Approximate variational coupled cluster theory

We show that it is possible to construct an accurate approximation to the variational coupled cluster method, limited to double substitutions, from the minimization of a functional that is rigorously extensive, exact for isolated two-electron subsystems and invariant to transformations of the underlying orbital basis. This approximate variational coupled cluster theory is a modification and enhancement of our earlier linked pair functional theory. It is first motivated by the constraint that the inverse square root of the matrix that transforms the cluster amplitudes must exist. Low-order corrections are then included to enhance the accuracy of the approximation of variational coupled cluster, while ensuring that the computational complexity of the method never exceeds that of the standard traditional coupled cluster method. The effects of single excitations are included by energy minimization with respect to the orbitals defining the reference wavefunction. The resulting quantum chemical method is demonstrated to be a robust approach to the calculation of molecular electronic structure and performs well when static correlation effects are strong.     

Quasi-variational coupled cluster theory

We extend our previous work on the construction of new approximations of the variational coupled cluster method. By combining several linked pair functional transformations in such a way as to give appropriately balanced infinite-order contributions, in order to approximate (L) well at all orders, we formulate a new quantum chemical method, which we name quasi-variational coupled cluster. We demonstrate this method to be particularly robust in the regime of strong static electron correlation, improving significantly on our earlier approximate variational coupled cluster approach.     

Alternative single-reference coupled cluster approaches for multireference problems: the simpler, the better

We report a general implementation of alternative formulations of single-reference coupled cluster theory (extended, unitary, and variational) with arbitrary-order truncation of the cluster operator. These methods are applied to compute the energy of Ne and the equilibrium properties of HF and C(2). Potential energy curves for the dissociation of HF and the BeH(2) model computed with the extended, variational, and unitary coupled cluster approaches are compared to those obtained from the multireference coupled cluster approach of Mukherjee et al. [J. Chem. Phys. 110, 6171 (1999)] and the internally contracted multireference coupled cluster approach [F. A. Evangelista and J. Gauss, J. Chem. Phys. 134, 114102 (2011)]. In the case of Ne, HF, and C(2), the alternative coupled cluster approaches yield almost identical bond length, harmonic vibrational frequency, and anharmonic constant, which are more accurate than those from traditional coupled cluster theory. For potential energy curves, the alternative coupled cluster methods are found to be more accurate than traditional coupled cluster theory, but are three to ten times less accurate than multireference coupled cluster approaches. The most challenging benchmark, the BeH(2) model, highlights the strong dependence of the alternative coupled cluster theories on the choice of the Fermi vacuum. When evaluated by the accuracy to cost ratio, the alternative coupled cluster methods are not competitive with respect to traditional CC theory, in other words, the simplest theory is found to be the most effective one.     

Coupled cluster theory with the polarizable continuum model of solvation

The environment may significantly affect molecular properties. Thus, it is desirable to account explicitly for these effects on the wave function and its derivatives, especially when the latter are evaluated with accurate methods, such as those belonging to coupled cluster (CC) theory. In this tutorial review, we discuss how to combine CC methods with the polarizable continuum model of solvation (PCM). We describe useful approximations that include the solvent response to the correlation and excited state equations while maintaining the computational cost comparable to in vacuo calculations. Although applied to PCM, the theoretical framework presented in this review is general and can be used with any polarizable embedding model. Representative applications of the CC-PCM method to ground and excited state properties of solvated molecules are presented, and comparisons with experiment, and between the full and approximate schemes are discussed.     

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.     

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.     

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrodinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational M?ller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed.     

Accurate theoretical near-equilibrium potential energy and dipole moment surfaces of HgClO and HgBrO

The complexes HgBrO and HgClO have been previously determined by ab initio methods to be strongly bound and were suggested to be important intermediates during mercury depletions events observed in the polar troposphere. In the present work accurate near-equilibrium potential energy surfaces (PESs) of these species are reported. The PESs are determined using accurate coupled cluster methods and a series of correlation consistent basis sets with subsequent extrapolation to the complete basis set limit. Additive corrections for both core-valence correlation energy and relativistic effects are also included. The anharmonic ro-vibrational spectra of HgBrO and HgClO have been calculated in variational calculations. Strong infrared band strengths are predicted for all fundamentals in these species. The spin-orbit splitting dominates over the vibronic coupling effect in both HgClO and HgBrO. The Renner-Teller vibronic energy levels corresponding to the bending mode of these molecules are calculated via perturbation theory.     

