Spin-projected coupled-cluster theory with single and double excitations

Coupled-cluster (CC) theory including single (S) and double (D) excitations and carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function is free from S + 1 spin contamination as can be confirmed by an analysis of the expectation value of the spin operator, Ŝ ². Contamination by the S + 2 contaminant can be projected out by an approximate procedure (APCCSD) with a projection operator, P^, represented by the product of the spin annihilation operators ? _{s+ 1} and ?_s+2. The computational cost of such a projection scales with O(M ⁶) (M is the number of basis functions). The APCCSD energy obtained after annihilation of the S + 2 contaminant can be improved by adding triple (T) excitations in a perturbative way, thus leading to APCCSD(T) energies. For the 17 examples studied, the deviation of the UHF-CCSD(T) energies from the corresponding full configuaration interaction values is reduced from 4.0 to 2.3 mhartree on the average as a result of annihilating the S + 2 contaminant in an approximate way. In the case of single-bond cleavage, APCSSD leads to a significant improvement of the energy in the region where the bonding electrons recouple from a closed shell to an open shell singlet electron pair. Received: 13 April 2000 / Accepted: 12 July 2000 / Published online: 24 October 2000     

A spin-adapted coupled-cluster based linear response theory for double ionization potentials

We developed in this article a spin-adapted formulation of the coupled-cluster based linear response theory (CC-LRT) for computing double-ionization potentials (DIPs), which may be experimentally observed by Auger spectroscopy. CC-LRT is a multireference generalization of the CC theory where the energy differences have no disconnected vacuum (core) diagrams, signifying core-extensivity. For the spin-adaptation of the CC-LRT equations for the singlet and triplet manifolds, we used the Young-Yamanouchi orthogonal spin-eigenfunctions. The orbital version of the CC-LRT equations are then automatically generated by the conjugate projection operators of Young-Yamanouchi spin functions. We illustrated the working of our spin-adaptation procedure by confining our CC-LRT equations to the space of 2h and 1p–3h ionized determinants. As numerical application of our formalism, we computed the Auger kinetic energies of HF and H₂O. We also analyzed the nature of size-extensivity of the DIPs generated by CC-LRT and showed explicitly that when the molecule is composed of two noninteracting fragments the computed DIPs are either DIPs of fragment A or B or a composite DIP depending on both A and B, which are just not sum of ionization potentials (IPs) of A and B. This analysis is done to underscore the fact that DIPs from CC-LRT is only core-extensive and not fully extensive. © 1996 John Wiley & Sons, Inc.     

Calculation of excited-state properties using general coupled-cluster and configuration-interaction models

Using string-based algorithms excitation energies and analytic first derivatives for excited states have been implemented for general coupled-cluster (CC) models within CC linear-response (LR) theory which is equivalent to the equation-of-motion (EOM) CC approach for these quantities. Transition moments between the ground and excited states are also considered in the framework of linear-response theory. The presented procedures are applicable to both single-reference-type and multireference-type CC wave functions independently of the excitation manifold constituting the cluster operator and the space in which the effective Hamiltonian is diagonalized. The performance of different LR-CC/EOM-CC and configuration-interaction approaches for excited states is compared. The effect of higher excitations on excited-state properties is demonstrated in benchmark calculations for NH(2) and NH(3). As a first application, the stationary points of the S(1) surface of acetylene are characterized by high-accuracy calculations.     

Degenerate symmetry-adapted perturbation theory of weak interactions between closed- and open-shell monomers: application to Rydberg states of helium hydride

Symmetry-adapted perturbation theory is extended to the (quasi) degenerate, open-shell case. The new formalism is tested in calculations of the interaction energies for a helium atom in the ground state interacting with an excited hydrogen atom. It is shown that the method gives satisfactory results if the coupling with higher Rydberg states of the dimer is small, as is the case for the A²Σ⁺,B²Π,E²Π,3²Π, and 1²Δ states of HeH. For the C²Σ⁺ state convergence of the method is very slow, but it can be improved by including the n=3 states in the model space. Received: 3 June 1998 / Accepted: 9 September 1998 / Published online: 7 December 1998     

Theoretical study of the valence π → π* excited states of polyacenes: anthracene and naphthacene

