Coupled Cluster Techniques Research Articles

Electronic correlation in cyclic polyenes. Performance of coupled-cluster methods with higher excitations

In this paper we consider the electrically neutral annulenes CMHM (M=6,10,14,18) and their cations CMHM4+ (M=10,14,18), having the cyclic geometry corresponding to the CM point group, and described by the electronic Hamiltonian of the Pariser–Parr–Pople (PPP) model (in which the strength of electronic correlations is controlled by the magnitude of the resonance integral β). We study the ground-state electronic-correlation effects in these systems by means of the single-reference coupled-cluster (CC) theory employing the restricted Hartree–Fock wave function as the reference. It is known that the basic CC technique—the coupled cluster singles and doubles (CCSD) method (for the annulenes equivalent to the CCD method)—breaks down in the strongly correlated regime of annulenes. In this paper we analyze the performance of the standard extensions of the CCD method, taking into account the connected triple (T) and/or quadruple (Q) excitations in the CC operator T̂: the CCDT, CCDQ, and CCDTQ methods. For comparison we use some modifications of the CCD method that emulate the coupling between the D and Q excitations: the ACP and ACPQ methods. Whenever available, the full configuration-interaction results serve as the reference. We study not only the ground-state correlation energies, but also the quality of the CC amplitudes corresponding to the double excitations, as well as the magnitude of quasidegeneracy effects. Our results provide evidence that not only the CCD, but also the CCDT, CCDQ, and CCDTQ methods break down when the correlation effects become sufficiently strong. This indicates a failure of the standard CC theory (in which the CCD method is gradually augmented by taking into account the T, Q etc. excitations) in the strongly correlated regime of the PPP annulene model.

Anchoring the water dimer potential energy surface with explicitly correlated computations and focal point analyses

Ten stationary points on the water dimer potential energy surface have been characterized with the coupled-cluster technique which includes all single and double excitations as well as a perturbative approximation of triple excitations [CCSD(T)]. Using a triple-ζ basis set with two sets of polarization functions augmented with higher angular momentum and diffuse functions [TZ2P(f,d)+dif], the fully optimized geometries and harmonic vibrational frequencies of these ten stationary points were determined at the CCSD(T) theoretical level. In agreement with other ab initio investigations, only one of these ten stationary points is a true minimum. Of the other nine structures, three are transition structures, and the remaining are higher order saddle points. These high-level ab initio results indicate that the lowest lying transition state involved in hydrogen interchange is chiral, of C1 symmetry rather than Cs as suggested by recently developed 6D potential energy surfaces. The one- and n-particle limits of the electronic energies of these ten stationary points were probed by systematic variation of the atomic orbital basis sets and the treatment of electron correlation within the framework of the focal-point analysis of Allen and co-workers. The one-particle limit was approached via extrapolation of electronic energies computed with the augmented correlation consistent basis sets (aug-cc-pVXZ, X=D−6), and, independently, by estimating the basis set incompleteness effect with the explicitly-correlated second-order Møller-Plesset method (MP2-R12). Electron correlation was evaluated at levels as high as the Brueckner coupled cluster method with double excitations and perturbatively treated triple and quadruple excitations [BD(TQ)]. Core correlation and relativistic effects were also assessed. Consideration of the aforementioned electronic effects as well as basis set superposition error leads to an estimate of 21.0 kJ mol−1 for the electronic dissociation energy of (H2O)2.

Ab initio investigations of the potential energy surfaces of the XO + HO2 reaction (X = chlorine or bromine)

The potential energy surfaces of the title reactions have been studied computationally using coupled cluster techniques. Many true minimum and transition state structures have been located, which connect the reactants with various product channels. The potential surfaces for the bromine reactions are found to be very similar to those of the chlorine analogues. On the singlet surface it is found that XO and HO2 come together to form chain HOOOX, which is 64 kJ mol(-1) (Cl) and 72 kJ mol(-1) (Br) more stable than the reactants. The energy barrier for HOOOX dissociation to either HOX + O-2 ((1)Delta) or HX + O-3 is calculated to be very high (at least 90 kJ mol(-1) for both the chlorine and bromine surfaces). By contrast, reaction along the triplet surface to form HOX + O-2 ((3)Sigma) is found to be energetically facile, with a small (ca. 10 kJ mol(-1)) negative activation barrier with respect to the reactants. The title reactions are therefore predicted to proceed along the triplet surface, implying that the branching ratio into the minor product channels (HX + O-3) is essentially zero. Extensive comparisons are drawn between the present studies and previous experimental and theoretical work. The present calculations predict a slight negative temperature dependence for the overall rate coefficient of the reactions along the triplet surface, in agreement with the current experimental and theoretical consensus. The atmospheric implications of the present studies are discussed.

