Showing papers on "Coupled cluster published in 1993"

The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties

Abstract: A comprehensive overview of the equation of motion coupled‐cluster (EOM‐CC) method and its application to molecular systems is presented. By exploiting the biorthogonal nature of the theory, it is shown that excited state properties and transition strengths can be evaluated via a generalized expectation value approach that incorporates both the bra and ket state wave functions. Reduced density matrices defined by this procedure are given by closed form expressions. For the root of the EOM‐CC effective Hamiltonian that corresponds to the ground state, the resulting equations are equivalent to the usual expressions for normal single‐reference CC density matrices. Thus, the method described in this paper provides a universal definition of coupled‐cluster density matrices, providing a link between EOM‐CC and traditional ground state CC theory.Excitation energy,oscillator strength, and property calculations are illustrated by means of several numerical examples, including comparisons with full configuration interaction calculations and a detailed study of the ten lowest electronically excited states of the cyclic isomer of C4.

Coupled cluster theory for high spin, open shell reference wave functions

Abstract: The coupled cluster method restricted to single and double excitations (CCSD) is considered for the case of a spin restricted Hartree–Fock open shell reference determinant. A spin–orbital based formulation, in which the cluster operator spans exactly the minimal first order interacting space, is presented, and computationally optimal working equations are given. In the limit of a large number of closed shell orbitals, the cost is identical to that of an optimum treatment of an equivalent closed shell problem, which is obtained as a special case of the formulation presented. The theory is applied to the calculation of a number of diatomic potential energy functions and compared with spin‐unrestricted theory.

Coupled‐cluster methods with noniterative triple excitations for restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients

Abstract: A new, noniterative triples correction to the coupled‐cluster singles and doubles (CCSD), method, for general single determinant reference functions is proposed and investigated numerically for various cases, including non‐Hartree–Fock (non‐HF) reference functions. It is correct through fourth‐order of perturbation theory for non‐HF references, and unlike other such methods, retains the usual invariance properties common to CC methods, while requiring only a single N7 step. In the canonical Hartree–Fock case, the method is equivalent to the usual CCSD(T) method, but now permits the use of restricted open‐shell Hartree‐Fock (ROHF) and quasirestricted Hartree–Fock (QRHF) reference determinants, along with many others. Comparisons with full configuration interaction (FCI) results are presented for CH2, CH2+, CH3, NH2, and SiH2. The paper also reports the derivation and initial computational implementation of analytical gradients for the ROHF‐CCSD(T) method, which includes unrestricted Hartree–Fock (UHF) CCSD...

A state-selective multireference coupled-cluster theory employing the single-reference formalism

Abstract: A new state‐selective multireference (MR) coupled‐cluster (CC) method exploiting the single‐reference (SR) particle‐hole formalism is described. It is an extension of a simple two‐reference formalism, which we presented in our earlier paper [N. Oliphant and L. Adamowicz, J. Chem. Phys. 94, 1229 (1991)], and a rigorous formulation of another method of ours, which we obtained as an approximation of the SRCC approach truncated at triple excitations (SRCCSDT) [N. Oliphant and L. Adamowicz, J. Chem. Phys. 96, 3739 (1992)]. The size extensivity of the resulting correlation energies is achieved by employing a SRCC‐like ansatz for the multideterminantal wave function. General considerations are supplemented by suggesting a hierarchy of approximate schemes, with the MRCCSD approach (MRCC approach truncated at double excitations from the reference determinants) representing the most important one. Our state‐selective MRCCSD theory emerges through a suitable selection of the most essential cluster components appearing in the full SRCCSDTQ method (SRCC method truncated at quadruple excitations), when the latter is applied to quasidegenerate states. The complete set of equations describing our MRCCSD formalism is presented and the possibility of the recursive intermediate factorization [S. A. Kucharski and R. J. Bartlett, Theor. Chim. Acta 80, 387 (1991)] of our approach, leading to an efficient computer algorithm, is discussed.

