formation and are some 6 kJ mol−1 more stable than their 9-isomer in accord with intuition based on steric hindrance. We find that anthrone is more stable than 9-anthrol by 13.7 ± 6.4 kJ mol−1, in satisfactory agreement with the value of 23 ± 8 kJ mol−1 suggested elsewhere by experiment and its associated analysis.