Fully quantum rovibrational calculation of the He(H2) bound and resonance states

In a recent paper [J. Chem. Phys. 2005, 122, 124318], a full-dimensional quantum method, designed to efficiently compute the rovibrational states of triatomic systems with long-range interactions, was applied to the benchmark Li-(H2) ion-molecule system. The method incorporates several key features in order to accurately represent the rovibrational Hamiltonian using only modestly sized basis sets: (1) exact analytical treatment of Coriolis coupling; (2) a single bend-angle basis for all rotational states; (3) phase space optimization of the vibrational basis; (4) G(4) symmetry adaptation of the rovibrational basis. In this paper, the same methodology is applied for the first time to a van der Waals complex system, He(H2). As in the Li-(H2) study, all of the rovibrational bound states, and a number of resonance states, are computed to very high accuracy (1/10,000 of a wavenumber or better). Three different isotopologues are considered, all of which are found to have a single bound state with a very low binding energy. Several extremely long-lived Feshbach resonances are also reported.     

Rovibrational states of the H2O-H2 complex: an ab initio calculation

All bound rovibrational levels of the H(2)O-H(2) dimer are calculated for total angular momentum J = 0-5 on two recent intermolecular potential surfaces reported by Valiron et al. [J. Chem. Phys. 129, 134306 (2008)] and Hodges et al. [J. Chem. Phys. 120, 710 (2004)] obtained through ab initio calculations. The method used handles correctly the large amplitude internal motions in this complex; it involves a discrete variable representation of the intermolecular distance coordinate R and a basis of coupled free rotor wave functions for the hindered internal rotations and the overall rotation of the dimer. The basis is adapted to the permutation symmetry associated with the para/ortho (p/o) nature of both H(2)O and H(2) as well as to inversion symmetry. Dimers containing oH(2) are more strongly bound than dimers with pH(2), as expected, with dissociation energies D(0) of 33.57, 36.63, 53.60, and 59.04 cm(-1)for pH(2)O-pH(2), oH(2)O-pH(2), pH(2)O-oH(2), and oH(2)O-oH(2), respectively, on the potential of Valiron et al. that corresponds to a binding energy D(e) of 235.14 cm(-1). Rovibrational wave functions are computed as well and the nature of the bound states in the four different dimer species is discussed. Converged rovibrational levels on both potentials agree well with the high-resolution spectrum reported by Weida and Nesbitt [J. Chem. Phys. 110, 156 (1999)]; the hindered internal rotor model that was used to interpret this spectrum is qualitatively correct.     

Exploring the new three-dimensional ab initio interaction energy surface of the Ar-HF complex: rovibrational calculations for Ar-HF and Ar-DF with vibrationally excited diatoms

Several features and the performance of the recently published [P. Jankowski and M. Ziolkowski, Mol. Phys. 104, 2293 (2006)] three-dimensional intermolecular potential energy surface for the Ar-HF complex have been investigated. This full-dimensional surface has been obtained using the method of the local expansion of the exact interaction energy surface [P. Jankowski, J. Chem. Phys. 121, 1655 (2004)] in the Taylor series with respect to intramolecular coordinates. The interaction energies have been calculated with the coupled-cluster supermolecular method with single, double, and noniterative triple excitations. The convergence of the interaction energy with respect to the size of the basis set is discussed. The two-dimensional surfaces resulting from averaging of the full-dimensional surface over the intramolecular vibration of HF have been obtained and directly compared to the empirical H6(4,3,2) set of surfaces proposed by Hutson [J. Chem. Phys. 96, 6752 (1992)]. A very good agreement has been observed. The averaged potentials have been used to calculate the rovibrational energy levels of the Ar-HF and Ar-DF complexes and compared to the experimental data. The accuracy of rovibrational calculations achieved with the new surface is much better than with any of the ab initio surfaces available so far. Predictions of the rovibrational energy levels and spectroscopic constants have also been done for Ar-HF with HF in the v=4,5 vibrational states, and for Ar-DF and DF in the v=3,4 states. The full-dimensional surface studied in this paper is the first ab initio surface which is fully compatible with the empirical H6(4,3,2) surface proposed by Hutson.     

