Application of the quasi-variational coupled cluster method to the nonlinear optical properties of model hydrogen systems

We present a pilot application of the recently proposed quasi-variational coupled cluster method to the energies, polarizabilities, and second hyperpolarizabilities of model hydrogen chains. Relative to other single-reference methods of equivalent computational complexity, we demonstrate this method to be highly robust and especially useful when traditional coupled cluster theory fails to perform adequately. In particular, our results indicate it to be a suitable method for the black-box treatment of multiradicals, making it of widespread general interest and applicability.     

Gaussian induced dipole polarization model

A new induced dipole polarization model based on interacting Gaussian charge densities is presented. In contrast to the original induced point dipole model, the Gaussian polarization model is capable of finite interactions at short distances. Aspects of convergence related to the Gaussian model will be explored. The Gaussian polarization model is compared with the damped Thole-induced dipole model and the point dipole model. It will be shown that the Gaussian polarization model performs slightly better than the Thole model in terms of fitting to molecular polarizability tensors. An advantage of the model based on Gaussian charge distribution is that it can be easily generalized to other multipole moments and provide effective damping for both permanent electrostatic and polarization models. Finally, a method of parameterizing polarizabilities is presented. This method is based on probing a molecule with point charges and fitting polarizabilities to electrostatic potential. In contrast to the generic atom type polarizabilities fit to molecular polarizability tensors, probed polarizabilities are significantly more accurate in terms of reproducing molecular polarizability tensors and electrostatic potential, while retaining conformational transferability.     

How important are temperature effects for cluster polarizabilities?

State-of-the-art first-principle all-electron density functional theory calculations on small sodium clusters are performed to study the temperature dependency of their polarizabilities. For this purpose Born-Oppenheimer molecular dynamics simulations with more than 100,000 time steps (>200 ps) are recorded employing gradient corrected functionals in combination with a double-zeta valence polarization basis set. For each cluster 18 trajectories between 50 and 900 K are collected. The cluster polarizabilities are then calculated along these trajectories employing a triple-zeta valence polarization basis set augmented with field-induced polarization functions. The analysis of these calculations shows that the temperature dependency of the sodium cluster polarizabilities varies strongly with cluster size. For several clusters characteristic changes in the polarizability per atom as a function of temperature are observed. It is shown that the inclusion of finite temperature effects resolves the long-standing mismatch between calculated and measured sodium cluster polarizabilities.     

Evaluation of electronic correlation contributions for optical tensors of large systems using the incremental scheme

A new method is developed to calculate the optical tensors of large systems based on available wave function correlation approaches (e.g., the coupled cluster ansatz) in the framework of the incremental scheme. The convergence behaviors of static first- and second-order polarizabilities with respect to the order of the incremental expansion are examined and discussed for the model system Ga(4)As(4)H(18). The many-body increments of optical tensors originate from the dipole-dipole coupling effects and the corresponding contributions to the incremental expansion are compared among local domains with different distances and orientations. The weight factors for increments of optical tensors are found to be tensorial in accordance with the structural symmetry as well as the polarization and the external electric field directions. The long-term goal of the proposed approach is to incorporate the sophisticated molecular correlation methods into the accurate wave function calculation of optical properties of large compounds or even crystals.     

Brueckner coupled cluster response functions

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.     

One-electron properties and electrostatic interaction energies from the expectation value expression and wave function of singles and doubles coupled cluster theory

One-electron density matrices resulting from the explicitly connected commutator expansion of the expectation value were implemented at the singles and doubles coupled cluster (CCSD) level. In the proposed approach the one-electron density matrix is obtained at a little extra cost in comparison to the calculation of the CCSD correlation energy. Therefore, in terms of the computational time the new method is significantly less demanding than the conventional linear-response CCSD theory which requires additionally an expensive calculation of the left-hand solution of the CCSD equations. The quality of the new density matrices was investigated by computing a set of one-electron properties for a series of molecules of varying sizes and comparing the results with data obtained using the full configuration interaction method or higher level coupled cluster theory. It has been found that the results obtained using the new approach are of the same quality as those predicted by the linear-response CCSD method. The novel one-electron density matrices have also been applied to study the energy of the electrostatic interaction for a number of van der Waals complexes, including the benzene and azulene dimers.     

Electron-correlated calculations of the nuclear-shielding polarizability and magnetizability polarizability of H2, N2, HF, and CO

The effects of a uniform static electric field on the NMR shielding and magnetizability of H₂, N₂, HF, and CO are reported. The appropriate defining quantities are the shielding and magnetizability polarizabilities and these are calculated in a mixed numeric-analytic scheme with allowance for electron correlation via third-order Møller-Plesset (MP3) theory or linearized coupled cluster double excitation (L-CCD) theory. This is the first time that these theories have been applied to these properties. Our primary conclusion for the shielding polarizabilities is that, with the exception of H₂, the use of coupled cluster theory is necessary to establish the definitive values for these properties because of their extreme sensitivity to electron correlation. For the magnetizability polarizabilities we find the MP3 values to be in better agreement with the L-CCD results than the MP2 values are.     

