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An efficient and highly vectorized implementation of the coupled cluster singles and doubles (CCSD) model using a direct atomic integral technique is presented. The minimal number of n6processes has been implemented for the most time consuming terms and point group symmetry is used to further reduce operation counts and memory requirements. The significantly increased application range of the CCSD method is illustrated with sample calculations on several systems with more than 500 basis functions. Furthermore, we present the basic trends of an open ended algorithm and discuss the use of integral prescreening. © 1996 American Institute of Physics.

A derivation of the linear response function for the Brueckner coupled cluster method is presented that enables the calculation of second-order molecular properties such as frequency-dependent polarizabilities. By using the Brueckner orbital variant of coupled cluster theory, the spurious pole structure inherent in the standard coupled cluster approach with orbital relaxation is avoided. © 1994 John Wiley & Sons, Inc.

We review recently developed methods to efficiently utilize the Cholesky decomposition technique in electronic structure calculations. The review starts with a brief introduction to the basics of the Cholesky decomposition technique. Subsequently, examples of applications of the technique to ab inito procedures are presented. The technique is demonstrated to be a special type of a resolution-of-identity or density-fitting scheme. This is followed by explicit examples of the Cholesky techniques used in orbital localization, computation of the exchange contribution to the Fock matrix, in MP2, gradient calculations, and so-called method specific Cholesky decomposition. Subsequently, examples of calibration of the method with respect to computed total energies, excitation energies, and auxiliary basis set pruning are presented. In particular, it is demonstrated that the Cholesky method is an unbiased method to derive auxiliary basis sets. Furthermore, details of the implementational considerations are put forward and examples from a parallel Cholesky decomposition scheme is presented. Finally, an outlook and perspectives are presented, followed by a summary and conclusions section. We are of the opinion that the Cholesky decomposition method is a technique that has been overlooked for too long. We have just recently started to understand how to efficiently incorporate the method in existing ab initio programs. The full potential of the Cholesky technique has not yet been fully explored.

The implementation of two simple ideas concerning the optimization of a many-electron ground state wavefunction is reported. Firstly, the wavefunction is written as a sum of non-orthogonal Slater determinants. Secondly, the optimization is carried out by adding one determinant at a time and determining the best possible orbitals to be used in that determinant. Technical details of gradient-optimization methods are included. Calculations on the electronic ground state of Be, BH and H2O indicate that near full-CI accuracy can be attained using a comparatively small number of determinants. Finally, it is conjectured that a geminal approach might provide an effective solution to the problem of initiating the optimization sequence for each successively added determinant. © 1993.

Decomposing the Hartree-Fock one-electron density matrix and a virtual pseudodensity matrix, we obtain an orthogonal set of normalized molecular orbitals with local character to be used in post-Hartree-Fock calculations. The applicability of the procedure is illustrated by calculating CCSD(T) energies and CCSD molecular properties in reduced active spaces. © 2010 American Institute of Physics.

A matrix decomposition method for the determination of the lowest eigenvalue of a Hermitian matrix is formulated as an approach to full configuration-interaction calculations on the ground state of many-electron systems. For a wavefunction of the form | ψ 〉 = ∑ | α,β 〉 C αβ the expansion coefficients are written as a separable sum of product terms, P α Q β The elements P a and Q β are then determined from the variation principle for each term. The corresponding Hermitian eigenvalue problem has a dimension which is essentially the square root of the dimension of the original problem. Preliminary calculations on the ground state of the beryllium atom indicate that nearly full configuration-interaction results can be obtained using a comparatively small number of product terms.

We introduce a response function formalism that enables smaller number of parameters than that defined in standard coupled cluster response theory. This is essential in the development of reduced scaling methods. The formalism is general and it applies to all parameterizations at all levels of the coupled cluster hierarchy. We show that to achieve physically reasonable results the parameterization must fulfill certain criteria. The linear response functions are derived and discussed in the context of optimized virtual orbitals and Cholesky decomposition of the cluster amplitudes. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

The computation of the frequency dependent linear and quadratic response functions is formulated at the full configuration interaction (FCI) level of theory. It is demonstrated that the frequency dependent polarizability (for real and imaginary frequencies) may be obtained with quadratic dependence on the error in the solution of the response equations. An efficient solution of the FCI response equations for large imaginary frequencies is developed. Initial application is to the Be atom in the standard 9s9p5d basis. Reported results include transition energies and dipole moments for the first few singlet and triplet S, P, and D states, the first polarizability at real and imaginary frequencies, the C6coefficient, and the static second hyperpolarizability. Comparison to prior theoretical results in this basis, and to experiment, is made where possible. It is the first time that many of these properties have been computed at the FCI level of theory for any system. © 1991 American Institute of Physics.