Comparison of ab initio and density functional calculations of electric field gradients: The Fe57 nuclear quadrupole moment from Mössbauer data

The difficulty in accurate determination of the nuclear quadrupole moment of the first I=3/2 excited nuclear state of Fe57 from electronic structure calculations of the iron electric field gradient combined with Mössbauer measurements of the nuclear quadrupole splitting in the isomer shift is addressed by comparing ab initio with density functional calculations for iron pentacarbonyl, Fe(CO)5, ferrocene, Fe(C5H5)2, and the Δg5 electronic ground states of FeCl2 and FeBr2. While the ligand field gradient tensor components change relatively little with the method applied, the iron electric field gradient is sensitive to the specific density functional used. Single reference many-body perturbation theory for electron correlation also performs poorly for the iron electric field gradient and shows extreme oscillatory behavior with a change in the order of the perturbation series. Even with larger basis sets and coupled cluster techniques a precise value for the iron electric field gradient could not be determined from electronic structure calculations due to limitations in the theoretical procedures. In order to avoid uncertainties in the measured isomer shift which enters into the nuclear quadrupole coupling constant we determined the Mössbauer spectrum of Fe(C5H5)2 between temperatures of 4.2 and 295 K. In this range two phase transitions are observed, but the quadrupole splitting is not very dependent on the solid state structure in each phase. Solid state effects for the Fe(CO)5 are determined by comparing the iron electric field gradient of the isolated molecule with the value obtained from first principle solid state calculations at various levels of theory. These calculations show that the influence of near neighboring effects to the iron electric field gradient is small. Fully relativistic Dirac–Hartree–Fock calculations for Fe(CO)5 reveal that relativistic effects for the iron electric field gradient are small as well. Fe(CO)5 is therefore an ideal test molecule for the determination of an accurate nuclear quadrupole moment from electronic structure calculations if combined with an experimental nuclear quadrupole coupling constant. Our best estimate for the Fe57 nuclear quadropole moment is 0.14(2) barn in reasonable agreement with recent nuclear structure calculations.

Chemically accurate conformational energies for aziridine-2-carbonitrile

Extensive ab initio computations have been carried out to characterize the energy of trans-aziridine-2-carbonitrile relative to cis-aziridine-2-carbonitrile (also known as 2-cyanoaziridine). Correlation consistent basis sets of double-, triple-, quadruple-, and pentuple-ζ quality have been employed to approach the one-particle basis set limit for energies obtained with the restricted Hartree–Fock method and second-order Møller–Plesset perturbation theory. Contributions from higher-order excitations have been determined with the popular coupled-cluster technique which includes single and double excitations as well as a perturbative estimate of triple excitations [CCSD(T)] and with the Brueckner doubles method including a perturbative estimate of triple as well as quadruple excitations [BD(TQ)]. From a focal point analysis, the electronic energy separation is found to be 3.62 kJ mol−1, which is in excellent agreement with previous theoretical estimates, but is in disagreement with an experimentally estimated lower bound to the free energy difference of 11 kJ mol−1. The electronic energy of the transition structure connecting the two conformers was determined to be 77.15 kJ mol−1 higher than the cis-isomer.

Time-dependent density-functional determination of arbitrary singlet and triplet excited-state potential energy surfaces: Application to the water molecule

Over the past few years a large number of density-functional schemes have been developed for molecular excited states, many of which have been shown to produce poor results for water. We apply the time-dependent density-functional method using hybrid and asymptotically corrected functionals to evaluate the vertical excitation energies, C2v-relaxation energies and vibration frequencies, and dissociation pathways for up to eight singlet and six triplet excited states of water. The results are compared to experimental data as well as ab initio calculated data obtained using direct and equations-of-motion coupled-cluster techniques, as well as multireference configuration-interaction techniques. For most properties, the asymptotically corrected density-functional method produces results of comparable quality to those produced by the ab initio methods. However, the time-dependent methods produce very poor results for systems involving molecular dissociation. In fact, only the multireference approaches produce good descriptions of molecular dissociation, but in the regions of the (C2v) minima of the potential energy surfaces single-reference techniques are found to be both more accurate and much more robust.

