Explicitly correlated Gaussian calculations of the 2P(o) Rydberg spectrum of the lithium atom

Accurate quantum-mechanical nonrelativistic variational calculations are performed for the nine lowest members of the (2)P(o) Rydberg series (1s(2)np(1), n = 2, ..., 10) of the lithium atom. The effect of the finite nuclear mass is included in the calculations allowing for determining the isotopic shifts of the energy levels. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are variationally optimized with the aid of the analytical energy gradient determined with respect to those parameters. The calculated state energies are compared with the available experimental data.     

Explicitly correlated Gaussian functions with r factors for calculations of the ground state of the helium atom

Explicitly correlated Gaussian functions with r exp( ? β r ) factors have been used in variational calculations of the ground state of the helium atom. Additional correlation factors in the form of even powers of r _ij were introduced to the Gaussian functions with exponential correlation components by differentiating these functions with respect to the correlation exponent β. The algorithm of this method and its computational implementation is described. A number of calculations were performed for the ground state of helium atom to test the performance of the basis sets comparising different numbers of the Gaussians with the exp( ? β r ) and r exp( ? β r ) correlation factors. The numerical results indicate that including functions with r factors does not lead to improved results, contrary to what was anticipated initially. © 1994 by John Wiley & Sons, Inc.     

Explicitly correlated RMP2 for high-spin open-shell reference states

We present an explicitly correlated version of the high-spin open-shell RMP2 method. The theory is derived in a unitarily invariant form, which is suitable for the insertion of local approximations. It is demonstrated that the rapid basis set convergence of closed-shell MP2-F12 is also achieved in RMP2-F12, and similar Ansatze and approximations can be employed. All integrals are computed using efficient density fitting approximations, and many-electron integrals are avoided using resolution of the identity approximations. The performance of the method is demonstrated by benchmark calculations on a large set of ionization potentials, electron affinities and atomization energies. Using triple-zeta basis sets RMP2-F12 yields results that are closer to the basis set limit than standard RMP2 with augmented quintuple-zeta basis sets for all properties. Different variants of perturbative corrections for the open-shell Hartree-Fock treatment are described and tested.     

Refinement of the experimental energy levels of higher 2D Rydberg states of the lithium atom with very accurate quantum mechanical calculations

Very accurate variational non-relativistic calculations are performed for four higher Rydberg (2)D states (1s(2)nd(1), n = 8,..., 11) of the lithium atom ((7)Li). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions and finite nuclear mass is used. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The results of the calculations allow for refining the experimental energy levels determined with respect to the (2)S 1s(2)2s(1) ground state.     

Application of explicitly correlated Gaussian functions for calculations of the ground state of the beryllium atom

The electronic energy of atoms and molecules may be evaluated accurately by the use of wave functions where the interelectronic distances are explicitly present. In particular, explicitly correlated Gaussian-type functions make these types of calculations feasible and computationally tractable even for more extended systems. The resulting multielectron integrals may be reduced to standard one- and two-electron integrals that are readily evaluated. Initial calculations have been made for the Be atom where all four electrons were correlated at the same time. The preliminary results show that accurate results may be obtained. © 1993 John Wiley & Sons, Inc.     

Jastrow correlated and quantum Monte Carlo calculations for the low-lying states of the carbon atom

Different computational methods are employed to calculate excitation energies of the carbon atom. Explicitly correlated wave functions have been obtained in a Variational Monte Carlo calculation. Fixed node Diffusion Monte Carlo calculations for the lowest energy excited states of a given symmetry are reported. A systematic and quantitative analysis of the performance of the different schemes in the calculation of the excitation energy of up to 27 excited states of the carbon atom is carried out. The quality of the different methods have been studied in terms of the deviation with respect to the experimental excitation energies. A good agreement with the experimental values has been reached.     