Glycine conformational analysis

Abstract: Ab initio quantum mechanical methods, including the self-consistent field (SCF), single and double excitation configuration interaction (CISD), the single and double excitation coupled cluster (CCSD), and the single, double, and perturbative triple excitation coupled cluster [CCSD(T)] have been applied to five C s conformers and four of their C l counterparts on the potential energy hypersurface of glycine. A large basis set TZ2P+f designated H(5s2p1d/3s2p1d) and C,N,O(10s6p2d1f/5s3p2d1f) was chosen to evaluate the importance of d functions on hydrogen and f functions on carbon, nitrogen, and oxygen

Application of Hilbert-space coupled-cluster theory to simple (H 2 ) 2 model systems. II. Nonplanar models

Abstract: In this series, the recently developed explicit formalism of orthogonally spin-adapted Hibert space (or state universal), multireference (MR) coupled-cluster (CC) theory, exploiting the model space spanned by two closed-shell-type reference configurations, is applied to a simple minimum-basis-set four-electron model system consisting of two interacting hydrogen molecules in various geometrical arrangements. In this paper, we examine the nonplanar geometries of this system, generally referred to as the T4 models, and their special cases designated as P4 and V4 models. They correspond to different cross sections of the H[sub 4] potential-energy hypersurface, involving the dissociation or simultaneous stretching of two H---H bonds. They involve various quasidegeneracy types, including the orbital and configurational degeneracies, the twofold degeneracy of the ground electronic state and interesting cases of broken-symmetry solutions. We employ the CC with singles and doubles (SD) approximation, so that the cluster operators are approximated by their one- and two-body components. Comparing the resulting CC energies with exact values, which are easily obtained for these models by using the full configuration-interaction method, and performing a cluster analysis of the exact solutions, we assess the performance of various MRCC Hilbert-space approaches at both linear and nonlinear levels of approximation, while a continuous transition ismore » being made between the degenerate and nondegenerate or strongly correlated regimes. We elucidate the sources and the type of singular behavior in both linear and nonlinear versions of MRCC theory, examine the role played by various intruder states, and discuss the potential usefulness of broken-symmetry MRCCSD solutions.« less

Coupled cluster Green's function method: Working equations and applications

Abstract: Detailed working equations are derived for the ionization part of the single-particle Green's function within the coupled cluster Green's function (CCGF) framework. The CCGF method is applied to the calculation of vertical ionization potentials (IPs) of a number of small molecules, notably, HF, N2, CO, F2, CS, C2H4, H2O, and H2CO. The results for the outer-valence IPs, with an average error of 0.12 eV, compare favorably to third-order equation-of-motion calculations within the same basis set (average error 0.28 eV) and outer-valence GF (OVGF) values taken from the literature (average error 0.17 eV). Ground-state properties that derive from the CCGF are compared to expectation values obtained in the related normal coupled cluster methods (NCCM) approximation from a formal point of view. Correlation energies obtained in CCGF are compared to CCSD results for the above series of molecules and, in addition, the so-called true correlation energy density as obtained from the CCGF is compared to the result from an accurate MR–CI calculation for a highly correlated system: the HF molecule at large internuclear separation. © 1993 John Wiley & Sons, Inc.

Many‐body methods for excited state potential energy surfaces. I. General theory of energy gradients for the equation‐of‐motion coupled‐cluster method

Abstract: The formal theory is presented for calculating the analytic first derivative of the energy with respect to arbitrary perturbations within the equation‐of‐motion coupled‐cluster (EOM‐CC) approximation. Through use of the Dalgarno–Stewart interchange theorem (Z‐vector method), terms involving derivatives of the ground state cluster amplitudes are eliminated, leading to the definition of a new quasiparticle de‐excitation operator which simplifies the theory and significantly reduces the expected cost associated with studying potential energy surfaces for excited electronic states. For both illustrative and pragmatic reasons, the final equations are cast in a form similar to that developed for ground state CC energy derivatives, involving contraction of effective one‐ and two‐particle density matrices with matrix elements of the differentiated Hamiltonian. Some aspects regarding calculation of the gradient are discussed with particular attention devoted to similarities between the structure of the present formulas and those which have been previously implemented for the ground state problem.

Open-shell coupled-cluster theory

Abstract: An efficient formulation of a recently proposed open-shell singles and doubles coupled-cluster (OCCSD) method is presented. This formulation is in terms of spatial orbital one- and two-electron integrals. Our new OCCSD method is based on 'symmetric spin orbitals' and is thus symmetric (or antisymmetric) in the spin indices. It therefore contains about half the number of independent parameters in the coupled-cluster wave function compared to other open-shell CCSD methods. It is shown that the formulation presented here contains less than half the number of n exp 6 steps (where n is the number of molecular orbitals) of other recently proposed open-shell CCSD methods. A new approach by which amplitudes in our method may be compared with amplitudes in a previous OCCSD method is examined.