Spectroscopy of Ar-SH and Ar-SD. II. Determination of the three-dimensional intermolecular potential-energy surface

All the pure rotational transitions reported in the previous studies [J. Chem. Phys. 113, 10121 (2000); J. Mol. Spectrosc. 222, 22 (2003)] and newly observed rotation-vibration transitions, P = 1/2 <-- 3/2, for Ar-SH and Ar-SD [J. Chem. Phys. (2005), the preceding paper] have been simultaneously analyzed to determine a new intermolecular potential-energy surface of Ar-SH in the ground state. A Schrodinger equation considering the three-dimensional freedom of motion for an atom-diatom complex in the Jacobi coordinate, R, theta, and r, was numerically solved to obtain energies of the rovibrational levels using the discrete variable representation method. A three-dimensional potential-energy surface is determined by a least-squares fitting with initial values of the parameters for the potential obtained by ab initio calculations at the RCCSD(T)/aug-cc-pVTZ level of theory. The potential well reproduces all the observed data in the microwave and millimeter wave regions with parity doublings and hyperfine splittings. Several low-lying rovibrational energies are calculated using the new potential-energy surface. The dependence of the interaction energy between Ar and SH(2pi(i)) on the bond length of the SH monomer is discussed.     

Basis set convergence of molecular correlation energy differences within the random phase approximation

The basis set convergence of energy differences obtained from the random phase approximation (RPA) to the correlation energy is investigated for a wide range of molecular interactions. For dispersion bound systems the basis set incompleteness error is most pronounced, as shown for the S22 benchmark [P. Jurecka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The use of very large basis sets (> quintuple-zeta) or extrapolation to the complete basis set (CBS) limit is necessary to obtain a reliable estimate of the binding energy for these systems. Counterpoise corrected results converge to the same CBS limit, but counterpoise correction without extrapolation is insufficient. Core-valence correlations do not play a significant role. For medium- and short-range correlation, quadruple-zeta results are essentially converged, as demonstrated for relative alkane conformer energies, reaction energies dominated by intramolecular dispersion, isomerization energies, and reaction energies of small organic molecules. Except for weakly bound systems, diffuse augmentation almost universally slows down basis set convergence. For most RPA applications, quadruple-zeta valence basis sets offer a good balance between accuracy and efficiency.     

Three-dimensional potential energy surface of the Ar-OH(2Pi i) complex

Pure rotational transitions in the ground state for Ar-OH and Ar-OD [Y. Ohshima et al., J. Chem. Phys. 95, 7001 (1991) and Y. Endo et al., Faraday Discuss. 97, 341 (1994)], those in the excited states of the OH vibration, nu(s)=1 and 2, observed by Fourier-transform microwave spectroscopy in the present study, rotation-vibration transitions observed by infrared-ultraviolet double-resonance spectroscopy [K. M. Beck et al., Chem. Phys. Lett. 162, 203 (1989) and R. T. Bonn et al., J. Chem. Phys. 112, 4942 (2000)], and the P-level structure observed by stimulated emission pumping spectroscopy [M. T. Berry et al., Chem. Phys. Lett. 178, 301 (1991)] have been simultaneously analyzed to determine the potential energy surface of Ar-OH in the ground state. A Schrodinger equation, considering all the freedom of motions for an atom-diatom system in the Jacobi coordinate, R, theta, and r, was numerically solved to obtain energies of the rovibrational energy levels using the discrete variable representation method. A three-dimensional potential energy surface is determined by a least-squares fitting. In the analysis the potential parameters, obtained by ab initio calculations at the RCCSD(T) level of theory with a set of basis functions of aug-cc-pVTZ and midbond functions, are used as initial values. The determined intermolecular potential energy surface and its dependence on the OH monomer bond length are compared with those of an isovalent radical complex, Ar-SH.     