Barrier to Methyl Internal Rotation of 1-Methylvinoxy Radical in the X̃(2A‘ ‘) and B̃(2A‘ ‘) States: Experiment and Theory

The jet-cooled laser induced fluorescence spectrum of the {tilde B} {yields} {tilde X} electronic transition of the 1-methylvinoxy radical is assigned, including both hot and cold bands. The barrier to methyl internal rotation in both {tilde X} and {tilde B} states is determined by fitting pure torsional transitions to a one-dimensional hindered-rotor model. The resulting 3-fold torsional barrier parameters are V{sub 3}' = -740 {+-} 30 cm{sup -1} for the {tilde B} state (minimum-energy conformation with one methyl CH bond cis to the frame CO bond) and V{sub 3}' = +130 {+-} 30 cm{sup -1} for the {tilde X} state (methyl CH bond trans to CO). The intensity pattern clearly indicates a change in the preferred methyl conformation upon excitation, while ab initio calculations provide the absolute conformations in each state. A variety of ab initio methods including CASSCF, multireference Cl, and coupled-cluster techniques were applied to both the {tilde X} and the {tilde B} states of 1-methylvinoxy. Only the largest coupled-cluster calculations yield a {tilde B}-state barrier in good quantitative agreement with experiment. In unsubstituted vinoxy, a {tilde B}-state geometry adjusted earlier to fit experimental rotational constants is evidently in error.

Gaussian-3 theory using coupled cluster energies

Variations of Gaussian-3 (G3) theory are presented in which the quadratic configuration interaction (QCISD(T)) energy calculation is replaced by a coupled cluster (CCSD(T)) energy calculation. This modification is made to four G3 methods that have been previously introduced. The replacement of the QCISD(T) energy by the CCSD(T) energy results in little change in the accuracy of the methods as assessed on the G2/97 test set, although the maximum deviations decrease slightly. These new G3 methods based on the coupled cluster technique are a useful alternative to the G3 methods based on quadratic configuration interaction.

Bosonized squeezed-state coupled-cluster approach to electron correlations in nonlinear spectroscopy

The signatures of excited-state correlations in the third-order optical response of many-electron systems are calculated using a time-dependent quasiparticle picture which maps the optical excitations onto a system of interacting bosons, following a transformation to boson (oscillator) variables. The many-body wavefunction is approximated by a Gaussian wavepacket representing a squeezed state in the quasiparticle space. Unlike the standard coupled-cluster technique, the present approach constitutes a generalized coherent state representation which makes it possible to derive simple closed equations of motion for its parameters. The time-dependent Hartree–Fock approximation is recovered for weakly correlated systems where squeezing is negligible.

Vibrational—rotational dependence of molecular properties. Electric field gradients for HCl, LiCl, NaCl and KCl

The vibrational—rotational dependence of the nuclear quadrupole coupling constant (NQCC) for the isotopes 2H, 7Li, 23Na, 39K, and 35Cl is analysed in detail for the diatomic Group 1 chlorides HCl, LiCl, NaCl and KCl. The potential energy curves were calculated pointwise by using coupled cluster techniques. The electric field gradients (EFGs) and dipole moments were obtained analytically from a QCISD procedure using the Z vector method. Generally the calculated spectroscopic properties are in very good agreement with experimental data. Relativistic effects taken into account by a coupled cluster Douglas—Kroll procedure can safely be neglected for the electric field gradients up to potassium. The Inglis model which explains the trend and magnitudes of EFGs within an ionic model of weakly polarized atoms is analysed. According to this model the derivatives of the EFG, ∂ n q(R)/∂R n, with respect to the internuclear distance R should show alternating sign behaviour with increasing power n. Hence, the mechanical anharmonicity (deviation from Hooke's law potential) and the electrical anharmonicity (curvature of q(R)) are of different sign, and we expect partial cancellation of anharmonicity effects in the vibrational dependence of the NQCCs. Nevertheless, a perturbative vibrational—rotational analysis reveals a strong dependence of the chlorine and Group 1 element NQCCs on the vibrational level due to dominating mechanical anharmonicity.

Determination of the Complete Polarizability Tensor of 1,3-Butadiene by Combination of Refractive Index and Light Scattering Measurements and Accurate Quantum Chemical ab Initio Calculations

We have combined accurate quantum chemical calculations and light scattering measurements to obtain a reliable estimate of the electric dipole polarizability anisotropy of 1,3-butadiene. The theoretical investigation was based on finite-field many-body perturbation theory and coupled cluster techniques. An extensive study of basis set, electron correlation, and molecular geometry effects leads to a static value of α = 54.04 e2a02Eh-1 for the mean dipole polarizability of trans-butadiene, in very good agreement with the experimental result of 54.64 e2a02Eh-1 obtained from an extrapolation to infinite wavelength of refractivity data [Hohm, U.; Trümper, U. Ber. Bunsenges. Phys. Chem. 1992, 96, 1061]. The measured value of the dipole polarizability anisotropy of trans-butadiene is 42.5(1.7) e2a02Eh-1 at 514.5 nm. To our knowledge, these are the first light-scattering experiments to be reported for 1,3-butadiene. The present investigation brings forth new possibilities for the extension of accurate determination of electric polarizabilities to molecules of some size. cis-Butadiene is less polarizable and less anisotropic than the trans isomer.