The valence π → π ^* excited states of anthracene and naphthacene are studied with multireference perturbation theory with complete active space self-consistent field reference functions. The predicted spectra provide a consistent assignment of all one- and two-photon spectra and T-T spectra of low-lying valence π → π ^* excited states of anthracene and naphthacene. The present theory predicts the valence π → π ^* excitation energies with an accuracy of 0.15 eV for anthracene and of 0.25 eV or better for naphthacene. The excited states of anthracene and naphthacene are compared with those of benzene and naphthalene studied previously. The present calculations predict that, going from anthracene to naphthacene, there is a symmetry reversal of the two lowest singlet state transitions, but not for the triplet, just as indicated by the experimental data. Some general trends of polyacene excited states are discussed based on the calculated results for benzene to naphthacene. Conclusive results obtained for anthracene and naphthacene can be used as a model for understanding the excited states of larger polyacenes. Received: 22 April 1998 / Accepted: 6 July 1998 / Published online: 28 September 1998     

Cyanovinyl radical: an illustration of the poor performance of unrestricted perturbation theory and density functional theory procedures in calculating radical stabilization energies

Stabilization energies for the 1-cyanovinyl radical (CH₂=CCN) have been calculated using a variety of conventional ab initio (M?ller–Plesset, quadratic configuration interaction and coupled-cluster) and density functional theory (B-LYP, B3-LYP) procedures, as well as with a range of compound methods. Compared with a high-level benchmark value (that predicts a stabilization energy of 17.1 kJ mol⁻¹), UMP2 and UMP4 give the wrong sign and magnitude of the stabilization energy (both methods predicting desta- bilization instead of stabilization), while B-LYP and B3-LYP overestimate the degree of stabilization. The RMP2, RMP4, QCISD(T) and CCSD(T) techniques, and several, but not all, variants of G2 and CBS theories give radical stabilization energies in good agreement with the benchmark value. Received: 15 June 1998 / Accepted: 19 August 1998 /  Published online: 15 February 1999     

Structure and stabilities of (HA1NH)n (n = 2–4)

Ab initio molecular electronic structure methods have been used to study the relative stability of the planar inorganic ring (HAlNH)_n (n = 2–4) during homodesmotic and monomer polymerization reactions. Optimized geometries, frequencies and energies through restricted Hartree-Fock/6-31G* are reported, and energies at the self-consistent field optimized geometries including M?ller-Plesset fourth perturbation theory with single, double and quadruple excitation (MP4SDQ) corrections are also reported for both reactions. Homodesmotic reactions with MP4SDQ −28.5 kcal/mol for (AlN)₂, 1.9 kcal/mol for (AlN)₃ and −0.97 kcal/mol for (AlN)₄. On analysing a π-molecular orbitals diagram, only one, three and three strongly bonding π-molecular orbitals exist for the planar four-, six- and eight-membered AlN rings, respectively. Received: 9 March 1998 / Accepted: 19 March 1998 / Published online: 23 June 1998     

Ab initio correlation corrections to the Hartree-Fock quasi band-structure of periodic systems employing Wannier-type orbitals

A size-consistent ab initio formalism to calculate correlation corrections to ionization potentials as well as electron affinities of periodic systems is presented. Our approach is based on a Hartree-Fock scheme which directly yields local orbitals without any a posteriori localization step. The use of local orbitals implies non-zero off-diagonal matrix elements of the Fock operator, which are treated as an additional perturbation and give rise to localization diagrams. Based on the obtained local orbitals, an effective Bloch Hamiltonian is constructed to second order of perturbation theory with all third-order localization diagrams included. In addition, the summation of certain classes of diagrams up to infinite order in the off-diagonal Fock elements as well as the Epstein-Nesbet partitioning of the full Hamiltonian are discussed. The problem of intruder states, frequently encountered in many-body perturbation theory, is dealt with by employing the theory of intermediate Hamiltonians. As model systems we have chosen cyclic periodic structures up to an oligoethylene ring in double-zeta basis; however, the theory presented here straightforwardly carries over to infinite periodic systems. Received: 30 April 1998 / Accepted: 27 July 1998 /  Published online: 7 October 1998     

Transition energies of Rn- and Fr-like actinide ions by relativistic intermediate Hamiltonian Fock-space coupled-cluster methods