Rovibrational spectroscopy calculations of neon dimer using a phase space truncated Weyl-Heisenberg wavelet basis

In a series of earlier articles [B. Poirier J. Theor. Comput. Chem. 2, 65 (2003); B. Poirier and A. Salam J. Chem. Phys. 121, 1690 (2004); B. Poirier and A. Salam J. Chem. Phys. 121, 1740 (2004)], a new method was introduced for performing exact quantum dynamics calculations in a manner that formally defeats exponential scaling with system dimensionality. The method combines an optimally localized, orthogonal Weyl-Heisenberg wavelet basis set with a simple phase space truncation scheme, and has already been applied to model systems up to 17 degrees of freedom (DOF's). In this paper, the approach is applied for the first time to a real molecular system (neon dimer), necessitating the development of an efficient numerical scheme for representing arbitrary potential energy functions in the wavelet representation. All bound rovibrational energy levels of neon dimer are computed, using both one DOF radial coordinate calculations and a three DOF Cartesian coordinate calculation. Even at such low dimensionalities, the approach is found to be competitive with another state-of-the-art method applied to the same system [J. Montgomery and B. Poirier J. Chem. Phys. 119, 6609 (2003)].     

Close-coupling study of rotational energy transfer of CO (upsilon=2) by collisions with He atoms

Quantum close-coupling scattering calculations of rotational energy transfer in the vibrationally excited CO due to collisions with He atom are presented for collision energies between 10(-5) and approximately 1000 cm-1 with CO being initially in the vibrational level upsilon=2 and rotational levels j=0,1,4, and 6. The He-CO interaction potential of Heijmen et al. [J. Chem. Phys. 107, 9921 (1997)] was adopted for the calculations. Cross sections for rovibrational transitions and state-to-state rotational energy transfer from selected initial rotational levels were computed and compared with recent measurements of Carty et al. [J. Chem. Phys. 121, 4671 (2004)] and available theoretical results. Comparison in all cases is found to be excellent, providing a stringent test for the scattering calculations as well as the reliability of the He-CO interaction potential by Heijmen et al.     

Estimated MP2 and CCSD(T) interaction energies of n-alkane dimers at the basis set limit: comparison of the methods of Helgaker et al. and Feller

The MP2 (the second-order M?ller-Plesset calculation) and CCSD(T) (coupled cluster calculation with single and double substitutions with noniterative triple excitations) interaction energies of all-trans n-alkane dimers were calculated using Dunning's [J. Chem. Phys. 90, 1007 (1989)] correlation consistent basis sets. The estimated MP2 interaction energies of methane, ethane, and propane dimers at the basis set limit [EMP2(limit)] by the method of Helgaker et al. [J. Chem. Phys. 106, 9639 (1997)] from the MP2/aug-cc-pVXZ (X=D and T) level interaction energies are very close to those estimated from the MP2/aug-cc-pVXZ (X=T and Q) level interaction energies. The estimated EMP2(limit) values of n-butane to n-heptane dimers from the MP2/cc-pVXZ (X=D and T) level interaction energies are very close to those from the MP2/aug-cc-pVXZ (X=D and T) ones. The EMP2(limit) values estimated by Feller's [J. Chem. Phys. 96, 6104 (1992)] method from the MP2/cc-pVXZ (X=D, T, and Q) level interaction energies are close to those estimated by the method of Helgaker et al. from the MP2/cc-pVXZ (X=T and Q) ones. The estimated EMP2(limit) values by the method of Helgaker et al. using the aug-cc-pVXZ (X=D and T) are close to these values. The estimated EMP2(limit) of the methane, ethane, propane, n-butane, n-pentane, n-hexane, n-heptane, n-octane, n-nonane, and n-decane dimers by the method of Helgaker et al. are -0.48, -1.35, -2.08, -2.97, -3.92, -4.91, -5.96, -6.68, -7.75, and -8.75 kcal/mol, respectively. Effects of electron correlation beyond MP2 are not large. The estimated CCSD(T) interaction energies of the methane, ethane, propane, and n-butane dimers at the basis set limit by the method of Helgaker et al. (-0.41, -1.22, -1.87, and -2.74 kcal/mol, respectively) from the CCSD(T)/cc-pVXZ (X=D and T) level interaction energies are close to the EMP2(limit) obtained using the same basis sets. The estimated EMP2(limit) values of the ten dimers were fitted to the form m0+m1X (X is 1 for methane, 2 for ethane, etc.). The obtained m0 and m1 (0.595 and -0.926 kcal/mol) show that the interactions between long n-alkane chains are significant. Analysis of basis set effects shows that cc-pVXZ (X=T, Q, or 5), aug-cc-pVXZ (X=D, T, Q, or 5) basis set, or 6-311G** basis set augmented with diffuse polarization function is necessary for quantitative evaluation of the interaction energies between n-alkane chains.     