How do coinage metal ions bind to benzene?

The interaction of the metal ions Cu+, Ag+, and Au+ with a benzene molecule has been investigated employing various quantum chemical strategies such as density functionals, Hartree—Fock, second-order perturbation theory and coupled cluster techniques. The three coinage metal cations show interesting differences in their preferred site of complexation with the π system of benzene. Cu+ prefers a highly symmetric η6 arrangement. In the Ag+—C6H6 complex the metal ion can change its position above the whole π plane of benzene virtually barrier free. For Au+ the calculations predict as favoured site of complexation a position above the carbon backbone, i.e., at the periphery and not in the centre of the benzene ring. Unlike copper or silver, this latter site of complexation is significantly less stable in the case of gold. At our most sophisticated level of theory, the computationally predicted binding energies agree well with the experimental numbers for the copper and silver complexes. For the gold complex only an estimate is available experimentally and the calculated number probably provides the most accurate result for this property so far.

How do coinage metal ions bind to benzene?

The interaction of the metal ions Cu+, Ag+, and Au+ with a benzene molecule has been investigated employing various quantum chemical strategies such as density functionals, Hartree—Fock, second-order perturbation theory and coupled cluster techniques. The three coinage metal cations show interesting differences in their preferred site of complexation with the π system of benzene. Cu+ prefers a highly symmetric η6 arrangement. In the Ag+—C6H6 complex the metal ion can change its position above the whole π plane of benzene virtually barrier free. For Au+ the calculations predict as favoured site of complexation a position above the carbon backbone, i.e., at the periphery and not in the centre of the benzene ring. Unlike copper or silver, this latter site of complexation is significantly less stable in the case of gold. At our most sophisticated level of theory, the computationally predicted binding energies agree well with the experimental numbers for the copper and silver complexes. For the gold complex only an estimate is available experimentally and the calculated number probably provides the most accurate result for this property so far.

Quenching of Li ( 2 P) by H 2 : potential energy surfaces, conical intersection seam, and diabatic bases

The quenching of Li (1s 22p; 2P) to Li (1s 22s; 2S) by H2 is considered using coupled-cluster and multireference configuration-interaction techniques. C 2 v (2A1, 2B2) and C ∞ v (2Π,2Σ+) sections of the 12A′ and 22A′ potential energy surfaces are determined. The C 2 v portion of the 12A′−22A′ seam of conical intersection is studied. Perhaps the most significant finding is a surprising trifurcation of this seam into a portion with only C s symmetry and the aforementioned C 2 v portion. The adiabatic-to-diabatic state transformation is considered in the vicinity of the seam of conical intersection using both perturbation theory and the dipole moment operator. The 2B2 section of the 22A′ potential energy surface exhibits an exciplex in the general vicinity of the seam of conical intersection. The 2Π section of the 22A′ potential energy surface possesses a global minimum lying 1.86kcal/mol below the Li (2P)+H2 asymptote. A van der Waals-like minimum with C ∞ v symmetry was found on the 12A′ potential energy surface.

Ab initio potential energy surface and vibrational frequencies of Ã( [formula omitted]) HCF

An extensive ab initio MRCI study of the Ã( 1 A″ ) surface of HCF is reported that includes characterization of the equilibrium geometry and the barriers to dissociation and linearity. An analytic potential energy surface in the equilibrium region was fitted to the computed energies that allowed the variational calculation of the vibrational fundamentals, overtones and combination bands to ∼6800 cm −1. The computed bend progression is in good agreement with the experimentally observed progression. The spectroscopic constants of HCF in the ground X̃( 1 A′ ) and lowest excited ã( 3 A″ ) states were also computed using MRCI and coupled cluster techniques.