CH+5: The never‐ending story or the final word?

Abstract: The closely related Cs(1), Cs(2), and C2v(3) structures of CH5+ have been reinvestigated with high level ab initio theory through the coupled cluster with single and double substitutions (CCSD), and CCSD with perturbatively included connected triple excitations [CCSD(T)] levels, employing a triple‐ζ plus double polarization functions basis set, with f‐functions on carbon as well as d‐functions on the hydrogens [TZ2P(f,d)]. Vibrational frequencies have been computed up to TZ2P+f CCSD; the inclusion of f‐functions on carbon is critical for the configuration interaction with single and double excitations (CISD) and coupled cluster methods using the triple‐ζ basis sets. The changes in geometries between the CISD and CCSD levels are very small, e.g., the C–H bond lengths vary by at most 0.005 A. Thus, the optimizations are essentially converged within theoretical limits. The differences in energies of 1, 2, and 3 decrease and essentially vanish at the most sophisticated levels when the zero point vibrational e...

A coupled‐cluster based effective Hamiltonian method for dynamic electric polarizabilities

Abstract: A coupled‐cluster based approach for calculating dynamic polarizabilities is described. In this procedure, the polarizability is calculated by a strategy that is formally equivalent to a sum over states corresponding to the diagonal representation of a similarity transformed Hamiltonian operator. However, the explicit evaluation of excited state wave functions and energies is avoided. The present treatment is closely related to the equation of motion coupled‐cluster approximation for excited states and offers an accurate approximation to the second derivative of the energy with respect to an applied electric field; the two approaches are equivalent in the limit that the spectrum of states corresponding to the effective Hamiltonian is exact within the basis set. Terms contributing to the second derivative, but neglected in the proposed approach are shown to be insignificant for a representative set of small molecules. The method is applied to calculate the polarizability of benzene at the wavelength of the...

A systematic theoretical study of the harmonic vibrational frequencies for polyatomic molecules: The single, double, and perturbative triple excitation coupled‐cluster [CCSD(T)] method

Abstract: Analytic gradient methods have been used to predict the harmonic vibrational frequencies and the infrared (IR) intensities of HCN, HNC, CO2, CH4, NH4+, C2H2, H2O, H2CO, and NH3 at the single, double, and perturbative triple excitation coupled‐cluster [CCSD(T)] level of theory. All studies were performed using a double zeta plus polarization (DZ+P) basis set with a contraction scheme of (9s5p1d/4s2p1d) for C, N, and O and (4s1p/2s1p) for H. The results of previous studies using the same basis set with self‐consistent field (SCF), single and double excitation configuration interaction (CISD), and the single and double excitation coupled‐cluster (CCSD) methods are included to allow a detailed comparison. The theoretical harmonic frequencies of all nine molecules are compared to the 28 (out of a total of 35 possible) known experimental harmonic vibrational frequencies. IR intensities are also compared to known experimental values. The absolute average error in frequencies for the CCSD(T) method with respect t...

The water dimer: correlation energy calculations

Abstract: The binding energy of the water dimer at the experimental geometry has been calculated employing the Hartree-Fock (HF) method, MOller-Plesset theories MP2, MP3, and MP4, and the coupled cluster method with double excitations. We have also used configuration interaction wavefunctions both at the HFSDCI (single and double excitations from the HF configuration) and MRSDCI (single and double excitations from multiple reference configurations) levels to calculate the interaction energy. Binding energies within quasi-degenerate variation perturbation theory, linearized coupled cluster method, and the average pair correction model are also calculated. The basis set developed and employed in the study yields -76.0674 au for the HF energy of the water monomer at the experimental geometry

Accurate coupled cluster reaction enthalpies and activation energies for X+H2→XH+H (X=F, OH, NH2, and CH3)

Abstract: Coupled cluster calculations at the CCSD(T)/[5s4p3d/4s3p] and CCSD(T)/[5s4p3d2 f1g/4s3p2d] level of theory are reported for reactions X+H2→XH+H [X=F (1a), OH (1b), NH2 (1c), and CH3 (1d)] utilizing analytical energy gradients for geometry, frequency, charge distribution, and dipole moment calculations of reactants, transition states, and products. A careful analysis of vibrational corrections leads to reaction enthalpies at 300 K, which are within 0.04, 0.15, 0.62, and 0.89 kcal/mol of experimental values. For reaction (1a) a bent transition state and for reactions (1b) and (1c) transition states with a cis arrangement of the reactants are calculated. The cis forms of transition states (1b) and (1c) are energetically favored because of electrostatic interactions, in particular dipole–dipole attraction as is revealed by calculated charge distributions. For reactions (1a)–(1d), the CCSD(T)/[5s4p3d2 f1g/4s3p2d] activation energies at 300 K are 1.1, 5.4, 10.8, and 12.7 kcal/mol which differ by just 0.1, 1.4, ...

