Doubles Wave Function Research Articles

Symmetry projection to coupled-cluster singles plus doubles wave function through the Monte Carlo method

A new method for calculating the symmetry-projected energy of coupled-cluster singles and doubles (CCSD) wave function through the Monte Carlo method is proposed. We present benchmark calculations in considering the three-level Lipkin model which is a simple and minimal model with two phases: spherical and deformed ones. It is demonstrated that this new method gives good ground state energy and low-lying spectra.

Symmetry conserving coupled cluster doubles wave function and the self-consistent odd particle number RPA

Mixing single and triple fermions an exact killing operator of the Coupled Cluster Doubles (CCD) wave function with good symmetry was found in \cite{Tohy13}. Using these operators with the equation of motion (EOM) method the so-called self-consistent odd particle number random phase approximation (odd-RPA) was set up. Together with the stationarity condition of the two body density matrix it is shown that the killing conditions allow to reduce the order of correlation functions contained in the matrix elements of the odd-RPA equations to a fully self consistent equation for the single particle occupation numbers. Excellent results for the latter and the ground state energies are obtained in an exactly solvable model from weak to strong couplings.

A Quasi-Diabatic Representation of the 1,21A States of Methylamine.

We report a full 15-dimensional two-state quasi-diabatic potential energy matrix (PEM) for the 1,21A states of methylamine (CH3NH2) suitable for the description of its two distinct photodissociation channels, CH3NH2(11A) + hν → CH3NH2(21A) → CH3 + NH2 or CH3NH + H. The PEM is fit to ab initio electronic structure data (energies, energy gradients, and derivative couplings) obtained from multireference configuration interaction single and double excitation wave functions at 7732 geometries, using a diabatic representation based on symmetry-adapted polynomials. The root-mean-square error is 78.34 cm-1 for the energies and 2.98% for the gradients. The computed T0(21A) = 42 461 cm-1 (41 669 cm-1), D0(CH3NH+H) = 33 639 cm-1 (34 250 cm-1), and D0(CH3+NH2) = 28 543 cm-1 (29 300 cm-1) are in good agreement with the experimental values given in the parentheses. The absorption spectrum of CH3NH2 is computed using this diabatic PEM and a normal mode based kinetic energy operator. Agreement with experimental data is quite satisfactory. Our accurate representation of the PEM over a wide range of nuclear configuration space offers the possibility for quality nonadiabatic dynamics simulations involving the CH3 + NH2 and CH3NH + H dissociation channels. Surface hopping trajectories are used to illustrate the types of nuclear motion supported by the PEM.

Multistate, multichannel coupled diabatic state representations of adiabatic states coupled by conical intersections. CH2OH photodissociation.

A coupled diabatic state representation, Hd, of the 1, 2, 3 2A states of CH2OH suitable for the description of the three channel, three state photodissociation process CH2OH(1 2A) + hv → CH2OH(2, 3 2A) → CH2O(X, A) + H, cis-CHOH + H, trans-CHOH + H, is reported. The representation is based on electronic structure data (energies, energy gradients, and derivative couplings) obtained exclusively from multireference configuration interaction single and double excitation wave functions. Diabat shifting is employed to improve the representation's agreement with accurate experimental energetics. A careful analysis of the numerous minima, saddle points, and conical intersection seams is reported. The computed T0(3 2A) ∼ 35 220 cm-1 is in excellent agreement with the experimental estimate of 35 053 cm-1, and the computed channel dissociation energies, D0, for CH2O 9453 (10 160), cis-HCOH 30 310.2 (29 923), and trans-HCOH 28 799 (28 391) cm-1 are in good accord with the measured values given parenthetically. These accurate energetics over a wide range of nuclear configurations strongly support the ability of this Hd to enable quality simulations of nonadiabatic dynamics.

Approximating electronically excited states with equation-of-motion linear coupled-cluster theory.

A new perturbative approach to canonical equation-of-motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order Møller-Plesset partitioning of the Hamiltonian is used to obtain the well known equation-of-motion many-body perturbation theory equations and two new equation-of-motion methods based on the linear coupled-cluster doubles and linear coupled-cluster singles and doubles wavefunctions. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical equation-of-motion coupled-cluster singles and doubles state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.