Using correlated ab initio methods, the polarizability of large [4n + 2]-annulenes is determined, showing that there exists an almost linear relation between the exaltation of magnetic susceptibility (a measure of aromaticity) and an equivalent enlargement of polarizability.

Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field (CASSCF) method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra- μ -acetato-dicopper(II), and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxiliary basis sets constructed from Cholesky decomposition of the atomic electron repulsion integrals. © 2008 American Institute of Physics.

We present a novel approach to the calculation of the Coulomb and exchange contributions to the total electronic energy in self consistent field and density functional theory. The numerical procedure is based on the Cholesky decomposition and involves decomposition of specific Hadamard product matrices that enter the energy expression. In this way, we determine an auxiliary basis and obtain a dramatic reduction in size as compared to the resolution of identity (RI) method. Although the auxiliary basis is determined from the energy expression, we have complete control of the errors in the gradient or Fock matrix. Another important advantage of this method specific Cholesky decomposition is that the exchange energy and Fock matrix can be evaluated with a linear scaling effort contrary to the RI method or standard Cholesky decomposition of the two-electron integral matrix. The methods presented show the same scaling properties as the so-called local density fitting methods, but with full error control. © 2008 American Institute of Physics.

In this work we present a theoretical and experimental study of the i 3Π−g→b 3∑+u transition dipole moment in molecular hydrogen. By means of translational spectroscopy the functional dependence on internuclear distance of the transition dipole moment was directly probed. Selective excitation of the i 3Π−g, N=1 level, being unaffected by rotational couplings with other 3d singly excited states, allows for straightforward comparison with ab initio calculations. Excellent agreement is found.

We report second order Møller-Plesset (MP2) and MP2-F12 total energies on He, Ne, Ar, H2 O, C H4, C2 H2, C2 H4, and C6 H6, using the correlation consistent basis sets, aug-cc-pVXZ (X=D-7). Basis set extrapolation techniques are applied to the MP2 and MP2-F12/B methods. The performance of the methods is tested in the calculations of the atoms, He, Ne, and Ar. It is indicated that the two-point extrapolation of MP2-F12/B with the basis sets (X=5,6) is the most reliable. Similar accuracy is obtained using two-point extrapolated conventional MP2 with the basis sets (X=6,7). For the molecules investigated the valence MP2 correlation energy is estimated within 1 m Eh. © 2007 American Institute of Physics.

In J. Chem. Phys. [107, 10823 (1997)], Rozyczko and Bartlett report an open-ended formula for equation-of-motion coupled cluster (EOM-CC) hyperpolarizabilities. We demonstrate that this formula is incompatible with the generic definition of EOM-CC properties and converges to a wrong full configuration limit. We derive the correct expressions for the EOM-CC quadratic and cubic response functions.

High-level quantum-chemical methods show that the binding in the inclusion complex of hexamethylbenzene (HMB) in 6-cycloparaphenilacetylene (6-CPPA) cannot be explained only in terms of electrostatic interactions - caused by the polarization associated to curved π-conjugated systems - and the inclusion of dispersion forces is definitely needed. The theoretical description of van der Waals interactions is notoriously complicated and in fact some DFT methods cannot even predict the existence of the relatively small supramolecular nanoring studied here. However, ab initio MP2 calculations agree with experimental data and show that, in the considered complex, the HMB fragment is placed at the center of the 6-CPPA ring. The binding energy, which is not available experimentally, is calculated to be around -14 kcal mol-1 with a lower limit of -19 kcal mol-1. © 2006 Wiley-VCH Verlag GmbH & Co. KGaA.