The extrapolated intermediate Hamiltonian (XIH) Fock-space coupled cluster method in the 1-hole 1-particle sector is applied to calculate excitation energies of Xe-like La³⁺ and the Rn-like actinides Ac³⁺, Th⁴⁺, Pa⁵⁺ and U⁶⁺. Large basis sets and model spaces are used, the latter made possible by the XIH scheme. Comparison with experiment for the La ion shows very good agreement, with a mean absolute error of 0.11 eV for 14 excitations in the largest basis (37s33p25d23f14g12h11i6k), lending credence to predicted energies for the actinide ions. Significant Breit term contributions appear, and the DCB Hamiltonian is therefore used. Excellent results are obtained in the one-particle sector, where more experimental values are available. The MAE for 17 transition energies of La²⁺ is below 0.01 eV, and 18 levels of the Fr-like actinide ions Ac²⁺, Th³⁺ and U⁵⁺ give a MAE of 0.06 eV. Second-order perturbation theory values differ considerably from all-order and experimental energies.     

Quasirelativistic valence ab initio calculation of the potential-energy curves for Cd–rare gas atom pairs

The results of large-scale valence ab initio calculations of the potential-energy curves for the ground states and several excited states of Cd–rare gas (RG) van der Waals molecules are reported. In the calculations, Cd²⁰⁺ and RG⁸⁺ cores are simulated by energy-consistent pseudopotentials, which also account for scalar-relativistic effects and spin-orbit interaction within the valence shell. The potential energies of the Cd–RG species in the ΛS coupling scheme have been evaluated by means of ab initio complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) calculations with a total 28 valence electrons, but the spin-orbit matrix has been computed in a reduced configuration interaction space restricted to the CASSCF level. Finally, the Ω potential curves are obtained by diagonalization of the modified spin-orbit matrix (its diagonal elements before diagonalization substituted by the corresponding CASPT2 eigenenergies). The calculated potential curves, especially the spectroscopic parameters derived for the ground states and several excited states of the Cd–RG species are presented and discussed in the context of available experimental data. The theoretical results exhibit very good agreement with experiment. Received: 20 April 2000 / Accepted: 1 September 2000 / Published online: 21 December 2000     

Covalent modification of a glassy carbon electrode with penicillamine for simultaneous determination of hydroquinone and catechol

A simple and highly selective electrochemical method has been developed for the simultaneous determination of hydroquinone (HQ) and catechol (CC) at a glassy carbon electrode covalently modified with penicillamine (Pen). The electrode is used for the simultaneous electrochemical determination of HQ and CC and shows an excellent electrocatalytical effect on the oxidation of HQ and CC upon cyclic voltammetry in acetate buffer solution of pH 5.0. In differential pulse voltammetric measurements, the modified electrode was able to separate the oxidation peak potentials of HQ and CC present in binary mixtures by about 103 mV although the bare electrode gave a single broad response. The determination limit of HQ in the presence of 0.1 mmol L⁻¹ CC was 1.0 × 10⁻⁶ mol L⁻¹, and the determination limit of CC in the presence of 0.1 mmol L⁻¹ HQ was 6.0 × 10⁻⁷ mol L⁻¹. The method was applied to the simultaneous determination of HQ and CC in a water sample. It is simple and highly selective.     

The X˜1A1, a˜3B1, a˜1B˜1, and B˜1A1 electronic states of SiH2

Four electronically low-lying states of silylene (SiH₂) have been studied systematically using high level ab initio electronic structure theory. Self-consistent field (SCF), two-configuration (TC) SCF, complete active space (CAS) SCF, configuration interaction with single and double excitations (CISD), and CASSCF second-order (SO) CI levels of theory were employed with eight distinct basis sets. The zeroth-order wave functions of the ground (X˜ ¹A₁ or 1 ¹A₁) and B˜ ¹A₁ (or 2 ¹A₁) excited states are appropriately described by the first and second eigenvectors of the TCSCF secular equations. The TCSCF-CISD, CASSCF, and CASSCF-SOCI wave functions for the B˜ ¹A₁ (or 2 ¹A₁) state were obtained by following the second root of the CISD, CASSCF, and SOCI Hamiltonian matrices. At the highest level of theory, the CASSCF-SOCI method with the triple zeta plus triple polarization augmented with two sets of higher angular momentum functions and two sets of diffuse functions basis set [TZ3P(2f,2d)+2diff], the energy separation (T₀) between the ground (X˜ ¹A₁) and first excited (a˜ ³B₁) states is determined to be 20.5 kcal/mol (0.890eV,7180cm⁻¹), which is in excellent agreement with the experimental T₀ value of 21.0 kcal/mol (0.910eV,7340cm⁻¹). With the same method the T₀ value for the a˜ ¹B₁−X˜ ¹A₁ separation is predicted to be 45.1 kcal/mol (1.957 eV,15780 cm⁻¹), which is also in fine agreement with the experimental value of 44.4 kcal/mol (1.925 eV,15530 cm⁻¹). The T₀ value for the B˜ ¹A₁−X˜ ¹A₁ separation is determined to be 79.6 kcal/mol (3.452 eV,27 840 cm⁻¹). After comparison of theoretical and experimental T₀ values for the a˜ ³B₁ and a˜ ¹B₁ states and previous studies, error bars for the B˜ ¹A₁ state are estimated to be ±1.5 kcal/mol (±525 cm⁻¹). The predicted geometry of the B˜ ¹A₁ state is r_e(SiH)=1.458 and θ_e=162.3^∘. The physical properties including harmonic vibrational frequencies of the B˜ ¹A₁ state are newly determined. Received: 10 March 1997 / Accepted: 2 April 1997     