Double photoionization of helium: a generalized Sturmian approach

In this work we study the double photoionization of helium induced by low intensities laser fields in the regime where only one photon absorption occurs. The method proposed here is based on a Generalized Sturmian Functions (GSF) spectral approach which allows the imposition of outgoing boundary conditions for both ejected electrons. These, in turn, construct an hyperspherical flux characteristic of double continuum wave functions. We compare our calculated cross sections at 20 and 40 eV above threshold with absolute and relative measurements, and with other calculations. Our results definitively demonstrate the applicability of the GSF approach for dealing with break-up Coulomb problems.

Approximate account of connected triply and quadruply excited clusters in single reference coupled cluster theory via cluster analysis of projected unrestricted coupled cluster with single and double wave function

The projected unrestricted coupled cluster wave function with singly and doubly excited clusters (PUCCSD) has been used as a source of information about the T3 and T4 cluster contributions in the externally corrected CCSD approach. In order to remove the spin contamination of the UCCSD wave function the group invariant average of the unitary group was adapted. Preliminary results presented here for the DZ H8 model system show surprisingly good agreement with the exact results, particularly in the case of the energy contribution of the T4 cluster to the quasidegenerate region with errors of less than 0.1milihartree.

Photo-double-ionization of the nitrogen molecule

The triple differential cross sections of the photo-double-ionization of the nitrogen molecule to the $X$ ${}^{1}{\ensuremath{\Sigma}}^{+}{}_{g}$ and ${a}^{3}$\ensuremath{\Pi}${}_{u}$ ${{\mathrm{N}}_{2}}^{2+}$ states have been measured at about 20 eV above their respective ionization thresholds in the equal energy sharing kinematics and calculated using a model which makes use of correlated two-center double continuum wave functions. The comparison of the results with those obtained by the Gaussian parametrization method applied in the past with success to heliumlike targets shows the influence of the molecular nature of the ${\mathrm{N}}_{2}$ target in the photo-double-ionization.

Time Dependent Entropy and Decoherence in a Modified Quantum Damped Harmonic Oscillator

The time dependence of probability and Shannon entropy of a modified damped harmonic oscillator is studied by using single and double Gaussian wave functions through the Feynman path method. We establish that the damped coefficient as well as the system frequency and the distance separating two consecutive waves of the initial double Gaussian function influences the coherence of the system and can be used to control its decoherence.

Quantum Monte Carlo with coupled-cluster wave functions

We introduce a many-body method that combines two powerful many-body techniques, viz., quantum Monte Carlo and coupled cluster theory. Coupled cluster wave functions are introduced as importance functions in a Monte Carlo method designed for the configuration interaction framework to provide rigorous upper bounds to the ground-state energy. We benchmark our method on the homogeneous electron gas in momentum space. The importance function used is the coupled cluster doubles wave function. We show that the computational resources required in our method scale polynomially with system size. Our energy upper bounds are in very good agreement with previous calculations of similar accuracy, and they can be systematically improved by including higher order excitations in the coupled cluster wave function.

Accurate predictions of the energetics of silicon compounds using the multireference correlation consistent composite approach

Theoretical studies, using the multireference correlation consistent composite approach (MR-ccCA), have been carried out on the ground and lowest lying spin-forbidden excited states of a series of silicon-containing systems. The MR-ccCA method is the multireference equivalent of the successful single reference ccCA method that has been shown to produce chemically accurate (within ±1.0 kcal mol(-1) of reliable, well-established experiment) results. The percentage contributions of the SCF configurations to complete active space self-consistent field wave functions together with the Frobenius norm of the t(1) vectors and related D(1) diagnostics of the coupled-cluster single double wave function with the cc-pVTZ basis set have been utilized to illustrate the multi-configurational characteristics of the compounds considered. MR-ccCA incorporates additive terms to account for relativistic effects, atomic spin-orbit coupling, scalar relativistic effects, and core-valence correlation. MR-ccCA has been utilized to predict the atomization energies, enthalpies of formation, and the lowest energy spin-forbidden transitions for Si(n)X(m) (2 ≤ n + m ≥ 3 where n ≠ 0 and X = B, C, N, Al, P), silicon hydrides, and analogous compounds of carbon. The energetics of small silicon aluminides and phosphorides are predicted for the first time.