Explicitly correlated coupled cluster calculations for the propargyl cation (H2C3H+) and related species

The vibrations of the propargyl cation (H(3)C(3)H(+)) have been studied by vibrational configuration interaction (VCI) calculations, using explicitly correlated coupled cluster theory at the CCSD(T*)-F12a level to determine the underlying 12-dimensional potential energy surface. The wavenumbers of the fundamental vibrations are predicted with an accuracy of ca. 5 cm(-1). Harmonic wavenumber shifts for three different energy minima of the complex H(2)C(3)H(+)·Ar are combined with the corresponding VCI values in order to provide a comparison with recent infrared photodissociation (IRPD) spectra (A. M. Ricks et al., J. Chem. Phys., 2010, 132, 051101). An excellent agreement between experiment and theory is obtained for bands ν(2) (symm. CH stretch), ν(3) (pseudoantisymm. CC stretch), and ν(4) (CH(2) scissoring). However, reassignments are suggested for the bands observed at 3238 cm(-1), the "doublets" around 3093 and 1111 cm(-1), and the band at 3182 cm(-1). The assignment of the latter to the asymmetric CH stretching vibration of c-C(3)H·Ar is certainly wrong; the combination tone ν(3) + ν(5) of H(2)C(3)H(+)·Ar is a more likely candidate. Furthermore, accurate proton affinities are predicted for the carbenes H(2)C(n) with n = 3-8, thereby providing data of interest for interstellar cloud chemistry.     

Measurement of the polarizabilities ofn 2 D Rydberg states of cesium

The tensor polarizabilities of thenD states of cesium withn=22–55 were determined by Doppler-free two-photon absorption spectroscopy. In general the results are in agreement with theoretical predictions. The large discrepancy between them forn>45 is discussed.Sponsored by NSFC     

Ab initio and quantum-defect calculations for the Rydberg states of ArH

Potential energy curves were evaluated for the ground and thirteen low-lying excited electronic states of the ArH molecule over a wide range of internuclear distances by the multi-reference averaged quadratic coupled cluster method. The ab initio energy differences and transition dipole moments were used to estimate Einstein emission coefficients, absorption oscillator strengths and radiative lifetimes. Diagonal and off-diagonal quantum defects, as functions of internuclear distance, were extracted from ab initio potentials of the lowest Rydberg states of the neutral ArH molecule by taking account of configuration interaction between Rydberg series converging to the ground and two electronic excited states of the ArH(+) cation. The derived quantum-defect functions were used to generate manifolds of higher excited Rydberg states. The agreement between experimental and calculated energies and radiative transition probabilities was found to be as good as or better than that obtained by earlier calculations.     

Explicitly correlated treatment of H2NSi and H2SiN radicals: electronic structure calculations and rovibrational spectra

Various ab initio methods are used to compute the six dimensional potential energy surfaces (6D-PESs) of the ground states of the H(2)NSi and H(2)SiN radicals. They include standard coupled cluster (RCCSD(T)) techniques and the newly developed explicitly correlated RCCSD(T)-F12 methods. For H(2)NSi, the explicitly correlated techniques are viewed to provide data as accurate as the standard coupled cluster techniques, whereas small differences are noticed for H(2)SiN. These PESs are found to be very flat along the out-of-plane and some in-plane bending coordinates. Then, the analytic representations of these PESs are used to solve the nuclear motions by standard perturbation theory and variational calculations. For both isomers, a set of accurate spectroscopic parameters and the vibrational spectrum up to 4000 cm(-1) are predicted. In particular, the analysis of our results shows the occurrence of anharmonic resonances for H(2)SiN even at low energies.     

Newton–Raphson optimization of the explicitly correlated Gaussian functions for calculations of the ground state of the helium atom

Explicitly correlated Gaussian functions have been used in variational calculations on the ground state of the helium atom. The major problem of this application, as well as in other applications of the explicitly correlated Gaussian functions to compute electronic energies of atoms and molecules, is the optimization of the nonlinear parameters involved in the variational wave function. An effective Newton–Raphson optimization procedure is proposed based on analytic first and second derivatives of the variational functional with respect to the Gaussian exponents. The algorithm of the method and its computational implementation is described. The application of the method to the helium atom shows that the Newton–Raphson procedure leads to a good convergence of the optimization process. © 1994 by John Wiley & Sons, Inc.     