Density functional study on zerovalent lanthanide bis(arene)-sandwich complexes

Several zerovalent lanthanide bis(arene)-sandwich complexes, Ln(η⁶-C₆H₆)₂, Ln = La, Ce, Eu, Gd and Lu, have been studied by means of density functional theory. The calculated geometries are in good agreement with experiment. The calculated dissociation energies of the bond Ln-(η⁶-C₆H₆) may be considerably underestimated, but they correctly reveal the variation regularity. The bonding in these molecules can be described in terms of a relatively weak π-electron donation from benzene to Ln and a stronger electron back-donation from Ln 5d to the benzene π* orbitals. During bond formation, there is electron promotion from Ln 6s to 5d instead of from 4f to 5d, in opposition to the proposal of Anderson et al. The relativistic effect only slightly influences the molecular geometry, but decreases the bonding energy considerably through lowering the Ln 6s level and raising the 5d level. It enhances the trend of the bonding energy to decrease along the lanthanide series. Received: 22 June 1998 / Accepted: 9 September 1998 / Published online: 17 December 1998     

Electronic excitation of sulfur-organic compounds – performance of time-dependent density functional theory

 To define the scope and limitations of the time-dependent density functional theory (TDDFT) method, spectral absorption data of a series of about 100 neutral or charged sulfur-organic compounds with up to 24 non-hydrogen atoms and up to four sulfur atoms were calculated in the near-UV, visible and IR regions. Although the theoretical vertical transition energies correspond only approximately to experimental absorption band maxima, the mean absolute deviation was calculated to be 0.21 eV (1600 cm⁻¹). The main absorption features of various compounds with monocoordinated or dicoordinated sulfur atoms are well reproduced. As far as possible TDDFT results were compared with those of semiempirical Zerner's intermediate neglect of differential overlap (ZINDO/S) and of Pariser–Parr–Pople (PPP) calculations. TDDFT also works well in cases where the semiempirical methods fail. Limitations of TDDFT were encountered with calculations of spectral absorptions of dye molecules. The “vinylene shift” of polymethine dyes is not reproduced by TDDFT. Whereas electronic excitation energies delocalized polar and betainic chromophores are reasonably well reproduced, excitation energies of charge-transfer-type and charge-resonance-type transitions of weakly interacting composite chromophores are significantly underestimated. Received: 30 October 2000 / Accepted: 29 November 2000 / Published online: 22 May 2001     

Analytic UHF-CCSD(T) second derivatives: implementation and application to the calculation of the vibration-rotation interaction constants of NCO and NCS

An implementation of analytic open-shell UHF-CCSD(T) second derivatives is presented. To demonstrate applicability and test the accuracy of the UHF-CCSD(T) approach for the determination of spectroscopical parameters, vibration-rotation interaction constants were calculated for the ground (1²Π) and first electronically excited (1²Σ) states of the NCO and NCS radicals. In addition, harmonic vibrational frequencies for both states, the Renner-Teller parameter for the ground state, as well as the 1²Π→1²Σ excitation energy are reported. While the computed values are in good agreement with reliable experimental information for NCO, most of the data presented for NCS are predictions of quantities not well known from experiment. Received: 4 May 1998 / Accepted: 27 July 1998 / Published online: 12 October 1998     

