Dynamic (hyper)polarizabilities of the sulphur dioxide molecule: coupled cluster calculations including vibrational corrections

In this work we report results for dynamical (hyper)polarizabilities of the sulphur dioxide molecule with inclusion of vibrational corrections. The electronic contributions were computed analytically at the single and double coupled cluster level through response theories for the frequencies 0, 0.0239, 0.0428, 0.0656, 0.0720, and 0.0886 hartree. Contributions of the connected triple excitations to the dynamic electronic properties were also estimated through the multiplicative correction scheme. Vibrational corrections were calculated by means of the perturbation theoretical method. The results obtained show that the zero point vibrational correction is very small for all properties studied while the pure vibrational correction is relevant for the dc-Pockels effect, intensity dependent refractive index, and dc-Kerr effect. For these nonlinear optical processes, the pure vibrational corrections represent approximately 75%, 13%, and 6% of the corresponding electronic contributions for the higher frequencies quoted. The results presented for the polarizability are in good agreement with experimental values available in the literature. For the hyperpolarizabilities we have not obtained experimental results with precision sufficient for comparison.     

Calculation of the O-H stretching vibrational overtone spectrum of the water dimer

The O-H stretching vibrational overtone spectrum of the water dimer has been calculated with the dimer modeled as two individually vibrating monomer units. Vibrational term values and absorption intensities have been obtained variationally with a computed dipole moment surface and an internal coordinate Hamiltonian, which consists of exact kinetic energy operators within the Born-Oppenheimer approximation of the monomer units. Three-dimensional ab initio potential energy and dipole moment surfaces have been calculated using the internal coordinates of the monomer units using the coupled cluster method including single, double, and perturbative triple excitations [CCSD(T)] with the augmented correlation consistent valence triple zeta basis set (aug-cc-pVTZ). The augmented correlation consistent valence quadruple zeta basis set (aug-cc-pVQZ), counterpoise correction, basis set extrapolation to the complete basis set limit, relativistic corrections, and core and valence electron correlations effects have been included in one-dimensional potential energy surface cuts. The aim is both to investigate the level of ab initio and vibrational calculations necessary to produce accurate results when compared with experiment and to aid the detection of the water dimer under atmospheric conditions.     

Ab initio characterization of XH3 (X=N, P). I. Ammonia, phosphine and their related ions and radicals: structure and thermochemistry

Ammonia, phosphine and their related cations, anions and radicals have been investigated at a high level of accuracy. The singles and doubles coupled cluster method including a perturbational correction for connected triple excitations, CCSD(T), in conjunction with correlation consistent basis sets ranging in size from triple to sextuple zeta have been employed. Extrapolation to the complete basis set limit has been used with accurate treatments of core–valence correlation effects in order to accurately predict structures, ionization potentials, electron affinities as well as N–H and P–H bond dissociation energies. For all the species studied, harmonic vibrational frequencies have also been evaluated in order to obtain zero-point corrections.     

Accurate Quantum‐Chemical Prediction of Enthalpies of Formation of Small Molecules in the Gas Phase

The coupled‐cluster approach, including single and double excitations and perturbative corrections for triple excitations, is capable of predicting molecular electronic energies and enthalpies of formation of small molecules in the gas phase with very high accuracy (specifically, with error bars less than 5 kJ mol^?1), provided that the electronic wavefunction is dominated by the Hartree–Fock configuration. This capability is illustrated by calculations on molecules containing O–H and O–F bonds, namely OH, FO, H₂O, HOF, and F₂O. To achieve this very high accuracy, it is imperative to account for electron‐correlation effects in a quantitative manner, either by using explicitly correlated two‐particle basis functions (R12 functions) or by extrapolating to the limit of a complete basis. Besides taking into account harmonic zero‐point vibrational energies, it is also necessary to account for anharmonic corrections to the zero‐point vibrational energies, to include the core orbitals into the coupled‐cluster calculations, and to account for spin–orbit corrections and scalar relativistic effects. These additional corrections constitute small but significant contributions in the range of 1–4 kJ mol^?1 to the enthalpies of formation of the aforementioned molecules. The highly accurate coupled‐cluster results, obtained by employing R12 functions and by including various corrections, are compared with standard Kohn–Sham density‐functional calculations as well as with the Gaussian‐2 and complete‐basis‐set model chemistries.     