Valence and excited states ofLiH−

Valence and excited dipole-bound states of the ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}$ anion are calculated with the recently developed electron-attachment equation-of-motion coupled-cluster technique. It is found that the first dipole-bound state of ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}$ corresponds to the second dissociation channel ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}{\ensuremath{\rightarrow}\mathrm{Li}}^{\mathrm{\ensuremath{-}}}{(}^{1}S)+\mathrm{H}{(}^{2}S).$ The second (excited) dipole-bound state of ${\mathrm{LiH}}^{\mathrm{\ensuremath{-}}}$ is below the neutral ground-state potential energy curve only for some range of the Li-H internuclear distance. This state appears at bond lengths larger than $\ensuremath{\approx}2.0\AA{}$ and decays at Li-H distances longer than \ensuremath{\approx}4.2 \AA{}, where the dipole moment of LiH becomes smaller than the critical value of 2.5 D. The adiabatic electron affinity of LiH calculated at the coupled-cluster level with the iterative inclusion of all single, double, and triple excitations and a large atomic natural orbital basis set is 0.327 eV, almost matching the recently obtained experimental value of $0.342\ifmmode\pm\else\textpm\fi{}0.012\mathrm{eV}.$

Ab initio characterization of the structure and energetics of the ArHF complex

The ArHF complex has been investigated using correlation consistent basis sets at several levels of theory, including Mo/ller–Plesset perturbation theory (MP2, MP3, MP4) and coupled cluster techniques [CCSD, CCSD(T)]. The three stationary points (the primary linear Ar–HF minimum, the secondary linear Ar–FH minimum, and the interposed transition state TS) on the counterpoise-corrected potential energy surface have been characterized. Calculations with the aug-cc-pV5Z basis set predict De for the Ar–HF minimum to be (with estimated complete basis set limits in parentheses) −215 (−218) cm−1 for MP4 and −206 (−211) cm−1 for CCSD(T). For the Ar–FH minimum and the TS, calculations with the d-aug-cc-pVQZ sets predict De’s (and CBS limits) of −97 (−99) and −76 (−78) cm−1 (MP4) and −93 (−94) and −75 (−76) cm−1 [CCSD(T)], respectively. The corresponding values for the H6(4,3,2) potential of Hutson [J. Chem. Phys. 96, 6752 (1992)] are −211.1±4 cm−1,−108.8±10 cm−1, and −82.6±10 cm−1. While the agreement of our CCSD(T) estimate with Hutson’s value is excellent for the global minimum, it is less so for the other two stationary points, suggesting that the H6(4,3,2) potential may be too attractive around the secondary minimum and the transition state.

Nuclear quadrupole coupling constants in alkali halide molecules: an ab initio quantum chemical study

The electric field gradients, and hence nuclear quadrupole coupling constants, plus the dipole moments of the alkali halide molecules LiF, LiCl, LiBr, NaF, NaCl, NaBr, KF, KCl and KBr have been calculated using ab initio quantum chemical methods that range from SCF to coupled cluster techniques with perturbative corrections for triple excitations [CCSD(T)], employing basis sets of quadruple zeta quality with multiple sets of polarization functions. Zero-level vibrational corrections to these quantities and spectroscopic constants also were computed. The level of agreement with experimental data is generally good, especially in the case of the light molecules. The field gradients at the Na and Cl nuclei in NaCl were analysed using the constrained spatial orbital variation technique in order to quantify the importance of polarization, charge transfer and Pauli repulsion contributions, and to understand why a simple electrostatic interpretation of the field gradients fails in the case of alkali halides. The dipole polarizabilities, Sternheimer antishielding constants γ∞ and electric field gradient–electric field hyperpolarizabilities ϵ of the alkali and halide ions also were calculated at a correlated level of theory (ACPF).

Correlated static‐exchange interaction for electron–molecule scattering: Case study for LiH and H2

The correlated static‐exchange potential for LiH and H2 molecules has been studied using many‐body coupled cluster technique. A general trend has been observed. Its importance to the low energy scattering of electrons from these diatomic targets has been pointed out.

Pseudorotational interconversion of the 2A1 and 2B2 states of HCOO

The lowest potential energy surface for the σ formyloxyl radical (σ-HCOO) is investigated with an equation-of-motion coupled cluster technique and basis sets that contain up to 195 contracted Gaussian functions. The 2 B 2 and 2 A 1 states of symmetric ( C 2v) σ-HCOO both lie on this surface and can be interconverted adiabatically by transporting the nuclei through nonsymmetric, but planar, intermediate geometries. In accord with previous high-level calculations, the potential energy surface that governs this pseudorotation process is predicted to be extremely flat. While the 2 A 1 state is found to be the highest point on the interconversion pathway when basis sets of modest size are used, this symmetric form is preferentially stabilized by basis set augmentation. Calculations with very large basis sets suggest that both the 2 A 1 and 2 B 2 C 2v structures are local minima on the surface, separated by a barrier of about 500 cm −1. These results are in qualitative agreement with conclusions reached in a recent electron photodetachment experiment.