We present a general formalism where different levels of coupled cluster theory can be applied to different parts of the molecular system. The system is partitioned into subsystems by Cholesky decomposition of the one-electron Hartree-Fock density matrix. In this way the system can be divided across chemical bonds without discontinuities arising. The coupled cluster wave function is defined in terms of cluster operators for each part and these are determined from a set of coupled equations. The total wave function fulfills the Pauli-principle across all borders and levels of electron correlation. We develop the associated response theory for this multi-level coupled cluster theory and present proof of principle applications. The formalism is an essential tool in order to obtain size-intensive complexity in the calculation of local molecular properties.

The vertical iron-cyclopentadienyl distance in ferrocene has been determined using ab initio coupled-cluster theory. At the CCSD level, a TZV2P basis set yields a metal-ligand distance of 1.664 Å with all 96 electrons correlated and 1.672 Å with 66 electrons correlated. With 66 electrons correlated at the CCSD(T) level the equilibrium distance is 1.660 Å, in agreement with experiment (1.66 Å). © 1996 American Institute of Physics.

A new implementation of the approximate coupled cluster singles and doubles CC2 linear response model using Cholesky decomposition of the two-electron integrals is presented. Significantly reducing storage demands and computational effort without sacrificing accuracy compared to the conventional model, the algorithm is well suited for large-scale applications. Extensive basis set convergence studies are presented for the static and frequency-dependent electric dipole polarizability of benzene and C60, and for the optical rotation of CNOFH2 and (−)-trans-cyclooctene (TCO). The origin-dependence of the optical rotation is calculated and shown to persist for CC2 even at basis set convergence. Alfredo.Sanchez@uv.es

We propose an inherently origin invariant formulation of specific optical rotation obtained from the conventional velocity gauge expression by subtracting the static limit from the electric dipole-magnetic dipole polarizability: 〈〈p→,L→〉〉ω→〈〈p→,L→〉〉ω-〈〈p→,L→〉〉0. London (gauge including) atomic orbitals are therefore not needed to ensure origin invariance and, consequently, this modified velocity gauge formulation may be employed in conjunction with variational and non-variational quantum chemical methods alike. Sample calculations on S-propylene oxide and 3,4- methylenedioxymethamphetamine using self-consistent field and coupled cluster wave functions underline this point and show that the basis set convergence of the modified velocity gauge formulation is similar to the conventional length gauge and London expressions. © 2004 Elsevier B.V. All rights reserved.

Large differences have been reported in previous SCF calculations of the NMR shielding tensor of the ethylenic carbon atom in tetrachlorocyclopropene. Our calculations show that these differences are due to the use of different molecular geometries, not to differences in the methods applied to obtain gauge-invariance.

The three-dimensional intermolecular electric dipole moment surface of Ar–CO is calculated at the coupled cluster singles and doubles level of theory with the aug-cc-pVTZ basis set extended with a 3s3p2d1f1g set of midbond functions. Using the rovibrational energies and wave functions of our recent study [J. Chem. Phys. 117, 6562 (2002)], temperature-dependent spectral intensities are evaluated and compared to available experimental data. Based on the theoretical spectrum, alternative assignments of the experimentally observed lines in the fundamental band of CO around 2160 and 2166 cm−1 are suggested. Thomas.Bondo@uv.es

The intermolecular potential-energy surface pertaining to the interaction between benzene and N2 is investigated theoretically and experimentally. Accurate intermolecular interaction energies are evaluated for the benzene–N2 van der Waals complex using the coupled cluster singles and doubles including connected triples [CCSD(T)] method and the aug-cc-pVDZ basis set extended with a set of 3s3p2d1f1g midbond functions. After fitting the energies to an analytic function, the intermolecular Schrödinger equation is solved to yield energies, rotational constants, and Raman-scattering coefficients for the lowest intermolecular levels of several benzene–N2 isotopomers. Experimentally, intermolecular Raman spectra of jet-cooled h6- and d6-benzene–N2 measured at 0.03 cm−1 resolution by mass-selective, ionization-detected stimulated Raman spectroscopies are reported. Seven intermolecular bands are assigned for each isotopomer, including transitions involving intermolecular bending and stretching vibrations and internal rotation about the benzene C6 axis. These Raman data, together with measured rotational constants and binding energies obtained by other groups on benzene–N2, agree well with the theoretical results. Such agreement points to the promise of the quantum chemical methodology employed herein in future investigations of larger van der Waals complexes. tbonpe@uv.es

The small numerical rank of the two-electron integral matrix for large molecular systems and large basis sets was demonstrated. Though, the current implementation still requires some improvements on the calculations done in the inner most loop of the decomposition do not exploit the parsity in the Cholesky vectors. With respect to the practical applicability of the presented method an efficient approach to geometrical derivatives was imperative. Such an approach was obtained including certain derivative product functions and decomposing an expanded integral matrix.