Resolution of identity approach for the Kohn-Sham correlation energy within the exact-exchange random-phase approximation

Two related methods to calculate the Kohn-Sham correlation energy within the framework of the adiabatic-connection fluctuation-dissipation theorem are presented. The required coupling-strength-dependent density-density response functions are calculated within exact-exchange time-dependent density-functional theory, i.e., within time-dependent density-functional response theory using the full frequency-dependent exchange kernel in addition to the Coulomb kernel. The resulting resolution-of-identity exact-exchange random-phase approximation (RI-EXXRPA) methods in contrast to previous EXXRPA methods employ an auxiliary basis set (RI basis set) to improve the computational efficiency, in particular, to reduce the formal scaling of the computational effort with respect to the system size N from N(6) to N(5). Moreover, the presented RI-EXXRPA methods, in contrast to previous ones, do not treat products of occupied times unoccupied orbitals as if they were linearly independent. Finally, terms neglected in previous EXXRPA methods can be included, which leads to a method designated RI-EXXRPA+, while the method without these extra terms is simply referred to as RI-EXXRPA. Both EXXRPA methods are shown to yield total energies, reaction energies of small molecules, and binding energies of noncovalently bonded dimers of a quality that is similar and in some cases even better than that obtained with quantum chemistry methods such as Mo?ller-Plesset perturbation theory of second order (MP2) or with the coupled cluster singles doubles method. In contrast to MP2 and to conventional density-functional methods, the presented RI-EXXRPA methods are able to treat static correlation.     

Orbital-optimized coupled-cluster theory does not reproduce the full configuration-interaction limit

It is shown that due to the mixing of the usual projection approach of coupled cluster with variational orbital optimization, orbital-optimized coupled cluster (OCC) fails to reproduce the full configuration-interaction (full CI) limit when the cluster operator becomes complete. It is pointed out that the fulfillment of the projected singles equations, which define the orbital gradient in Brueckner coupled cluster (BCC), is mandatory for a correct behavior. As numerical examples we present general OCC and BCC calculations up to the full CI limit on CH(2) and an active-space model of ozone. The observed deviations of OCC from full CI are of the order of the correlation error obtained in calculations with up to quadruples excitations. Thus the failure of OCC may be considered tolerable in more approximate calculations but clearly prohibitive for any benchmark application. For applications to active-space models a hybrid approach for OCC is suggested in which for active particle-hole rotations the Brueckner orbital gradient is employed, whereas for the remaining orbital rotations the variational orbital gradient is retained.     

Coupled cluster studies. III. Comparison of the numerical behaviour of coupled cluster doubles with configuration interaction and perturbation theory. Basis set and geometry optimizations

In the beryllium atom most of the valence electron correlation energy can be obtained with only three equivalent excitations. It is shown that this is possible also with only one primitive set of p-type gaussians, provided their exponent is carefully optimized. Further it is demonstrated that this is due to the near degeneracy of the 1s²2s² and 1s²2p² states of Be, because it does not occur in He and H₂. Møller—Plesset (MP) perturbation theory gives less correlation energy than coupled cluster doubles (CCD) in these cases but the same optimum exponent for the set of p functions. For the molecules CO and CO₂ where MP2 is known to overestimate the correlation energy in comparison to CCD the convergence properties of MP are studied up to fourth order. It is shown that the results of MP4(DQ) and CCD are very similar also in these cases. For comparison results for ethylene are also discussed. Due to size consistency CCD is superior over configuration interaction with double excitations (CID). Equilibrium properties computed with CCD and MP4(DQ) are shown to be as reliable as those given by CID, although the variational theorem does not hold for CCD and MP4(DQ). The effect of single excitations turned out to be negligible in these cases. In basis set optimizations all correlation methods studied worked out similar.     

