Coupled-cluster Singles Doubles Research Articles

Infrared Spectra of ThH2, ThH4, and the Hydride Bridging ThH4(H2)x (x = 1−4) Complexes in Solid Neon and Hydrogen

Laser-ablated Th atoms react with molecular hydrogen to give thorium hydrides and their dihydrogen complexes during condensation in excess neon and hydrogen for characterization by matrix infrared spectroscopy. The ThH2, ThH4, and ThH4(H2)x (x = 1-4) product molecules have been identified through isotopic substitution (HD, D2) and comparison to frequencies calculated by density functional theory and the coupled-cluster, singles, doubles (CCSD) method and those observed previously in solid argon. Theoretical calculations show that the Th-H bond in ThH4 is the most polarized of group 4 and uranium metal tetrahydrides, and as a result, a strong attractive "dihydrogen" interaction was found between the oppositely charged hydride and H2 ligands ThH4(H2)x. This bridge-bonded dihydrogen complex structure is different from that recently computed for tungsten and uranium hydride super dihydrogen complexes but is similar to that recently called the "dihydrogen bond" (Crabtree, R. H. Science 1998, 282, 2000). Natural electron configurations show small charge flow from the Th center to the dihydrogen ligands.

The limits of local correlation theory: Electronic delocalization and chemically smooth potential energy surfaces

Local coupled-cluster theory provides an algorithm for measuring electronic correlation quickly, using only the spatial locality of localized electronic orbitals. Previously, we showed [J. Subotnik et al., J. Chem. Phys. 125, 074116 (2006)] that one may construct a local coupled-cluster singles-doubles theory which (i) yields smooth potential energy surfaces and (ii) achieves near linear scaling. That theory selected which orbitals to correlate based only on the distances between the centers of different, localized orbitals, and the approximate potential energy surfaces were characterized as smooth using only visual identification. This paper now extends our previous algorithm in three important ways. First, locality is now based on both the distances between the centers of orbitals as well as the spatial extent of the orbitals. We find that, by accounting for the spatial extent of a delocalized orbital, one can account for electronic correlation in systems with some electronic delocalization using fast correlation methods designed around orbital locality. Second, we now enforce locality on not just the amplitudes (which measure the exact electron-electron correlation), but also on the two-electron integrals themselves (which measure the bare electron-electron interaction). Our conclusion is that we can bump integrals as well as amplitudes, thereby gaining a tremendous increase in speed and paradoxically increasing the accuracy of our LCCSD approach. Third and finally, we now make a rigorous definition of chemical smoothness as requiring that potential energy surfaces not support artificial maxima, minima, or inflection points. By looking at first and second derivatives from finite difference techniques, we demonstrate complete chemical smoothness of our potential energy surfaces (bumping both amplitudes and integrals). These results are significant both from a theoretical and from a computationally practical point of view.

A Comparison of Møller-Plesset and Coupled Cluster Linear Response Theory Methods for the Calculation of Dipole Oscillator Strength Sum Rules and C6 Dispersion Coefficients

Four correlated linear response theory methods - the second order polarization propagator approximation (SOPPA), the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes, SOPPA(CCSD), the CC2 and coupled cluster singles doubles (CCSD) linear response theory - were used to determine the dipole oscillator strength sum rules of the hydrogen halides HX (with X = F, Cl, Br and I) and the C6 dispersion coefficient for all pairs of interacting HX molecules via numerical integration of the Casimir-Polder formula. The dependence of the polarizabilities, their frequency dependence and the C6 coefficients on the level of correlation and the dependence of the C6 coefficients on the two intramolecular bond lengths were studied.

All‐electron all‐virtual spinor space relativistic coupled‐cluster calculations for molecules of heavy elements using contracted basis set: Prediction of atomization energy of PbH4*

AbstractAll‐electron all‐virtual spinor space (AVSS) relativistic second order Møller–Plesset (RMP2), coupled‐cluster singles doubles (RCCSD), RCCSD(T) (RCCSD plus the triple excitation correction included perturbationally) calculations are reported for tetrahedral (Td) PbH4 at various bond lengths using our finite contracted universal Gaussian basis set. Our relativistic calculations predict the RMP2, RCCSD, and RCCD(T) molecular correlation energy for PbH4 as −2.2563, −2.1917, and −2.2311 au, respectively. Ours are the first AVSS RMP2, RCCSD, and RCCSD(T) molecular calculations for electron correlation energy of the heavy element molecule PbH4. All‐electron AVSS coupled‐cluster calculations for the Pb atom are also reported and these were used (in conjunction with the corresponding molecular electron correlation energy calculations for PbH4) to predict atomization energy (Ae) of PbH4 at various levels of coupled‐cluster electron correlation. Our predicted atomization energy for PbH4 (at the optimized bond length of 1.749 Å) with our Dirac–Fock, RMP2, RCCSD, and RCCSD(T) calculations is 5.73, 7.27, 11.24, and 11.62 eV, respectively. Neither such relativistic molecular correlation energy nor atomization energy has been reported so far for heavy polyatomic with 86 electrons. Calculation of relativistic molecular correlation energy is no more a nightmare, and bottlenecks are broken for the calculation of relativistic correlation as well as atomization energy for molecules of heavy elements. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