Explicitly time-dependent coupled cluster singles doubles calculations of laser-driven many-electron dynamics

We report explicitly time-dependent coupled cluster singles doubles (TD-CCSD) calculations, which simulate the laser-driven correlated many-electron dynamics in molecular systems. Small molecules, i.e., HF, H(2)O, NH(3), and CH(4), are treated mostly with polarized valence double zeta basis sets. We determine the coupled cluster ground states by imaginary time propagation for these molecules. Excited state energies are obtained from the Fourier transform of the time-dependent dipole moment after an ultrashort, broadband laser excitation. The time-dependent expectation values are calculated from the complex cluster amplitudes using the corresponding configuration interaction singles doubles wave functions. Also resonant laser excitations of these excited states are simulated, in order to explore the limits for the numerical stability of our current TD-CCSD implementation, which uses time-independent molecular orbitals to form excited configurations.

First-order exchange energy of intermolecular interactions from coupled cluster density matrices and their cumulants

A new method for the calculation of the first-order intermolecular exchange energy is proposed. It is based on the partition of two-particle density matrices of monomers into the antisymmetrized product of one-particle density matrices and the remaining cumulant part. This partition is used to modify the formula for the first-order exchange energy developed by Moszynski et al. [J. Chem. Phys. 100, 5080 (1994)]. The new expression has been applied for the case of monomer density matrices derived from the expectation value expression for the coupled cluster singles and doubles wave function. In this way an accurate method of calculation of the first-order exchange energy for many-electron systems has been obtained, where both monomers are described on the coupled cluster level. Numerical results are presented for several benchmark van der Waals systems to illustrate the performance of the new approach.

Second-order exchange-induction energy of intermolecular interactions from coupled cluster density matrices and their cumulants

A new formulation of the second-order exchange-induction energy of symmetry-adapted perturbation theory is presented. In the proposed formalism the exchange-induction energy is expressed through one- and two-particle reduced density matrices of monomers, which are of zeroth and first order with respect to the effective electrostatic potential of another monomer. The resulting expression is further modified by using the partition of two-particle density matrices into the antisymmetrized product of one-particle density matrices and the remaining cumulant part. The proposed formalism has been applied to the case of closed-shell monomers and for density matrices obtained from the expectation-value expression with coupled cluster singles and doubles wave functions. The performance of the new approach has been demonstrated on several benchmark van der Waals systems, including dimers of argon, water, and ethyne.

Coupled‐cluster corrected MR‐CISD method with noniterative evaluation of connected triples

AbstractThe single‐reference coupled‐cluster (CC) analysis of the multi‐reference configuration interaction singles and doubles (MR‐CISD) wave function shows how the MR‐CISD results can be used to mimic more effective exponential cluster expansion. The CC corrections have been constructed relying on this analysis and used to improve the accuracy of the MR‐CISD energy and reduce the inextensivity error of the MR‐CISD method. Disconnected contributions that approximate those components which are not present in the MR‐CISD wave function generate the correction terms. Although the linear CI expansion is usually improved through the inclusion of disconnected contributions the coupled‐cluster methodology introduces a variety of corrections that, contrary to the CI case, account for higher excitation rank connected components. In this article, we present a combination of both approaches and illustrate its performance on some numerical examples. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Parallel Calculation of Coupled Cluster Singles and Doubles Wave Functions Using Array Files.