Renner-Teller bending frequencies of the approximately A 2Pi state of OCS+

There are inconsistencies among previously reported Renner-Teller bending frequencies for the approximately A 2Pi state of OCS+. To resolve these controversies, we have computed vibrational frequencies using high-level excited electronic state ab initio equation-of-motion coupled cluster methods. On the basis of equation-of-motion coupled cluster theory including single, double, and iterative inclusion of partial triple excitations (EOM-CC3) paired with the correlation-consistent polarized valence quadruple-zeta basis set (cc-pVQZ), we predict harmonic bending frequencies of 364 and 401 cm-1 for the A' and A" components of approximately A 2Pi OCS+, respectively. Particularly for the upper Renner-Teller component, these results are lower than the theoretical predictions of 370 and 459 cm-1 reported by Chen, Hochlaf, Rosmus, He, and Ng [J. Chem. Phys. 2002, 116, 5612]. Instead, the presently computed bending frequencies are more consistent with the experimentally derived average value of 357 +/- 5 cm-1 recently reported by Sommavilla and Merkt [J. Phys. Chem. A 2004, 108, 9970], lending credence to the spectral assignments made in this later work. The two components of the Renner-Teller bending frequencies of approximately X 2Pi OCS+ are similarly predicted to be 396 and 453 cm-1. Anharmonicity constants arising from a quartic force field computed at the cc-pVQZ EOM-CC3 level of theory are given, to provide a more complete characterization of the potential energy surface of the approximately A 2Pi state of OCS+.     

Ab initio potential energy surface and intermolecular vibrations of the naphthalene-argon van der Waals complex

The intermolecular potential energy surface (PES) of the naphthalene-argon (NpAr) complex is constructed using an ab initio method. The molecule-argon interaction energy is computed at the level of the second-order M?ller-Plesset (MP2) theory combined with the augmented correlation consistent polarized valence double-ζ basis set. The analytical PES fitted to a large set of single energy values is further improved with the help of correction functions determined by calculations of the interaction energy at the coupled cluster level including single and double excitations supplemented by triple excitations performed for a limited set of intermolecular configurations. The PES determined is very flat near its four equivalent global minima of -493 cm(-1) located from both sides of the Np plane at a distance of 3.435 A? and shifted from the center of Np by ±0.43 A? along its long symmetry axis. The large-amplitude motion of Ar in the complex is investigated, and dynamical consequence of a strong intermode coupling is discovered in the excited vibrational states. The theoretical results obtained allow for the reassignment of the spectral bands observed in the electronic transition S(1) ← S(0) of the NpAr complex.     

Potential-energy surface for the electronic ground state of NH3 up to 20,000 cm-1 above equilibrium

Ab initio coupled cluster calculations with single and double substitutions and a perturbative treatment of connected triple excitations [CCSD(T)] with the augmented correlation-consistent polarized valence triple-zeta aug-cc-pVTZ basis at 51 816 geometries provide a six-dimensional potential-energy surface for the electronic ground state of NH3. At 3814 selected geometries, CBS+ energies are obtained by extrapolating the CCSD(T) results for the aug-cc-pVXZ(X=T,Q,5) basis sets to the complete basis set (CBS) limit and adding corrections for core-valence correlation and relativistic effects. CBS** ab initio energies are generated at 51,816 geometries by an empirical extrapolation of the CCSD(T)/aug-cc-pVTZ results to the CBS+ limit. They cover the energy region up to 20,000 cm-1 above equilibrium. Parametrized analytical functions are fitted through the ab initio points. For these analytical surfaces, vibrational term values and transition moments are calculated by means of a variational program employing a kinetic-energy operator expressed in the Eckart-Sayvetz frame. Comparisons against experiment are used to assess the quality of the generated potential-energy surfaces. A "spectroscopic" potential-energy surface of NH3 is determined by a slight empirical adjustment of the ab initio potential to the experimental vibrational term values. Variational calculations on this refined surface yield rms deviations from experiment of 0.8 cm-1 for 24 inversion splittings and 0.4 (3.0) cm-1 for 34 (51) vibrational term values up to 6100 (10,300) cm-1.     