Ab Initio Study of Low-Lying Electronic States of SnCl2+

Complete active space self-consistent field (CASSCF), multireference configuration interaction (MRCI), and restricted-spin coupled-cluster singles-doubles with perturbative triples [RCCSD(T)] calculations have been carried out on low-lying doublet and quartet states of SnCl2+, employing basis sets of up to aug-cc-pV5Z quality. Effects of core correlation and off-diagonal spin-orbit interaction on computed vertical ionization energies were investigated. The best theoretical estimate of the adiabatic ionization energy (including zero-point vibrational energy correction) to the X2A1 state of SnCl2+ is 10.093+/-0.010 eV. The first photoelectron band of SnCl2 has also been simulated by employing RCCSD(T)/aug-cc-pV5Z potential energy functions and including Duschinsky rotation and anharmonicity.

Thirty years of relativistic self-consistent field theory for molecules: relativistic and electron correlation effects for atomic and molecular systems of transactinide superheavy elements up to ekaplutonium E126 with g-atomic spinors in the ground state configuration

Relativistic Hartree–Fock–Roothaan (RHFR) self-consistent field theory for molecules developed by Malli and Oreg (J Chem Phys 63, 830, 1975) is reviewed. Ab initio all-electron fully relativistic Dirac–Fock and the corresponding nonrelativistic Hartree–Fock calculations for a number of molecular systems of heavy and superheavy elements are discussed in order to asecrtain relativistic effects. It is pointed out for the first time that there are dramatic antibinding effects of relativity for diatomics of the superheavy elements ekagold and ekaastatine. These are first results of antibinding effects of relativity in relativistic quantum chemistry. Moreover, in order to take into account the relativistic and electron correlation effects simultaneously for these systems, relativistic Moeller Plesset second order (RMP2), coupled-cluster singles doubles (RCCSD) and RCCSD with inclusion of triple corrections perturbationally (RCCSD(T)) calculations performed by the author for a number of atomic and molecular systems of superheavy elements (SHE) including the primordial SHE ekaplutonium E126 (Z = 126) (with g atomic spinors occupied in the ground state atomic configuration) are reported. Such calculations and results have not been reported before for systems of superheavy elements.

Relativistic coupled-cluster single-double method applied to alkali-metal atoms

A relativistic version of the coupled-cluster single-double (CCSD) method is developed for atoms with a single valence electron. In earlier work, a linearized version of the CCSD method (with extensions to include a dominant class of triple excitations) led to accurate predictions for energies, transition amplitudes, hyperfine constants, and other properties of monovalent atoms. Further progress in high-precision atomic structure calculations for heavy atoms calls for improvement of the linearized coupled-cluster methodology. In the present work, equations for the single and double excitation coefficients of the Dirac-Fock wave function, including all nonlinear coupled-cluster terms that contribute at the single-double level, are worked out. Contributions of the nonlinear terms to energies, electric-dipole matrix elements, and hyperfine constants of low-lying states in alkali-metal atoms from Li to Cs are evaluated and the results are compared with other calculations and with precise experiments.

A near linear-scaling smooth local coupled cluster algorithm for electronic structure

We demonstrate near linear scaling of a new algorithm for computing smooth local coupled-cluster singles-doubles (LCCSD) correlation energies of quantum mechanical systems. The theory behind our approach has been described previously, [J. Subotnik and M. Head-Gordon, J. Chem. Phys. 123, 064108 (2005)], and requires appropriately multiplying standard iterative amplitude equations by a bump function, creating local amplitude equations (which are smooth according to the implicit function theorem). Here, we provide an example that this theory works in practice: we show that our algorithm leads to smooth potential energy surfaces and yields large computational savings. As an example, we apply our LCCSD approach to measure the post-MP2 correction to the energetic gap between two different alanine tetrapeptide conformations.