Communication: quasiclassical trajectory calculations of correlated product-state distributions for the dissociation of (H2O)2 and (D2O)2

Stimulated by recent experiments [B. E. Rocher-Casterline, L. C. Ch'ng, A. K. Mollner, and H. Reisler, J. Chem. Phys. 134, 211101 (2011)], we report quasiclassical trajectory calculations of the dissociation dynamics of the water dimer, (H(2)O)(2) (and also (D(2)O)(2)) using a full-dimensional ab initio potential energy surface. The dissociation is initiated by exciting the H-bonded OH(OD)-stretch, as done experimentally for (H(2)O)(2). Normal mode analysis of the fragment pairs is done and the correlated vibrational populations are obtained by (a) standard histogram binning (HB), (b) harmonic normal-mode energy-based Gaussian binning (GB), and (c) a modified version of (b) using accurate vibrational energies obtained in the Cartesian space. We show that HB allows opening quantum mechanically closed states, whereas GB, especially via (c), gives physically correct results. Dissociation of both (H(2)O)(2) and (D(2)O)(2) mainly produces either fragment in the bending excited (010) state. The H(2)O(J) and D(2)O(J) rotational distributions are similar, peaking at J = 3-5. The computations do not show significant difference between the ro-vibrational distributions of the donor and acceptor fragments. Diffusion Monte Carlo computations are performed for (D(2)O)(2) providing an accurate zero-point energy of 7247 cm(-1), and thus, a benchmark D(0) of 1244 ± 5 cm(-1).     

Explicitly correlated treatment of the Ar-NO+ cation

We present an application of the recently developed explicitly correlated coupled cluster method to the generation of the three-dimensional potential energy surface (PES) of the Ar-NO(+) cationic complex. A good overall agreement is found with the standard coupled clusters techniques employing correlation consistent atomic basis sets (aug-cc-pVnZ, n= D, T, Q) of Wright et al. This PES is then used in quantum close-coupling scattering and variational calculations to treat the nuclear motions. The bound states energies of the Ar-NO(+) complex obtained by both approaches are in good agreement with the available experimental results. The analysis of the vibrational wavefunctions shows strong anharmonic resonances between the low frequency modes (intermonomer bending and stretching modes) and the wavefunctions exhibit large amplitude motions.     

Solvent configuration-interaction calculations of intermolecular states in molecule-(atom)N clusters: application to Br2-4HeN

We describe variational calculations of J=0 intermolecular states in Br(2)-(4)He(N) clusters. The method employed is analogous to configuration-interaction calculations in electronic-structure work and relies on the ability to express the intermolecular Hamiltonian H(v) as a sum of one- and two-body terms. A basis set is built up from solutions to the Schr?dinger equation in which only the one-body terms of H(v) are included. These configurations are products of N=1 eigenstates. The matrix of H(v) in a symmetry-adapted configuration basis is then computed, the two-body terms of H(v) serving to couple different configurations. This computation involves integrals of dimension five or less. Filter diagonalization is then used to obtain energies and eigenfunctions within a selected energy range. Results on clusters having N=2-5 are reported.     