Coupled-cluster and explicitly correlated perturbation-theory calculations of the uracil anion

A valence-type anion of the canonical tautomer of uracil has been characterized using explicitly correlated second-order Moller-Plesset perturbation theory (RI-MP2-R12) in conjunction with conventional coupled-cluster theory with single, double, and perturbative triple excitations. At this level of electron-correlation treatment and after inclusion of a zero-point vibrational energy correction, determined in the harmonic approximation at the RI-MP2 level of theory, the valence anion is adiabatically stable with respect to the neutral molecule by 40 meV. The anion is characterized by a vertical detachment energy of 0.60 eV. To obtain accurate estimates of the vertical and adiabatic electron binding energies, a scheme was applied in which electronic energy contributions from various levels of theory were added, each of them extrapolated to the corresponding basis-set limit. The MP2 basis-set limits were also evaluated using an explicitly correlated approach, and the results of these calculations are in agreement with the extrapolated values. A remarkable feature of the valence anionic state is that the adiabatic electron binding energy is positive but smaller than the adiabatic electron binding energy of the dipole-bound state.     

Accurate ab initio predictions of ionization energies of hydrocarbon radicals: CH2, CH3, C2H, C2H3, C2H5, C3H3, and C3H5

The ionization energies for methylene (CH2), methyl (CH3), ethynyl (C2H), vinyl (C2H3), ethyl (C2H5), propargyl (C3H3), and allyl (C3H5) radicals have been calculated by the wave-function-based ab initio CCSD(T)/CBS approach, which involves the approximation to the complete basis set (CBS) limit at the coupled-cluster level with single and double excitations plus a quasiperturbative triple excitation [CCSD(T)]. When it is appropriate, the zero-point vibrational energy correction, the core-valence electronic correction, the scalar relativistic effect correction, the diagonal Born-Oppenheimer correction, and the high-order correlation correction have also been made in these calculations. The comparison between the computed ionization energy (IE) values and the highly precise experimental IE values determined in previous pulsed field ionization-photoelectron (PFI-PE) studies indicates that the CCSD(T)/CBS method is capable of providing accurate IE predictions for these hydrocarbon radicals achieving error limits well within +/-10 meV. The benchmarking of the CCSD(T)/CBS IE predictions by the PFI-PE experimental results also lends strong support for the conclusion that the CCSD(T)/CBS approach with high-level energy corrections can serve as a valuable alternative for reliable IE determination of radicals, particularly for those radicals with very unfavorable Franck-Condon factors for photoionization transitions near their ionization thresholds.     

Formation of ultracold SrYb molecules in an optical lattice by photoassociation spectroscopy: theoretical prospects

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the SrYb molecule in the Born-Oppenheimer approximation for the electronic ground state and the first fifteen excited singlet and triplet states. All the excited state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles and doubles framework and large basis-sets, while the ground state potential was computed using the coupled cluster method with single, double, and noniterative triple excitations. The leading long-range coefficients describing the dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. The electronic structure data were employed to investigate the possibility of forming deeply bound ultracold SrYb molecules in an optical lattice in a photoassociation experiment using continuous-wave lasers. Photoassociation near the intercombination line transition of atomic strontium into the vibrational levels of the strongly spin-orbit mixed b(3)Σ(+), a(3)Π, A(1)Π, and C(1)Π states with subsequent efficient stabilization into the v' = 1 vibrational level of the electronic ground state is proposed. Ground state SrYb molecules can be accumulated by making use of collisional decay from v' = 1 to v' = 0. Alternatively, photoassociation and stabilization to v' = 0 can proceed via stimulated Raman adiabatic passage provided that the trapping frequency of the optical lattice is large enough and phase coherence between the pulses can be maintained over at least tens of microseconds.     