The structure and binding energies of the van der Waals complexes of Ar and N2 with phenol and its cation, studied by high level ab initio and density functional theory calculations

We have investigated, using both ab initio and density functional theory methods, the minimum energy structures and corresponding binding energies of the van der Waals complexes between phenol and argon or the nitrogen molecule, and the corresponding complexes involving the phenol cation. Structures were obtained at the MP2 level using a large basis, and the corresponding energies were corrected for basis set superposition error (BSSE), higher order electron correlation effects, and for basis set size. The structures of the global minima were further refined for the effects of BSSE and the corresponding binding energies were evaluated. For each neutral species, we find only a single true minimum, pi bonded for argon and OH bonded for nitrogen. For both cationic species, we find that the OH-bonded complex is preferred over other minima which we have identified as having Ar or N(2) between exogeneous atoms. The ab initio calculations are generally in excellent agreement with experimental binding energies and rotational constants. We find that the B3LYP functional is particularly poor at describing these complexes, while a density functional theory (DFT) method with an empirical correction for dispersive interactions (DFT-D) is very successful, as are some of the new functionals proposed by Zhao and Truhlar [J. Phys. Chem. A 109, 5656 (2005); J. Chem. Theory Comput. 2, 1009 (2006); Phys. Chem. Chem. Phys. 7, 2701 (2005); J. Phys. Chem. A 108, 6908 (2004)]. Both the ab initio and DFT-D methods accurately predict the intermolecular vibrational modes.     

Ab initio design of picosecond infrared laser pulses for controlling vibrational-rotational excitation of CO molecules

Optimal control of rovibrational excitations of the CO molecule using picosecond infrared laser pulses is described in the framework of the electric-nuclear Born-Oppenheimer approximation [G. G. Balint-Kurti et al., J. Chem. Phys. 122, 084110 (2005)]. The potential energy surface of the CO molecule in the presence of an electric field is calculated using coupled cluster theory with a large orbital basis set. The quantum dynamics of the process is treated using a full three dimensional treatment of the molecule in the laser field. The detailed mechanisms leading to efficient control of the selected excitation processes are discussed.     

Effect of the overall rotation on the cis-trans isomerization of HONO induced by an external field

Rovibrational eigenenergies of HONO are computed and compared to experimental energies available in the literature. For their computation, we use a previously developed potential energy surface (PES) and a newly derived exact kinetic energy operator (KEO) including the overall rotation for a tetra-atomic molecule in non-orthogonal coordinates. In addition, we use the Heidelberg Multi-Configuration Time-Dependent Hartree (MCTDH) package. We compare the experimental rovibrational eigenvalues of HONO available in the literature with those obtained with MCTDH and a previously developed potential energy surface (PES) [F. Richter et al., J. Chem. Phys., 2004, 120, 1306.] for the cis geometry. The effect of the overall rotation on the process studied in our previous work on HONO [F. Richter et al., J. Chem. Phys., 2007, 127, 164315.] leading to the cis→trans isomerization of HONO is investigated. This effect on this process is found to be weak.     