Coupled-cluster theory for bosons in rings and optical lattices

Bosons in optical lattices and rings are attractive and active fields of research in cold-atom physics. Here, we apply our recently developed coupled-cluster approach for bosons in external traps to these systems, and extend it to the lowest-in-energy excited states with total quasi- or angular-momentum k. In the coupled-cluster approach the exact many-boson ground state is obtained by applying an exponential operator exp{ T}, T = ∑ n = 1 N T n to the ground configuration, which is (usually) the state where the bosons occupy a single orbital. For excited states, a second exponential operator exp{ T ( k) }, T ( k ) = ∑ n = 1 N T n ( k ) is employed to accommodate the remaining excitations from the unperturbed excited configuration. Due to the conservation of momentum, T 1 and T 1 ( k ) can vanish. Working equations for coupled-cluster (singles) doubles (CCD) are provided and their implications are briefly discussed.

Coupled-cluster theory for systems of bosons in external traps

A coupled-cluster approach for systems of $N$ bosons in external traps is developed. In the coupled-cluster approach the exact many-body wavefunction is obtained by applying an exponential operator $\exp{T}$ to the ground configuration $|\phi_0>$. The natural ground configuration for bosons is, of course, when all reside in a single orbital. Because of this simple structure of $|\phi_0>$, the appearance of excitation operators $T=\sum_{n=1}^N T_n$ for bosons is much simpler than for fermions. We can treat very large numbers of bosons with coupled-cluster expansions. In a substantial part of this work, we address the issue of size consistency for bosons and enquire whether truncated coupled-cluster expansions are size consistent. We show that, in contrast to the familiar situation for fermions for which coupled-cluster expansions are size consistent, for bosons the answer to this question {\it depends} on the choice of ground configuration. Utilizing the natural ground configuration, working equations for the truncated coupled-cluster with $T=T_1+T_2$, i.e., coupled-cluster singles doubles (CCSD) are explicitly derived. Finally, an illustrative numerical example for a condensate with up to N=10000 bosons in an harmonic trap is provided and analyzed. The results are highly promising.

Theoretical studies of UO2(H2O)n2+,NpO2(H2O)n+, and PuO2(H2O)n2+ complexes (n=4–6) in aqueous solution and gas phase

Extensive ab initio calculations both in gas phase and solution have been carried out to study the equilibrium structure, vibrational frequencies, and bonding characteristics of various actinyl (UO2(2+), NpO2(+), and PuO2(2+)) and their hydrated forms, AnO2(H2O)n(z+) (n=4, 5, and 6). Bulk solvent effects were studied using a continuum method. The geometries were fully optimized at the coupled-cluster singles + doubles (CCSD), density-functional theory (DFT), and Møller-Plesset (MP2) level of theories. In addition vibrational frequencies have been obtained at the CCSD as well as MP2/DFT levels. The results show that both the short-range and long-range solvent effects are important. The combined discrete-continuum model, in which the ionic solute and the solvent molecules in the first and second solvation shells are treated quantum mechanically while the solvent is simulated by a continuum model, can predict accurately the bonding characteristics. Moreover, our values of solvation free energies suggest that five- and six-coordinations are equally preferred for UO2(2+), and five-coordinated species are preferred for NpO2(+) and PuO2(2+). On the basis of combined quantum-chemical and continuum treatments of the hydrated complexes, we are able to determine the optimal cavity radii for the solvation models. The coupled-cluster computations with large basis sets were employed for the vibrational spectra and equilibrium geometries both of which compare quite favorably with experiment. Our most accurate computations reveal that both five- and six-coordination complexes are important for these species.

Si2CN: a stable nitrogen-containing radical with cyclic ground state.

The structures and isomerization of Si(2)CN species are explored at density functional theory and ab initio levels. Fourteen minimum isomers are located connected by 23 interconversion transition states. At the coupled-cluster single double (CCSD)(T)/6-311+G(2df)//QCISD/6-311G(d) +zero-point vibrational energies level, the thermodynamically most stable isomer is a four-membered ring form cSiSiCN 1 with Si-C cross bonding. Isomer 1 has very strong C-N multiple bonding characters, formally suggestive of a radical adduct between Si(2) and CN. Such a highly pi-electron localization can effectively stabilize isomer 1 to be the ground state. The second low-lying isomer is a linear form SiCNSi 5 (9.8 kcal/mol above 1) with resonating structure among [Si=C-*N=Si], *[Si=C=N=Si], and [Si=C=N-Si*]* with the former two bearing more weight. The species 1 and 5 have very high kinetic stability stabilized by the barriers of at least 25 kcal/mol. Both isomers should be experimentally or astrophysically observable. In light of the fact that no cyclic nitrogen-containing species have been detected in space, the cyclic species 1 could be a very promising candidate. The calculated results are compared to those of the analogous molecules C(3)N, C(3)P, SiC(2)N, and SiC(2)P. Implications of Si(2)CN in interstellar and N-doped SiC vaporization processes are also discussed.