On relativistic effects in ground state potential curves of Zn2, Cd2, and Hg2 dimers. A CCSD(T) study

The ground state potential curves of the Zn2, Cd2, and Hg2 dimers calculated at different levels of theory are presented and compared with each other as well as with experimental and other theoretical studies. The calculations at the level of Dirac-Coulomb Hamiltonian (DCH), 4-component spin-free Hamiltonian, nonrelativistic Lévy-Leblond Hamiltonian and at the level of simple Coulombic correction to DCH are presented. The potential curves are calculated in an all-electron supermolecular approach including the correction to basis set superposition error (BSSE). Electron correlation is treated at the coupled cluster level including single and double excitations and noniterative triple corrections, CCSD(T). In addition, simulations of the temperature dependence of dynamic viscosities in the low-density limit using the obtained ground state potential curves are presented.     

Electronic and vibrational hyperpolarizabilities of alkali- and alkaline-earth-doped boron nitride nanotubes

This work reports the results of the vibrational corrections and frequency dependence to the first hyperpolarizabilities of the alkali- and alkaline-earth-doped boron nitride nanotubes. The electronic contributions were computed by means of the density functional theory with the M06-2X functional, and the vibrational corrections were calculated using the perturbation theoretical method and the field-induced coordinates methodology. The results for the electronic contribution show that such materials exhibit large first hyperpolarizabilities and electride characteristic. We also show that the distribution of the excess electron, which originates from the doping atoms, plays an important role in the large electronic hyperpolarizabilities (β^el). Moreover, our findings strongly indicate that the effect of vibrations on the hyperpolarizabilities can be quite important and can even be much larger than the electronic counterpart.     

ChemInform Abstract: Investigation of Heterodimeric and Homodimeric Radical Cations of the Series: [F2O2]+, [F2Cl2]+, [Cl2O2]+, [F4]+, and [Cl4]+.

Structures, thermochemical stability, Born‐Fajans‐Haber cycles, and vibrational data of the title ions are quantum‐chemically obtained by coupled‐cluster calculations with single and double substitution as well as perturbative triple excitations.     

Elementary constituents of microdevices: the Ge2H fragment

Highly correlated ab initio electronic structure theory has been used to systematically investigate the linear (X 2Pi) GeGeH and H-bridged (X 2B1 and A 2A1) GeHGe structures and the isomerization transition state (A 2A') connecting X 2Pi with A 2A1. The equilibrium structures and physical properties have been predicted employing self-consistent field, configuration interaction with single and double excitations, coupled cluster with single and double excitations (CCSD), and CCSD with perturbative triple excitations [CCSD(T)]. Four correlation-consistent polarized valence-[cc-pVXZ and aug-cc-pVXZ (X=T and Q)] type basis sets were used in the study. For the H-bridged GeHGe isomer, the X 2B1 ground state is predicted to lie only 0.74 [0.95 with zero-point vibrational energy (ZPVE) corrections] kcal mol-1 below the A 2A1 excited state at the CCSD(T) level of theory with the augmented correlation-consistent polarized valence quadruple zeta (aug-cc-pVQZ) basis set. The X 2B1 state of the H-bridged GeHGe isomer lies 8.6 kcal mol-1 below the X 2Pi ground state of the linear GeGeH isomer. The forward isomerization barrier from the linear ground state to the A 2A' transition state is predicted to be 3.7 kcal mol-1. The reverse isomerization barrier between the A 2A1 GeHGe structure and the X 2Pi GeGeH structure is predicted to be 11.6 (10.8 with the ZPVE corrections) kcal mol-1 at the aug-cc-pVQZ CCSD(T) level of theory.     

Two-particle density matrix cumulant of coupled cluster theory

A two-particle density matrix obtained from the expectation value expression for the coupled cluster wave function is separated into the antisymmetrized product of the one-particle density matrices and the remaining cumulant part. It is demonstrated that the proposed formula for the coupled cluster cumulant is a valid cumulant expression, since it is a connected, and therefore size-extensive quantity. It is also shown that the density matrices from coupled cluster gradient theory, when used to define a cumulant, result in the expression containing disconnected terms. The proposed formulation of the coupled cluster cumulant makes it easy to develop size-extensive truncation schemes. As an example, explicit equations for the cumulant at the coupled cluster single, double and triple excitation level are presented.     