The vertical spectrum of tetracyanoethylene was studied using coupled cluster theory. It was found that the lowest singlet-singlet transition, which corresponds to the excitation from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) excitation, occurs at 5.16 eV in the gas phase and is lowered approximately 0.1 eV due to solvent effects in acetonitrile. A parallel study on the ethene spectrum showed the quality of the basis sets and methods used, by placing the V state 7.92 eV above the ground state and giving an energy for the 0-0 transition of 5.42 eV to be compared with the experimental value of 5.50 eV.

A study of the intermolecular potential-energy surface (IPS) and the intermolecular states of the perprotonated and perdeuterated benzene–He complex is reported. From a fit to ab initio data computed within the coupled cluster singles and doubles including connected triples model for 280 interaction geometries, an analytic IPS including two- to four-body atom–atom terms is obtained. This IPS, and two other Lennard-Jones atom–atom surfaces from the literature, are each employed in dynamically exact (within the rigid-monomer approximation) calculations of J = 0 intermolecular states of the isotopomers. Rotational constants and Raman-scattering coefficients for intermolecular vibrational transitions are also calculated for each of the three surfaces. The calculated results are compared with experimental results reported herein pertaining to intermolecular Raman spectra of benzene–He. The calculated rotational constants are compared with experimental values from the literature. The fitted IPS of this work leads to calculated observables that match the experimental results very well. The IPSs from the literature are not as successful, specifically in regard to the intermolecular Raman spectra. Thomas.Bondo@uv.es

The first three-dimensional ab initio intermolecular potential energy surface of the Ar–CO van der Waals complex is calculated using the coupled cluster singles and doubles including connected triples model and the augmented correlation-consistent polarized valence quadruple zeta (aug-cc-pVQZ) basis set extended with a (3s3p2d1f1g) set of midbond functions. The three-dimensional surface is averaged over the three lowest vibrational states of CO. Rovibrational energies are calculated up to 50 cm−1 above the ground state, thus enabling comprehensive comparison between theory and available experimental data as well as providing detailed guidance for future spectroscopic investigations of higher-lying states. The experimental transitions are reproduced with a root-mean-square error of 0.13 cm−1, excluding states observed around 25 cm−1 above the ground state. The latter states are at variance with the experimentally deduced ordering.

An implementation of triples corrections for the calculation of the electronic ground states and for singlet and triplet excitation energies within the CC3 model is discussed. At most objects of size V2O2 and V3O are kept in memory and on disc, respectively (V is the number of virtual orbital and O is the number of occupied orbitals). The used strategy means that more terms that scales as V4O3 has to be calculated than if the triples amplitudes are kept on disc but it allows larger cases to be handled. Sample calculations are presented for the triplet excitation energies of benzene.

In a recent Letter, M. Rode et al. [Chem. Phys. Lett. 314 (1999) 326] claim the incapability of the coupled cluster singles and doubles model including connected triple excitations to describe the intermolecular interaction in the CO dimer. We have investigated the problem and found several facts in favor of the coupled cluster singles and doubles model including connected triple excitations being accurate even for the CO dimer.