Multireference coupled cluster method for electronic structure of molecules

Abstract: In this review we present a systematic derivation of the multireference coupled cluster theory based on the single reference formalism. The coupled cluster theories have recently emerged as one of the major method development activities in the electronic structure theory of atoms and molecules. Due to its size-extensive nature, using the coupled cluster method the total electronic energy of the system can be determined with the same relative accuracy as the total electronic energies of the fragments which the system separates into in the process of chemical decomposition. This feature is essential for the correct theoretical determination of dissociation energies as well as other molecular properties. One of the most difficult challenges in advancing the coupled cluster theory has been the development of the multireference coupled cluster methodology, i.e. generating a scheme which allows the reference function to incorporate more than one Slater determinant. Such development would enable a very ...

Pulsed laser evaporated boron atom reactions with acetylene. Infrared spectra and quantum chemical structure and frequency calculations for several novel organoborane BC2H2 and HBC2 molecules

Abstract: Pulsed laser evaporated boron atoms react with C 2 H 2 to form new organoborane products during condensation with excess argon. Isotopic frequencies have been obtained for the 11 B, 10 B, C 2 H 2 , 13 C 2 H 2 , and C 2 D 2 reactions. Several structures of the HBC 2 and BC 2 H 2 molecules have been studied ab initio using large basis sets and augmented coupled cluster methods

A comparison of unrestricted Hartree–Fock‐ and restricted open‐shell Hartree–Fock‐based methods for determining the magnetic hyperfine parameters of NO (X 2Π)

Abstract: The magnetic hyperfine structure parameters of NO X 2Π have been determined through a variety of ab initio methods based on restricted and unrestricted Hartree–Fock zeroth order wave functions. Examples of the former include singles configuration interaction (CI), multireference CI, and averaged coupled pair functional theory. Examples of the latter include Mo/ller–Plesset perturbation theory (through fifth order, with estimates to infinite order), coupled cluster methods, and quadratic CI (with approximate inclusion of triple and quadruple excitations). The performance of the various methods in reproducing the difficult‐to‐describe 14N and 17O isotropic hyperfine interactions is judged in light of both experimental data, where available, and estimated full CI values. The full CI limit was approached through a systematic sequence of ever‐more‐extensive, selected multireference CI wave functions that would, in principle, include the full CI as its final element. While the isotropic coupling constants were ...

Accurate ab initio quartic force fields for the ions HCO + and HOC +

Abstract: The quartic force fields of HCO+ and HOC+ have been computed using augmented coupled cluster methods and basis sets of spdf and spdfg quality. Calculations on HCN, CO, and N2 have been performed to assist in calibrating the computed results. Going from an spdf to an spdfg basis shortens triple bonds by about 0.004 A, and increases the corresponding harmonic frequency by 10–20 cm−1, leaving bond distances about 0.003 A too long and triple bond stretching frequencies about 5 cm−1 too low. Accurate estimates for the bond distances, fundamental frequencies, and thermochemical quantities are given. HOC+ lies 37.8±0.5 kcal/mol (0 K) above HCO+; the classical barrier height for proton exchange is 76.7±1.0 kcal/mol.

Ge2H2: a germanium-containing molecule with a low-lying monobridged equilibrium geometry

Abstract: Recent experimental sind theoretical studied reporting remarkable monobridged structures for Si 2 H 2 , Al 2 H 2 , and Ga 2 H 2 have motivated us to re-investigate the singlet potential energy surface of Ge 2 H 2 using the self-consistent-field (CCP), single and double excitation configuration interaction (CISD), and single and double excitation coupled cluster (CCSD) methods in conjunction with a double-ζ plus polarization basis set (DZP). In addition to the dibridged (or butterfly) ground state and the low-lying vinylidene-like minimum reported earlier by Grev and DeLeeuw, our study predicts the existence of a monobridged isomer, which is characterized as a minimum by means of harmonic vibrational frequency analyses

Degeneracy breaking in the Hilbert‐space coupled cluster method

Abstract: The Hilbert space multireference coupled cluster method with single and double excitations (HS–MRCCSD) is applied to excited states of the N2 molecule. Particular attention is given to the breaking of degeneracy, where sublevels which should be degenerate by symmetry come out separated by as much as 0.3 eV. This feature is explained by the fact that a truncated coupled cluster expansion starting from an open‐shell determinant does not preserve spin or spatial symmetry.