Quantum Monte Carlo and electron localization function study of the electronic structure of CO 2+

The atomization energy and heat of formation of CO 2 + are computed using the diffusion Monte Carlo (DMC) variant of quantum Monte Carlo (QMC) and compared with values determined at the Moller–Plesset second order (MP2), a generalized gradient approximation density functional theory (B3LYP-DFT), the coupled-cluster singles–doubles with perturbative triples [CCSD(T)] levels of theory. Hartree–Fock (HF) and complete active space self-consistent field (CASSCF) trial functions were used in the DMC calculations. A CASSCF trial function (TF) was found to yield an 8.1 kcal/mol improvement for both properties relative to the HF TF value. The DMC calculation with the HF TF gave an atomization energy of 374.0 kcal/mol, while the DMC result with the CASSCF TF yielded 382.1 kcal/mol; the experimental atomization energy is 381 kcal/mol. The DMC heat of formation is: 234.7 kcal/mol using the HF TF and 226.7 kcal/mol using the CASSCF TF. These values lie closer to experiment than results obtained from the MP2, DFT, and CCSD(T) methods, all at the complete basis set limit. The bonding character of CO 2 + and CS 2 + was examined using the electron localization function (ELF) method. The HF, MP2, and B3LYP-DFT wave functions were projected onto the single–triple and double–double resonance forms of the molecules to determine the relative contribution of the two forms to the ground state geometry. The double–double resonance form was found to be the larger contributor to the ground state for both systems.

Analytic second derivatives for the full coupled-cluster singles, doubles, and triples model: Nuclear magnetic shielding constants for BH, HF, CO, N2, N2O, and O3

An implementation of analytic second derivatives for the coupled-cluster singles, doubles, and triples (CCSDT) model is reported and applied to the calculation of nuclear magnetic shielding constants of BH, HF, CO, N2, N2O, and O3. The CCSDT calculations yield further evidence for the high accuracy provided by chemical shift calculations employing the coupled-cluster singles, doubles (CCSD) approach augmented by a perturbative triples correction [CCSD(T)].

A detailed study on the symmetry breaking and its effect on the potential surface of NO3

The tenacious symmetry breaking of the electronic wave function of the nitrate radical (NO3) and its effect on the ground-state potential energy surface is investigated in detail. The symmetry breaking of Hartree–Fock wave functions results from a dominance of the orbital localization effect over the resonance effect and leads to three different solutions, one symmetrical and two distorted ones, for the same electronic state. The respective equilibrium geometries of these solutions are points on different potential surfaces, making their comparison meaningless. The resonance effect is promoted by dynamic as well as static electron correlation. However, the dynamic correlation methods [e.g., many-body perturbation theory (MBPT) and coupled-cluster single double (CCSD)] cannot overcome the symmetry breaking of the reference function and the problem of multiple solutions persists. The symmetry breaking can be avoided by the complete active space self-consistent field (CASSCF) approach that yields unique, single-valued surfaces for all electronic states. However, a sufficiently large and appropriately selected active space has to be used to avoid unphysical distortion of the wave function. Still the orbital localization effect leads to equilibrium geometries of C2v symmetry which strongly depend on the state-averaging of the CASSCF wave function. Multireference single double configuration interaction (MR-SDCI) wave functions are also free of symmetry breaking, if the reference orbitals are and if the configuration space is invariant under the symmetry operations. MRCI geometry optimizations only result in D3h symmetric structures with bond lengths and harmonic frequencies in close agreement with experimental data.

Molecular-dynamics study of rotational alignment of NO+ drifting in helium—velocity and angular momentum distribution functions

Collision-induced rotational alignment of NO+ ions drifting in a helium buffer gas is studied with molecular dynamics using the ab initio potential surface of S. K. Pogrebnya et al. [Int. J. Mass Spectrom. Ion Proc. 149/150, 207 (1995)], obtained via a coupled-cluster singles–doubles approximation. We examine average translational and rotational temperatures, velocity and angular momentum distributions, and the dependence of these quantities on the applied electric field. The distributions show that angular momentum is preferentially aligned perpendicular to the electric field vector. We investigate the mechanism of this alignment through a multipolar moment expansion, and propose and demonstrate the accuracy of a bi-Maxwellian analytic form for describing the angular momentum distribution.