We introduce an alternative to Almlöf and Häser’s Laplace transform decomposition of orbital energy denominators used in obtaining reduced scaling algorithms in perturbation theory based methods. The new decomposition is based on the Cholesky decomposition of positive semidefinite matrices. We show that orbital denominators have a particular short and size-intensive Cholesky decomposition. The main advantage in using the Cholesky decomposition, besides the shorter expansion, is the systematic improvement of the results without the penalties encountered in the Laplace transform decomposition when changing the number of integration points in order to control the convergence. Applications will focus on the coupled-cluster singles and doubles model including connected triples corrections [CCSD(T)], and several numerical examples are discussed. Alfredo.Sánchez@uv.es

An atomic integral direct implementation of the second order polarization propagator approximation (SOPPA) for the calculation of electronic excitation energies and oscillator strengths is presented. The SOPPA equations are solved iteratively using an integral direct approach and, contrary to previous implementations, the new algorithm does not require two-electron integrals in the molecular orbital basis. The linear transformation of trial vectors are calculated directly from integrals in the atomic orbital basis. In addition, the eigenvalue solver is designed to work efficiently with only three trial vectors per eigenvalue. Both of these modifications dramatically reduce the amount of disk space required, thus, increasing the range of applicability of the SOPPA method. Calculations of the lowest singlet excitation energies and corresponding dipole oscillator strengths for naphthalene and anthracene employing basis sets of 238 and 329 atomic orbitals, respectively, are presented. The overall agreement of our results with experimental spectra is good. The differences between the vertical excitation energies calculated by SOPPA and the position of the maximum intensity peaks in the experimental spectra are within the range of +/- 0.35 eV with two exceptions, the 4 (1)A(g) state of naphthalene and anthracene where a 0.85 eV and 0.41 eV deviation is found, respectively. The relatively large discrepancy for this transition is due to large contributions from two-electron excitations which cannot accurately be described in SOPPA. For naphthalene we find additional excitations to Rydberg states of (1)A(u) and B-1(2u) symmetry as compared with previous calculations. (C) 2000 American Institute of Physics. [S0021- 9606(00)30908-4].

The mechanism of the protonation of ferrocene, the simplest model for the electrophilic attack on a metallocene, has been studied extensively. However, neither experiment nor computation have reached agreement on the details of the mechanism. The different model calculations applied [Hartree–Fock, Moller–Plesset, and density functional theory (HF, MP2, and DFT) with different functionals] come to contradicting conclusions. As a complement to our previous work, we report the results obtained for neutral and protonated ferrocene using the coupled-cluster method [CCSD(T)] with polarized double- and triple-zeta basis sets. These calculations show that the metal-protonated and the agostic forms represent minima on the potential energy surface, whereas the ring-protonated form is higher in energy with no minimum structure identified. With regard to the reaction, these results indicate an exo reaction path. The CCSD(T) results are in good agreement with the predictions made by the DFT calculations, whereas the results obtained from the Hartree–Fock and MP2 computations appear to be incorrect.

The dielectric, refractivity, Kerr, and hyperpolarizability second virial coefficients for the helium and argon gases are evaluated for a wide range of temperatures using a semiclassical approach and the high quality frequency-dependent interaction induced electric polarizabilities and second hyperpolarizabilities of the previous paper. For helium and argon we obtain satisfactory agreement with most of the experimental data for the dielectric and the refractivity second virial coefficients. Our results confirm that the helium gas second Kerr virial coefficient is very small at temperatures beyond 70 K. For argon we obtain a very good agreement with a recent experimental determination at 632.8 nm, whereas we suggest that previous experimental results for 458 nm might be inaccurate. The ESHG results indicate a possible disagreement between a recent experimental determination and the semiclassical ansatz for the second hyperpolarizability virial coefficients. © 1999 American Institute of Physics.

The ground state potential energy surface of the Ar–N2 van der Waals complex is evaluated using the coupled cluster singles and doubles model, including connected triples corrections (CCSD(T)) and the aug-cc-pVTZ basis set extended with midbond functions. From the calculated ab initio potential the rovibronic spectroscopic properties are determined and compared with the available experimental data. Considerable improvement is obtained when four of the potential parameters are refined based on the Ar–14N2 rotational transition frequencies. The small discrepancies remaining demonstrate that the coupled cluster method can be used to predict the spectroscopic properties of van der Waals complexes.

We introduce a time-dependent coupled cluster based Lagrangian that includes orbital rotation. This Lagrangian is shown to give gauge invariant response properties for one-electron operators in the limit of a complete one-electron basis. The pole structure of the linear response function is compatible with that of the exact response function and the notorious problem of unphysical second-order poles in the Brueckner coupled cluster response theory is not present in this model. The total energy of the model is identical to the coupled cluster model using optimized orbitals recently revived by Sherrill et al. [J. Chem. Phys. 109, 4171 (1998)]. The model provides a straightforward approach for calculating magnetic response properties in a gauge invariant manner using coupled cluster type wave functions. © 1999 American Institute of Physics.