A variational method to calculate static electronic properties

Using a coupled cluster form of the wave function, a variational method is formulated for calculation of static properties of any order. Corresponding to an appropriate perturbed hamiltonian H() including the relevant static property, a size consistent functional is set up. In a hierarchical fashion, properties of different orders may be found out using a variational method.     

XCC2--a new coupled cluster model for the second-order polarization propagator

A new coupled cluster model of the polarization propagator, denoted as XCC2, is presented. The XCC2 approach employs time-independent coupled cluster theory of polarization propagators of Moszynski et al. [Collect. Czech. Chem. Commun., 2005, 70, 1109] and excitation operators from the time-dependent (TD) CC2 method. The performance of XCC2 was investigated by calculating static and dynamic dipole polarizabilities for a test set of over 20 molecules and comparing them with TD-CCSD results. The quality of XCC2 dispersion coefficients for several noncovalent molecular complexes was also tested against the benchmark values. This numerical study reveals that the average percent error of XCC2 is significantly reduced in comparison to the TD-CC2 method (4-fold reduction for the mean polarizabilities and 2-fold reduction for anisotropic polarizabilities is observed). Since the computational requirements of both XCC2 and TD-CC2 methods are virtually the same, the new XCC2 method can be viewed as a practical alternative for TD-CC2 for property calculations, giving the second-order polarization propagators of near-CCSD quality in many cases, but retaining at the same time the lower computational cost of the TD-CC2 model.     

Nature of bonding in group 13 dimetallenes: a delicate balance between singlet diradical character and closed shell interactions

The nature of metal-metal bonding in group 13 dimetallenes REER (E = Al, Ga, In, Tl; R = H, Me, (t)Bu, Ph) was investigated by use of quantum chemical methods that include HF, second order M?ller-Plesset perturbation theory (MP2), coupled cluster (CCSD(T)), complete active space with (CASPT2) and without (CAS) second order perturbation theory, and two density functionals, namely, B3LYP and M06-2X. The results show that the metal-metal interaction in group 13 dimetallenes stems almost exclusively from static and dynamic electron correlation effects: both dialuminenes and digallenes have an important singlet diradical component in their wave function, whereas the bonding in the heavier diindenes and, in particular, dithallenes is dominated by closed shell metallophilic interactions. The reported calculations represent a systematic attempt to determine the metal and ligand dependent bonding changes in these systems.     

Theoretical Study of Structures and Spectra of Small Anticancer Drugs: Fluorouracil,Hydroxyurea, and Tirapazamine

The structures and spectra of anticancer drug molecules fluorouracil, hydroxyurea, and tirapazamine are studied with ab initio methods and density functional theory. We optimize the geometry of the three molecules in gas phase and compute the vibrational spectra, dipole moments, and static dipole polarizabilities. Based on the coupled cluster method with single and double excitations (CCSD) results as standard for comparison for the geometry of fluorouracil and hydroxyurea, we conclude that third‐order Moeller‐Plesset perturbation (MP3) theory is more reliable than its second‐order shortcut (MP2) or the popular method in density functional theory known as Becke three‐parameter Lee‐Yang‐Parr exchange‐correlation functional (B3LYP). Using the best methods based on past experience, we also calculate the vertical ionization energies of both valence and core electrons. Most of the results are new predictions, while others compare well with previous calculations and with available experimental data. On the other hand, the absorption spectra of the aqueous solution of three title molecules are studied with time‐dependent DFT using the polarizable continuum model in conjunction with the nonequilibrium solvation method. Out of over 30 exchange‐correlation functions/models, five are found to be more reliable than the others when compared with the observed UV/visible spectra of fluorouracil and tirapazmine.     

Ground-state properties and static dipole polarizabilities of the alkali dimers from K2 n to Fr2 n(n=0,+1) from scalar relativistic pseudopotential coupled cluster and density functional studies

The newly adjusted energy-consistent nine-valence-electron pseudopotentials for K to Fr are used to calculate spectroscopic properties for the neutral and positively charged alkali dimers using coupled cluster and density functional theory. For the neutral dimers the static dipole polarizability was calculated. The coupled cluster results are all in excellent agreement with experimental values. The density functionals used can give quite different spectroscopic properties especially for the dipole polarizability, with the Perdew-Wang PW91 functional performing best.