Molecular structure of thiourea

The molecular structure of thiourea has been investigated under C(s), C(2), and C(2v) symmetry constraints. At the coupled-cluster level in conjunction with a triple-ζ basis set, only the C(2) conformer has been found to be a real minimum on the potential energy surface. Its equilibrium structure has therefore been accurately evaluated using both theoretical and experimental data. With respect to the former, high-level quantum-chemical calculations at the coupled-cluster level in conjunction with correlation-consistent basis sets ranging in size from triple- to quintuple-zeta have been carried out. Extrapolation to the complete basis-set limit as well as core-correlation effects and inclusion of full treatment of triple excitations in the cluster operator have been considered. On the basis of the vibrational ground-state rotational constants available for five isotopic species and the corresponding computed vibrational corrections, the semiexperimental equilibrium geometry of thiourea has also been determined for the first time.     

Accurate ab initio determination of spectroscopic and thermochemical properties of mono- and dichlorocarbenes

The best technically feasible values for the triplet-singlet energy gap and the enthalpies of formation of the HCCl and CCl2 radicals have been determined through the focal-point approach. The electronic structure computations were based on high-level coupled cluster (CC) methods, up to quadruple excitations (CCSDTQ), and large-size correlation-consistent basis sets, ranging from aug-cc-pVDZ to aug-cc-pV6Z, followed by extrapolation to the complete basis set limit. Small corrections due to core correlation, relativistic effects, diagonal Born-Oppenheimer correction, as well as harmonic and anharmonic zero-point vibrational energy corrections have been taken into account. The final estimates for the triplet-singlet energy gap, T0(?), are 2170+/-40 cm-1 for HCCl and 7045+/-60 cm-1 for CCl2, favoring the singlet states in both cases. Complete quartic force fields in internal coordinates have been computed for both the X and ? states of both radicals at the frozen-core CCSD(T)/aug-cc-pVQZ level. Using these force fields vibrational energy levels of {HCCl, DCCl, CCl2} up to {6000, 5000, 7000} cm-1 were calculated both by second-order vibrational perturbation theory (VPT2) and variationally. These results, especially the variational ones, show excellent agreement with the experimentally determined energy levels. The enthalpies of formation of HCCl (X1A') and CCl2(X1A1), at 0 K, are 76.28+/-0.20 and 54.54+/-0.20 kcal mol-1, respectively.     

On the role of higher-order correlation effects on the induction interactions between closed-shell molecules

High-order correlation contributions to the second-order induction energy were studied for various representative van der Waals complexes. It was found that the induction energy obtained by the truncation of the relaxed M?ller-Plesset expansion in the second or third order is in most cases quite close to the induction energy computed with the coupled-cluster method (restricted to single and double excitations). Also, the effect of triples excitations on this perturbation term is usually small. However, given an oscillatory behaviour of the M?ller-Plesset induction corrections, the coupled-cluster method seems to be better suited to a reliable calculation of the induction energy. The sources of the remaining differences between the interaction energies computed by symmetry-adapted perturbation theory and those computed by the supermolecule coupled-cluster method (restricted to single, double, and noniterative triple excitations) are examined. It has been found that they can be attributed to the higher-order correlation terms in the second-order dispersion and exchange-induction corrections.     

Uncoupled multireference state-specific Mukherjee's coupled cluster method with triexcitations

We have developed the uncoupled version of multireference Mukherjee's coupled cluster method with connected triexcitations. The method has been implemented in ACES II program package. The agreement between the uncoupled and the standard version of Mukherjee's multireference coupled cluster method has been reported previously at the singles and doubles level by Das et al. [J. Mol. Struct.: THEOCHEM 79, 771 (2006); Chem. Phys. 349, 115 (2008)]. The aim of this article is to investigate this method further, in order to establish how its performance changes with the size of the basis set, size of the model space, multireference character of different molecules, and inclusion of connected triple excitations. Assessment of the new method has been performed on the singlet methylene, potential energy curve of fluorine molecule, and third b?(1)Σ(g)(+) electronic state of oxygen molecule.