The calculation of ground and excited state molecular polarizabilities: A simple perturbation treatment

Second order perturbation theory has been coupled with the CNDO/S CI method of Del Bene and Jaffé to calculate the ground and excited state polarizabilities of various molecules. It is found that this treatment produces reasonably good polarizabilities with great computational ease.     

First-principles calculation of local atomic polarizabilities

Common methods of determining atomic polarizabilities suffer from the inclusion of nonlocal effects such as charge polarization. A new method is described for determining fully ab initio atomic polarizabilities based on calculating the response of atomic multipoles to the local electrostatic potential. The localized atomic polarizabilities are then used to calculate induction energies that are compared to ab initio induction energies to test their usefulness in practical applications. These polarizabilities are shown to be an improvement over the corresponding molecular polarizabilities, in terms of both absolute accuracy and the convergence of the multipolar induction series. The transferability of localized polarizabilities for the alkane series is also discussed.     

Reduced–size polarized basis sets for calculations of molecular electric properties. III. Second–row atoms

Reduced–size polarized (ZmPolX) basis sets are developed for the second–row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced–size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.     

Electric dipole polarizabilities and C6 dipole-dipole dispersion coefficients for sodium clusters and C60

The frequency-dependent polarizabilities of closed-shell sodium clusters containing up to 20 atoms have been calculated using the linear complex polarization propagator approach in conjunction with Hartree-Fock and Kohn-Sham density functional theories. In combination with polarizabilities for C(60) from a previous work [J. Chem. Phys. 123, 124312 (2005)], the C(6) dipole-dipole dispersion coefficients for the metal-cluster-to-cluster and cluster-to-buckminster-fullerene interactions are obtained via the Casimir-Polder relation [Phys. Rev. 73, 360 (1948)]. The B3PW91 results for the polarizability of the sodium dimer and tetramer are benchmarked against coupled cluster calculations. The error bars of the reported theoretical results for the C(6) coefficients are estimated to be 5%, and the results are well within the error bars of the experiment.     

Mixed-sector intermediate Hamiltonian Fock-space coupled cluster approach

An alternative formulation of the intermediate Hamiltonian Fock-space coupled cluster scheme developed before is presented. The methodological and computational advantages of the new formulation include the possibility of using a model space with determinants belonging to different Fock-space sectors. This extends the scope of application of the multireference coupled cluster method, and makes possible the use of quasiclosed shells (e.g., p2, d4) as reference states. Representative applications are described, including electron affinities of group-14 atoms, ionization potentials of group-15 elements, and ionization potentials and excitation energies of silver and gold. Excellent agreement with experiment (a few hundredths of an electronvolt) is obtained, with significant improvement (by a factor of 5-10 for p3 states) over Fock-space coupled cluster results. Many states not reachable by the Fock-space approach can now be studied.     

Size-Nonextensive Contributions in Singles-Only CI

The size-nonextensivity (SNE) of the configuration interaction scheme with single excitations only (CIS) is discussed. On the basis of model considerations the method is explicitly shown to give energies which have wrong dependence on the number of particles. The same model of a multimer of N noninteracting subsystems, each in the same singly excited state, is analyzed in terms of the many-body perturbation theory expansion. This suggests new computational schemes which will be either completely free of the size-nonextensive contributions or may have them removed a posteriori. The extension of the perturbation scheme leads to the singles-only coupled cluster approach with a singly excited reference function. The consequences of the present model study for computational methods for inexpensive calculations of the electronic spectra of molecules, are investigated.     

Multireference state-specific Mukherjee's coupled cluster method with noniterative triexcitations using uncoupled approximation

A new version of the multireference Mukherjee's coupled cluster method with perturbative triexcitations has been formulated, which is based on the uncoupled approximation applied to the triples equation. In contrast to the method developed by Evangelista et al. [J. Chem. Phys. 132, 074107 (2010)], the proposed approach does not require to solve the equation for T(3) amplitudes iteratively, yet yields results of essentially the same quality. The method, abbreviated as MR MkCCSD(Tu), has been implemented in the ACES II program package and its assessment has been performed on the BeH(2) model and on the tetramethyleneethane molecule.     

Time-dependent coupled-cluster calculations of polarizabilities and dispersion energy coefficients

Time-dependent coupled cluster theory, with unrestricted electron spins and full treatment of orbital rotation, is used to calculate polarizabilities at imaginary frequencies for Li, Ar, HCl, CO, N(2), O(2), and H(2)O, and to obtain dispersion energy coefficients for their pair interactions. Results obtained with augmented quadruple-zeta basis sets agree well with the best literature values of the C(6) dispersion energy coefficients. Time-dependent coupled cluster with single and double excitations theory will be useful as a benchmark for evaluating more approximate theories. (c) 2007 Wiley Periodicals, Inc. J Comput Chem, 2008.     

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell pi-conjugated systems

The basis set and electron correlation effects on the static polarizability (alpha) and second hyperpolarizability (gamma) are investigated ab initio for two model open-shell pi-conjugated systems, the C(5)H(7) radical and the C(6)H(8) radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C(6)H(8) whereas diffuse functions are compulsory for C(5)H(7), in particular, p diffuse functions. In addition to the 6-31G(*)+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for alpha and gamma of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order M?ller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order M?ller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order M?ller-Plesset method, provide for both compounds gamma values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged alpha and gamma values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of alpha and gamma have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.