Estimate of the experimental static hyperpolarizability of neon based on coupled cluster response calculations

The frequency-dependent electric field induced second harmonic generation (ESHG) hyperpolarizability of neon is calculated using coupled cluster singles doubles (CCSD) response theory. The CCSD dispersion curve shows that the most recent fit through the experimentally measured ESHG data is too flat due to the fact that one of the measured points in the infrared region is incorrect. Based on the CCSD dispersion curve, we suggest an adjusted extrapolation of the experimental ESHG data to a static limit result of γ 0 = 106.4±2 au. This estimate is corroborated by a CCSD(T) calculation using a large one-particle basis set and including core correlation effects that gives 107.1 au.

Regioselectivity in cycloaddition reaction between phosphaacetylene and diazomethane: Anab initio study

The [3 + 2] cycloaddition reaction of phosphaacetylene with diazomethane was investigated by means of high level ab initio calculations. It was deduced that the aromatic diazaphosphole is formed via a nonaromatic intermediate. The regiospecificity of the reaction is thus determined by the energy difference between the two transition states that lead to the two possible regioisomeric intermediates. Of the transition states in the concerted pathways, the one leading to the regioisomer with two PC bonds (3) was found to be more stable at all the levels of theory investigated, including coupled-cluster singles doubles (CCSD)(T)/6-311 + G*//Møller-Plessett(MP)2/6-311 + G* (+ basis set superposition, BSSE, correction). The energy difference between the two transition states, however, is always less than 2 kcal/mol. When the free energies in the two reactions are calculated by use of the harmonic frequencies, the energy separation between the two transition structures remains practically unchanged. The free energy of activation ΔG† was 21 kcal/mol at the CCSD(T)/6-311 + G* level of theory and use of the MP2/6-31 + G* frequencies. At the MP2 level, a rather stable complex is obtained in the initial phase of the reaction. However, the stability of the complexes decreases at the CCSD(T) level, and application of the BSSE correction results in unstable complexes. © 1997 by John Wiley & Sons, Inc.

Analytic energy derivatives for the equation-of-motion coupled-cluster method: Algebraic expressions, implementation and application to theS 1 state of HFCO

The general theory of analytic derivatives for the equation-of-motion coupled cluster (EOM-CC) method is reviewed. Special attention is paid to the EOM-CC singles and doubles (EOM-CCSD) approximation, which has the same computational scaling properties as the coupled-cluster singles doubles (CCSD) ground state method and is therefore applicable to a wide range of molecular systems. The detailed spin orbital equations that must be solved in EOM-CCSD gradient calculations are presented for the first time, and some guidelines are discussed regarding their computational implementation. Finally, use of the EOM-CCSD gradient method is illustrated by determining the structure, dipole moment components, harmonic frequencies and infrared intensities of formyl fluoride (HFCO) in its singlet excited (n, π*) state.

Description of core-excitation spectra by the open-shell electron-attachment equation-of-motion coupled cluster method

The theoretical description of core-excitation spectra presents a difficult problem due to the large excitation energies involved, and the extensive relaxation effects that occur upon promotion of a core electron to a valence or Rydberg level. For this reason we follow a two-step procedure to evaluate core-excitation energies. We start from a coupled cluster singles-doubles (CCSD) description of the core ion to include the large relaxation effects, followed by adding an extra electron to the core-ionized state to obtain the various core-excited states of the neutral by using the open-shell electron attachment equation-of-motion coupled cluster method (EA-EOMCC). An important feature of the approach is that the term values, the core-excitation energies relative to the relevant core-ionization potential, are calculated directly and this allows us to achieve high accuracy. This work describes the extension of the EA-EOMCC method to open-shell reference states and we make applications to a number of molecular systems. The assignment of recently obtained high-resolution core-excitation spectra for acetylene and ethylene is discussed, and we compare our open-shell EA-EOMCC results to results obtained from closed-shell EA-EOMCC calculations based on the equivalent core ion corresponding to the core-excited molecular system. Special attention is paid to the singlet–triplet splitting for core-excited states, and we address the multireference character of core-ionized and core-excited states for molecules that contain symmetry-equivalent heavy nuclei, which relates to a persistent controversy in the literature concerning localized versus delocalized core holes.