Rotational spectrum, potential energy surface, and bound states of the weakly bound complex He-N2O

Pure rotational transitions of the weakly bound complex He-N(2)O and three minor isotopomers (He-(14)N(15)NO, He-(15)N(14)NO, and He-(15)N(15)NO) were measured in the frequency region from 6 to 20 GHz. Predictions for the microwave transition frequencies were based on the infrared work by Tang and McKellar [J. Chem. Phys. 117, 2586 (2002)]. In the case of (14)N containing isotopomers, nuclear quadrupole hyperfine structure of the rotational transitions was observed and analyzed. The resulting spectroscopic parameters were used to determine geometrical and dynamical information about the complex. An ab initio potential energy surface was calculated at the coupled cluster level of theory with single and double excitations and perturbative inclusion of triple excitations. This surface was constructed using the augmented correlation consistent polarized valence triple zeta basis set for all atoms with the inclusion of bond functions for the van der Waals bond. Bound state calculations were done to determine the energies of low-lying rovibrational levels that are supported by the potential energy surface. The resulting transition energies agree with the experimental values to 1% or better.     

Simple coupled-cluster singles and doubles method with perturbative inclusion of triples and explicitly correlated geminals: The CCSD(T)R12 model

To approach the complete basis set limit of the "gold-standard" coupled-cluster singles and doubles plus perturbative triples [CCSD(T)] method, we extend the recently proposed perturbative explicitly correlated coupled-cluster singles and doubles method, CCSD(2)(R12) [E. F. Valeev, Phys. Chem. Chem. Phys. 8, 106 (2008)], to account for the effect of connected three-electron correlations. The natural choice of the zeroth-order Hamiltonian produces a perturbation expansion with rigorously separable second-order energy corrections due to the explicitly correlated geminals and conventional triple and higher excitations. The resulting CCSD(T)(R12) energy is defined as a sum of the standard CCSD(T) energy and an amplitude-dependent geminal correction. The method is technically very simple: Its implementation requires no modification of the standard CCSD(T) program and the formal cost of the geminal correction is small. We investigate the performance of the open-shell version of the CCSD(T)(R12) method as a possible replacement of the standard complete-basis-set CCSD(T) energies in the high accuracy extrapolated ab initio thermochemistry model of Stanton et al. [J. Chem. Phys. 121, 11599 (2004)]. Correlation contributions to the heat of formation computed with the new method in an aug-cc-pCVXZ basis set have mean absolute basis set errors of 2.8 and 1.0 kJmol when X is T and Q, respectively. The corresponding errors of the standard CCSD(T) method are 9.1, 4.0, and 2.1 kJmol when X=T, Q, and 5. Simple two-point basis set extrapolations of standard CCSD(T) energies perform better than the explicitly correlated method for absolute correlation energies and atomization energies, but no such advantage found when computing heats of formation. A simple Schwenke-type two-point extrapolation of the CCSD(T)(R12)aug-cc-pCVXZ energies with X=T,Q yields the most accurate heats of formation found in this work, in error on average by 0.5 kJmol and at most by 1.7 kJmol.     

Analytical treatment of Coriolis coupling for three-body systems

In a previous article [J. Chem. Phys. 108 (1998) 5216], an efficient method was presented for performing “exact” quantum calculations for the three-body rovibrational Hamiltonian, within the helicity-conserving approximation. This approach makes use of a certain three-body “effective potential,” enabling the same bend angle basis set to be employed for all values of the rotational quantum numbers, J, K and M. In the present work, the method is extended to incorporate Coriolis coupling, for which the relevant matrix elements are derived exactly. These can be used to solve the full three-body rovibrational problem, in the standard Jacobi coordinate vector embedding. Generalization of the method for coupled kinetic energy operators arising from other coordinate systems, embeddings, and/or system sizes, is also discussed.     