Paramagnetism of closed shell diatomic hydrides with six valence electrons

Abstract: We have investigated the potential temperature independent van Vleck paramagnetism of closed shell diatomic hydrides with six valence electrons. More specifically, we have studied the magnetizability of the first row hydrides BeH−, BH, CH+, of the second row hydrides MgH−, AlH, and SiH+, and of the third row hydride GeH+. The magnetizability was calculated using a gauge origin independent method at the uncorrelated SCF level within the random‐phase approximation (RPA) as well as at different correlated levels within the second‐order polarization propagator approximation (SOPPA) or various coupled cluster polarization propagator approximations (CCDPPA/CCSDPPA). We find that BH, CH+, and SiH+ are paramagnetic, MgH−, AlH, and GeH+ are diamagnetic and BeH− is a borderline case tilting towards paramagnetism. It is primarily variations in the diamagnetic contribution to the magnetizability that determine the overall sign of the magnetizability.

Pulsed laser evaporation of boron/carbon pellets: Infrared spectra and quantum chemical structures and frequencies for BC2

Abstract: Pulsed laser evaporation of pellets pressed from boron and graphite powder gave a new 1:4 doublet at 1232.5 and 1194.6 cm−1 in addition to the carbon cluster absorptions reported previously. The 1232.5 cm−1 band dominated boron‐10 experiments. The new bands increased as carbon cluster bands decreased with increasing B/C ratio in the pellet and with increasing laser power. Augmented coupled cluster and full‐valence complete active space SCF (CASSCF) calculations predict the global minimum BC2 structure to be an asymmetric triangle: however, the vibrationally averaged structure will be an isosceles triangle with a strong symmetric B–C2 stretching frequency near 1200 cm−1. The calculated boron‐10/boron‐11 frequency ratio (1.0323) is in excellent agreement with the observed ratio (1.0317), and confirms assignment of the 1194.6 cm−1 band to the BC2 ring. Calculations predict linear BCC to be less stable by 6.2±2 kcal/mol and to absorb in the 2000–2050 cm−1 range: the barrier towards rearrangement to the cyclic...

Striking similarities between elementary silicon and aluminum compounds: monobridged, dibridged, trans-bent, and vinylidene isomers of aluminum hydride (Al2H2)

Abstract: Ab initio quantum mechanical methods five been used to study the singlet potential energy surface of Al 2 H 2 . Optimum geometries and harmonic vibrational frequencies were obtained for four geometrical isomers using the self-consistent-field (SCF), configuration interaction (CI), and coupled cluster (CC) methods. Both correlation methods including single and double excitations (CISD, CCSD) were employed, and all wave functions were determined with both DZP and TZ2P basis sets. Final energy predictions are obtained using large atomic natural orbital basis sets, and including the effects of triple excitations perturbatively using CCSD(T) methods. We found the planar dibridged structure to be the global minimum, as predicted earlier by Baird

A coupled‐cluster study of XNO (X=H,F,Cl): An investigation of weak X–N single bonds

Abstract: Singles and doubles coupled‐cluster (CCSD) theory and the CCSD(T) method, CCSD plus a perturbational estimate of the effects of connected triple excitations, have been used to determine the equilibrium structures, dipole moment, vibrational frequencies, and infrared intensities of the HNO, FNO, and ClNO species. A double polarized triple‐zeta (TZ2P) quality basis set was used. The CCSD(T) results are found to be in very good agreement with experiment, indicating that the CCSD(T) method performs well in describing the weak X–NO single bond. The experimental heats of formation of the FNO, and ClNO species are examined for internal consistency with experimental data for FNO2 and ClNO2, by using an isodesmic reaction. It is concluded that the experimental data exhibit a small inconsistency. An approach, involving in addition the use of homodesmic reactions, by which a more consistent set of thermochemical data may be obtained is proposed and discussed.