The frequency-dependent interaction induced polarizability and second hyperpolarizability of the argon dimer are computed for a range of internuclear distances employing the coupled cluster singles and doubles response approach. The frequency dependence of the interaction-induced properties is treated through second order in the frequency arguments using expansions in Cauchy moments and hyperpolarizability dispersion coefficients. The dielectric, the refractivity, the Kerr and the hyperpolarizability second virial coefficients are computed for a range of temperatures employing a recent accurate ab initio potential for the ground state of the argon dimer. For most of the computed virial coefficients good agreement is obtained between the present ab initio results and the available experimental data.

A computationally tractable doubles correction to excitation energies obtained in the random-phase approximation (RPA(D)) is presented. It gives excitation energies correct through second order in the ground-state fluctuation potential. RPA(D) has been tested for H2O, N-2, Ne, CH2, BH and C-2 using full configuration interaction (FCI) results as benchmarks. Comparison is made with other existing models of similar complexity. Overall the accuracy of excitation energies calculated using RPA(D) is similar to that obtained in the CC2, CIS(D) and SOPPA methods. The errors of the random-phase approximation excitation energies are typically reduced by a factor of two using the RPA(D) correction. The mean absolute deviation of RPA(D) and FCI excitation energies is 0.51 eV and for the majority of the excitations the RPA(D) results are lower than the FCI results. (C) 1998 Published by Elsevier Science B.V.

Valence and all-electron correlation energies of Ne, N2, and H2O at fixed experimental geometries are computed at the levels of second-order perturbation theory (MP2) and coupled cluster theory with singles and doubles excitations (CCSD), and singles and doubles excitations with a perturbative triples correction (CCSD(T)). Correlation-consistent polarized valence and core-valence basis sets up to sextuple zeta quality are employed. Guided by basis-set limits established by rij-dependent methods, a number of extrapolation schemes for use with the correlation-consistent basis sets are investigated. Among the schemes considered here, a linear least-squares procedure applied to the quintuple and sextuple zeta results yields the most accurate extrapolations.

The indirect nuclear spin–spin coupling constants of the gas phase oxonium (H 3 O + ) and hydroxyl (OH − ) ions, their temperature dependence and isotope shifts are predicted by ab initio calculations. The coupling constants are calculated as a function of the symmetric stretching and the inversional coordinates of H 3 O + and as a function of the bond length of OH − at the uncorrelated level of the random phase approximation (RPA), at the correlated levels of the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes – SOPPA(CCSD) – and of the multiconfigurational random phase approximation (MCRPA) with a large complete active space wavefunction. Effective ro-vibrational state dependent coupling constants are obtained from these functions and the corresponding ro-vibrational wavefunctions. The effective coupling constants for several states are then used to determine the temperature dependence of the coupling constants. The results are compared with the coupling constants of H 2 O and the nuclear magnetic shielding constants of H 3 O + and OH − .

The energy difference between the ring and fullerene forms of C24have been calculated by means of ab initio methods, and compared to density functional methods. The calculations strongly suggest that the fullerene form is favored by ∼80 kcal/mol over a monocyclic ring structure, which is at variance with experimental findings. Density functional results vary considerably, although functionals including exact exchange (B3LYP and B3PW91) give reasonable results when basis sets of at least triple zeta quality are employed. © 1998 American Institute of Physics.

An atomic integral-direct implementation of molecular linear-response properties and excited-state one-electron properties is presented for the coupled cluster models CCS, CC2, and CCSD. Sample calculations are presented for the polarizability of N2and for excited-state one-electron properties and transition-properties of furan. © 1998 American Institute of Physics.