Electronic structure and spectrum of UO2 2+ and UO2Cl4 2-

A theoretical study is presented of the electronic spectra of the UO(2) (2+) and UO(2)Cl(4) (2-) ions, based on multiconfigurational perturbation theory (CASSCF/CASPT2), combined with a recently developed method to treat spin-orbit coupling [P.-A. Malmqvist et al., Chem. Phys. Lett. 357, 230 (2002); B. O. Roos and P.-A. Malmqvist, Phys. Chem. Chem. Phys. 6, 2919 (2004)]. The results are compared to the experimental spectroscopic data obtained for uranyl ions in Cs(2)UO(2)Cl(4) crystals from Denning [Struct. Bonding (Berlin) 79, 215 (1992)] and to previous theoretical calculations performed using a combined configuration-interaction spin-orbit treatment [Z. Zhang and R. M. Pitzer, J. Phys. Chem. A 103, 6880 (1999); S. Matsika and R. M. Pitzer, J. Phys. Chem. A. 105, 637 (2001)]. As opposed to the latter results, the calculations performed in this work point to a significant effect of the weakly bound equatorial chlorine ligands on the excitation energies.     

Variational formulation of perturbative explicitly-correlated coupled-cluster methods

We present a variational formulation of the recently-proposed CCSD(2)(R12) method [Valeev, Phys. Chem. Chem. Phys., 2008, 10, 106]. The centerpiece of this approach is the CCSD(2)(R12) Lagrangian obtained via L?wdin partitioning of the coupled-cluster singles and doubles (CCSD) Hamiltonian. Extremization of the Lagrangian yields the second-order basis set incompleteness correction for the CCSD energy. We also developed a simpler Hylleraas-type functional that only depends on one set of geminal amplitudes by applying screening approximations. This functional is used to develop a diagonal orbital-invariant version of the method in which the geminal amplitudes are fixed at the values determined by the first-order cusp conditions. Extension of the variational method to include perturbatively the effect of connected triples produces the method that approximates the complete basis-set limit of the standard CCSD plus perturbative triples [CCSD(T)] method. For a set of 20 small closed-shell molecules, the method recovered at least 94.5/97.3% of the CBS CCSD(T) correlation energy with the aug-cc-pVDZ/aug-cc-pVTZ orbital basis set. For 12 isogyric reactions involving these molecules, combining the aug-cc-pVTZ correlation energies with the aug-cc-pVQZ Hartree-Fock energies produces the electronic reaction energies with a mean absolute deviation of 1.4 kJ mol(-1) from the experimental values. The method has the same number of optimized parameters as the corresponding CCSD(T) model, does not require any modification of the coupled-cluster computer program, and only needs a small triple-zeta basis to match the precision of the considerably more expensive standard quintuple-zeta CCSD(T) computation.     

Unimolecular rovibrational bound and resonance states for large angular momentum: J=20 calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-->H+O2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.     

Accurate atomic Gaussian basis functions for second-row atoms: Small split-valence 3-21SP and 4-22SP basis sets

Small split-valence Gaussian 3-21SP and 4-22SP basis sets, previously reported for the first-row atoms [Chem. Phys. Lett., 229 , 151 (1996)], have been extended for the second-row elements of the Periodic Table. The total energies of the ground states of the second-row atoms calculated with the new basis sets are significantly lower than those obtained with the well-known 3-21G (J. Am. Chem. Soc., 104 , 2797 (1982)] and 4-31G [J. Chem. Phys., 56 , 5255 (1972)] basis sets. This is because, as first noted in our previous work for first-row atoms, that the 3-21G and 4-31G basis sets only correspond to a local minimum of the Hartree–Fock energy functional, which is relatively far from its global minimum. The proposed basis sets have been tested by performing geometry optimizations and calculations of normal frequencies in the harmonic approximation of some diatomic and polyatomic molecules at the Hartree–Fock level. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1200–1210     

A post-Hartree-Fock model of intermolecular interactions: inclusion of higher-order corrections

We have previously demonstrated that the dipole moment of the exchange hole can be used to derive intermolecular C(6) dispersion coefficients [J. Chem. Phys. 122, 154104 (2005)]. This was subsequently the basis for a novel post-Hartree-Fock model of intermolecular interactions [J. Chem. Phys. 123, 024101 (2005)]. In the present work, the model is extended to include higher-order dispersion coefficients C(8) and C(10). The extended model performs very well for prediction of intermonomer separations and binding energies of 45 van der Waals complexes. In particular, it performs twice as well as basis-set extrapolated MP2 theory for dispersion-bound complexes, with minimal computational cost.