A new parallel implementation of the Coupled Cluster Singles and Doubles (CCSD) and related wave functions (e.g Quadratic Configuration Interaction, QCI, and Coupled Electron Pair, CEPA) is described, based on the Array Files middleware. The program can handle large basis sets, even without utilizing symmetry, on modest distributed memory workstation clusters. High computational efficiency is achieved by formulating all major operations in terms of matrix multiplications. Timings are provided for systems with 50-228 valence electrons and up to 1144 basis functions, with little or no symmetry. Our largest calculation (QCISD/aug-cc-pVQZ for the parallel displaced benzene dimer) uses 1512 basis functions. Calculations on the benzene dimer show that the usual procedure of estimating the effect of basis set enlargement from second-order Møller-Plesset (MP2) calculations is less reliable than previously assumed. Replacing the weak pair amplitudes in CCSD/QCISD calculations by MP2 amplitudes affects the calculated energy only slightly.

Optically induced circular and axial birefringences in achiral fluids: an ab initio study of the optical Faraday effect

A computational analysis of the effects (intensity-dependent change in the refractive index and the optical Faraday effect, OFE) induced in an achiral fluid by circularly polarized, linearly polarized or unpolarized light is presented. The connection between the molecular parameters appearing in the expression of the observable, as derived by Woźniak in the 1990s, and the appropriate linear and cubic frequency dependent response functions is made for the general case of both chiral and non-chiral fluid. The parameters which are non-vanishing in the case of achiral systems are then computed employing a coupled cluster singles and doubles wave function model and a wide choice of correlation consistent basis sets, for a set of reference systems, including a rare gas (neon), a non-dipolar (N2) and a dipolar (CO) molecule. Contributions due to magnetic and quadrupolar interactions between the fields and the gases are neglected, since they are in principle of much less importance than the purely electric dipolar interactions. Nevertheless a rough estimate of their size is given. The aim of the study is to assess the detectability of OFE. To this end, the ab initio results are compared with those obtained in this work for the closely related optical Kerr effect (OKE) and with those yielded by the classical Faraday effect.

On the orbital dependence of compact, weight-selected configuration interaction and coupled-cluster wave functions

We recently reported that very compact coupled-cluster wave functions may be generated by selecting the most important configurations, by weight, from the full coupled-cluster wave function. Here, we consider how the choice of orbitals may affect these wave functions in the case of the symmetric dissociation of H2O. We employ unrestricted Hartree–Fock and complete-active-space self-consistent-field orbitals, as well as natural orbitals derived from a coupled-cluster singles and doubles wave function. For a given accuracy, some choices of orbitals can reduce the size of configuration interaction wave functions, but they have little effect on the weight-selected coupled-cluster wave functions.

A catalog of stellar magnetic rotational phase curves

Magnetized stars usually exhibit periodic variations of the effective (longitudinal) magnetic field B e caused by their rotation. We present a catalog of magnetic rotational phase curves, B e vs. the rotational phase ϕ , and tables of their parameters for 136 stars on the main sequence and above it. Phase curves were obtained by the least squares fitting of sine wave or double wave functions to the available B e measurements, which were compiled from the existing literature. Most of the catalogued objects are chemically peculiar A and B type stars (127 stars). For some stars we also improved or determined periods of their rotation. We discuss the distribution of parameters describing magnetic rotational phase curves in our sample.

A natural linear scaling coupled-cluster method

It is shown that using an appropriate localized molecular orbital (LMO) basis, one is able to calculate coupled-cluster singles and doubles (CCSD) wave functions and energies for very large systems by performing full CCSD calculations on small subunits only. This leads to a natural linear scaling coupled-cluster method (NLSCC), in which total correlation energies of extended systems are evaluated as the sum of correlation energy contributions from individual small subunits within that system. This is achieved by defining local occupied orbital correlation energies. These are quantities, which in the LMO basis become transferable between similar molecular fragments. Conventional small scale existing molecular CCSD codes are all that is needed, the local correlation effect being simply transmitted via the appropriate LMO basis. Linear scaling of electronic correlation energy calculations is thus naturally achieved using the NLSCC approach, which in principle can treat nonperiodic extended systems of infinite basis set size. Results are shown for alkanes and several polyglycine molecules and the latter compared to recent results obtained via an explicit large scale LCCSD calculation. (c) 2004 American Institute of Physics.