Equilibrium dissociation energies De of the benzene-argon van der Waals complex are calculated in the ground state S0 and in the excited state S1 using integral-direct coupled cluster methods. The results confirm previous investigations of S0, showing that high quality correlation consistent basis sets and connected triple excitations are imperative for a good description of the van der Waals complex. We estimate the CCSD(T) dissociation energy De=389±2 cm-1 for the ground state S0. Using the CCSD linear response approach the frequency shift (redshift) δve=19 cm-1 is obtained. Accurate spectroscopic structural data and frequency shifts δv0 for the 60 1 band of the S1←S0 transition are available for most of the benzene-rare gas atom complexes. However, the experimental determination of absolute dissociation energies of these complexes is connected with much larger uncertainties. The theoretical result agrees very well with the experimentally available redshift, showing that integral-direct coupled cluster methods will become an important tool in the study of van der Waals complexes in the future. © 1998 American Institute of Physics.

We present an ab initio study of gauge invariance within coupled cluster linear response theory, exemplified by the electric dipole oscillator strength. Through sample calculations using H2, Ne, N2 and H2O as model systems, it is demonstrated that the coupled cluster singles and doubles (CCSD) method, in conjunction with augmented basis sets, provides a reasonable agreement between length, velocity and mixed gauge electronic oscillator strengths.

Multiple basis sets are used in calculations of perturbational corrections for triples replacements in the framework of single-reference coupled-cluster theory. We investigate a computational procedure, where the triples correction is calculated from a reduced space of virtual orbitals, while the full space is employed for the coupled-cluster singles-and-doubles model. The reduced space is either constructed from a prescribed unitary transformation of the virtual orbitals (for example into natural orbitals) with subsequent truncation, or from a reduced set of atomic basis functions. After the selection of a reduced space of virtual orbitals, the singles and doubles amplitudes obtained from a calculation in the full space are projected onto the reduced space, the remaining set of virtual orbitals is brought into canonical form by diagonalizing the representation of the Fock operator in the reduced space, and the triples corrections are evaluated as usual. The case studies include the determination of the spectroscopic constants of N2, F2, and CO, the geometry of O3, the electric dipole moment of CO, the static dipole polarizability of F−, and the Ne⋯Ne interatomic potential.

The first implementation of frequency-dependent hyperpolarizabilities is presented using coupled cluster quadratic response theory. The quadratic response functions are derived for the coupled clusted model hierarchy CCS, CC2 and CCSD and implemented for general frequency-dependent first hyperpolarizabilities. Calculations are performed on the second harmonic generation and the optical rectification hyperpolarizabilities of FH and the results are compared with experimental results and former theoretical investigations.

A systematic, high-level ab initio investigation of the water dimer has been performed. The oxygen-oxygen bond distance has been estimated to be around 2.90 A, about 0.05 A shorter than the experimentally estimated distance, challenging the accuracy of the latter. The interaction energy has been obtained at −5.0±0.1 kcal/mol, which compares favourably with the experimentally estimated value of −5.4±0.7 kcal/mol. The importance of employing basis sets that include diffuse functions in correlated calculations on hydrogen-bonded systems is confirmed. In correlated calculations on the water dimer and the hydrogen fluoride dimer, the counterpoise-corrected interaction energies converge considerably slower towards the basis set limit than do the uncorrected energies, provided that the correlation-consistent basis sets are augmented with diffuse functions.

An integral-direct implementation of first-order one-electron properties in the coupled cluster singles and doubles ~CCSD! model is presented. The implementation increases the range of applicability of CCSD first-order one-electron property calculations significantly compared to nondirect approaches. As an application a thorough basis set investigation is performed on five diatomic molecules at the Hartree‐Fock and CCSD levels for the molecular electric dipole moment, the molecular electric quadrupole moment, and the electric field gradient at the nuclei. In general, basis sets of polarized triple-zeta quality are the smallest to be recommended, and the convergence towards the basis set limit is faster at the Hartree‐Fock level than at the CCSD level. Among the properties considered, the electric dipole moment is the easiest to converge. The electric dipole and especially the electric quadrupole moment require diffuse functions for high accuracy. With standard basis sets, it is not possible to calculate electric field gradients consistently within three thousandths of an atomic unit of the basis set limit—for this purpose, elaborate nonstandard basis sets are required. The electric field gradients at the nuclei in HCN and the electric dipole moment of the furan molecule are calculated at the CCSD level employing up to 417 basis functions, further demonstrating the large-scale applicability of the implementation. © 1997 American Institute of Physics. @S0021-9606~97!02927-9#