Experiments and quantum-chemical calculations on Rydberg states of H2CS in the region 5.6-9.5 eV

Absorption spectrum of H(2)CS in the region 5.6-9.5 eV was recorded with a continuously tunable light source of synchrotron radiation. After we subtracted absorption bands of CS(2), our spectrum clearly shows vibrational progressions associated with transitions (1)A(1)(pi,pi*)-X (1)A(1) and (1)B(2)(n,4s)-X (1)A(1) in the region 5.6-6.7 eV. A spectrum from which absorption of C(2)H(4) and CS(2) are subtracted shows several discrete bands in the region 6.9-9.5 eV. A Rydberg state (1)B(2)(n,4p(z)) lying below Rydberg state (1)A(1)(n,4p(y)) is confirmed, and the C-H symmetric stretching (nu(1)) and CH out-of-plane bending (nu(4)) modes for a transition (1)B(2)(n,4s)-X (1)A(1) are identified. New transitions to Rydberg states associated with excitation to 5s-11s, 5p(z)-7p(z), 5p(y)-7p(y), and 3d-6d are identified based on quantum defects and comparison with vertical excitation energies predicted with time-dependent density-functional theory (TD-DFT) and outer-valence Green's-function (OVGF) methods. For lower excited states predictions from these TD-DFT6-31+G calculations agree satisfactorily with experimental values, but for higher Rydberg states the OVGF method using aug-cc-pVTZ basis set augmented with extra diffuse functions yields more accurate predictions of excitation energies.     

Configuration interaction calculations on the 2P ground state of boron atom and C+ using Slater orbitals

Configuration Interaction (CI) calculations on the ground ²P state of boron atom are presented using a wave function expansion constructed with L‐S eigenfunction configurations of s‐, p‐, and d‐Slater orbitals. Two procedures of optimization of the orbital exponents have been investigated. First, CI(SD) calculations including few types of configurations and full optimization of the orbital exponents led to the energy ?24.63704575 a.u. Second, full‐CI (FCI) calculations including a large number of configuration types using a fixed set of orbital exponents for all configurations gave ?24.63405222 a.u. using the basis [4s3p2d] and 2157 configurations, and to an improved result of ?24.64013999 a.u. for 3957 configurations and a [5s4p3d] basis. This last result is better than earlier calculations of Schaefer and Harris (Phys Rev 1968, 167, 67), and compares well with the recent ones from Froese Fischer and Bunge (personal communication). In addition, using the same wave functions, CI calculations of the boron isoelectronic ion C⁺ have been performed obtaining an energy of ?37.41027598 a.u. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Explicitly correlated coupled cluster calculations for the benzenium ion (C6H7(+)) and its complexes with Ne and Ar

Explicitly correlated coupled cluster theory at the CCSD(T)-F12x (x = a, b) level (Adler, T. B.; Knizia, G.; Werner, H.-J. J. Chem. Phys. 2007, 127, 221106) has been employed in a study of the benzenium ion (C6H7(+)) and its complexes with a neon or an argon atom. The ground-state rotational constants of C6H7(+) are predicted to be A0 = 5445 MHz, B0 = 5313 MHz, and C0 = 2731 MHz. Anharmonic vibrational wavenumbers of this cation were obtained by combination of harmonic CCSD(T*)-F12a values with anharmonic contributions calculated by double-hybrid density functional theory at the B2PLYP-D level. For the complexes of C6H7(+) with Ne or Ar, the lowest energy minimum is of π-bonded structure. The corresponding dissociation energies D0 are estimated to be 160 and 550 cm(-1), respectively. There is no indication of H-bonds to the aromatic or aliphatic hydrogen atoms. Instead, three nonequivalent local energy minima were found for nuclear configurations where the rare-gas atom lies in the ring-plane and approximatly points to the center of one of the six CC bonds.     

The Rydberg states of trans-butadiene from generalized valence bond and configuration interaction calculations

Self-consistent ab initio generalized valence bond (GVB) and configuration interaction (Cl) calculations are presented for the Rydberg states of trans-1,3-butadiene. Five Rydberg series were identified, three optically allowed (np, np, and nf_{z ³}) and two optically forbidden (ns and nd_{z ²}). It is shown that, except for the Λ～ and F? bands (which correspond to the non-valence 1 ¹B _u and the valence 2 ¹A _g states, respectively) all the transitions observed in the ultra-violet (UV) and electron-impact (EI) spectra, and in the two-photon spectra, can be assigned to members of these Rydberg series.