Theoretical studies of the potential energy surface and wavepacket dynamics of the Li3 system

The three-dimensional (3D) potential energy surface of the ground state of Li₃ was determined by the multireference configuration interaction method. The vibrational motions and pseudorotation were investigated by a 3D time-dependent wavepacket formalism. The analytical expression of the 3D surface is given and the results of vibrational analyses at several critical points are presented. The low-lying excited states of Li₃ were examined for the C _{2 v} structure and the vertical and adiabatic excitation energies were calculated. The ground and singlet excited states of Li₂ were calculated and their spectroscopic constants compare well with the experimental values. A 3D wavepacket calculation was performed for simulations of the stimulated emission pumping spectrum in which the A state was taken as an intermediate. The recurrences of the autocorrelation functions were characterized by classical trajectory calculations. The autocorrelation functions obtained by wavepacket propagation are reproduced well by the accumulation of the classical trajectories in the short-time region. Received: 2 July 1998 / Accepted: 3 September 1998 / Published online: 8 February 1999     

Possible long-lived quartet resonance states of CO−

Two states of CO⁻ which are expected to live longer than the well-known ²Π shape resonance are examined and the results obtained are compared with the analogous states of the isoelectronic N₂ ⁻ system. The ⁴Σ⁻ and ⁴Π states are found to be stable with respect to dissociation. The latter state is also stable with respect to single-electron loss to its parent neutral state. The lifetime of this state is supposed to be long, but not necessarily long enough to allow detection in a mass spectrometer. Received: 28 May 1998 / Accepted: 23 July 1998 / Published online: 9 October 1998     

Application of the iterative difference-dedicated configuration interaction method to the determination of excitation energies in some benchmark systems: Be, CH+, BH and CH2

The iterative difference-dedicated CI method (IDDCI) has been applied to determine excitation energies in small systems for which benchmark FCI and other high-level calculations exist. Transitions to excited singlet and triplet states in Be and vertical transitions in CH⁺, BH and CH₂ are reported. The deviations from FCI results are lower than 0.1 eV and compare advantageously with SDCI including size-consistency corrections, (SC)²SDCI, and with coupled cluster calculations including the effect of triples, especially for the states which have a predominant double excitation character. The IDDCI procedure has been speeded up by using smaller subspaces for optimizing the molecular orbitals. Received: 17 January 1997 / Accepted: 31 July 1997     

Hydrogen Bonding Properties of the Complexes of Formaldehyde and its Derivatives with HF and HCl

Summary.  The complexes of formaldehyde and some of its derivatives with HF and HCl were investigated at HF/6-311 + +G^** and MP2/6-311 + +G^** levels of theory. Interaction energies were corrected for the basis set superposition error (BSSE). The full optimizations of dimers and monomers were performed during calculations. The Bader theory of atoms-in-molecules (AIM) was also applied for the localization of bond critical points (BCP) and for the calculation the electron densities and their Laplacians at these points. The relationships between H-bond energy and parameters obtained from calculations were also studied. Received June 29, 2001. Accepted (revised) October 29, 2001     

The spin-forbidden reaction CH(2∏) + N2→ HCN + N(4S) revisited I. Ab initio study of the potential energy surfaces

High-level ab initio electronic structure theories have been applied to investigate the detailed reaction mechanism of the spin-forbidden reaction CH(²∏) + N₂ → HCN + N(⁴S). The G2M(RCC) calculations provide accurate energies for the intermediates and transition states involved in the reaction, whereas the B3LYP/6-311G(d,p) method overestimates the stability of some intermediates by as much as about 10 kcal/mol. A few new structures have been found for both the doublet and quartet electronic states, which are mainly involved in the dative pathways. However, due to the higher energies of these structures, the dominant mechanism remains the one involving the C ₂ intersystem-crossing step. The C ₂ minima on the seam of crossing (MSX) structures and the spin-orbit coupling between the doublet and quartet electronic states are rather close to those found in previous studies. Vibrational frequencies orthogonal to the normal of the seam which have been applied in a separate publication to calculate the rate of the CH(²∏) + N₂ → HCN + N(⁴S) reaction with a newly proposed nonadiabatic transition-state theory for spin-forbidden reactions have been calculated at the MSX from first principles. Received: 23 June 1998 / Accepted: 21 September 1998 / Published online: 8 February 1999