Charge-transfer separability and size-extensivity in the equation-of-motion coupled cluster method: EOM-CCx

We study the charge-transfer separability (CTS) property of the Fock space (FS) and equation-of-motion (EOM) coupled cluster (CC) methods by analysing the charge-transfer (CT) excitation energy versus the donor-acceptor (D-A) distance. All FS-CC approaches fulfill the CT separability condition which is not the case for the standard EOM-CC approaches. This defect of the EOM-CC scheme can be fixed by slight modification of the H matrix's diagrammatic structure, namely by adding some "dressing" composed of disconnected terms. The latter guarantee CTS of the respective EOM-CC scheme and marginally improve local excitations. The newly proposed variant of the EOM-CCSD approach is termed EOM-CCSDx (size-extensive EOM-CCSD).     

Locally correlated equation-of-motion coupled cluster theory for the excited states of large molecules

We report an extension of the local correlation concept to electronically excited states via the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method. We apply the same orbital domain structure used successfully for ground-state CCSD by Werner and co-workers and find that the resulting localized excitation energies are in error generally by less than 0.2 eV relative to their canonical EOM-CCSD counterparts, provided the basis set is flexible and includes Rydberg-like functions. In addition, we account for weak-pair contributions efficiently using a correction to local-EOM-CCSD transition energies based on the perturbative (D) correction used with configuration interaction singles (CIS).     

Quantum chemical study of the electronic structure of NiCH2 + in its ground state and low-lying electronic excited states

The electronic structure of NiCH(2) (+), representative of transition metal carbene ions, is investigated by means of several methods of quantum chemistry. The relative stabilities of the four low-lying doublet electronic states ((2)A(1), (2)A(2), (2)B(1), and (2)B(2)) are determined at the coupled cluster singles and doubles level (CCSD) and triples level [CCSD(T) and CCSDT-3] with both a Hartree-Fock and density functional theory (Kohn-Sham) reference. The equation-of-motion coupled cluster for treatment of excited states in singles and doubles approximation (EOM-CCSD) is used to characterize the transition energies from the (2)A(1) electronic ground state to the low-lying doublet excited states. The (2)A(2) and (2)B(1) states are nearly degenerate, found to be separated by 940 cm(-1) at the EOM-CCSD level, in agreement with the CASSCF energy ordering. The (2)B(2) state is calculated to be higher in energy by more than 1.0 eV. The spin purity of the low-lying doublet and quadruplet states described by CCSD calculations based on the unrestricted open-shell Hartree-Fock reference is discussed.     

Ab initio calculation of the low-lying vibrational states of C2H2(A) in full dimensionality

We report full-dimensional calculations of vibrational energies of trans-C2H2(A) using the code MULTIMODE and with a full-dimensional potential energy surface obtained by fitting singles and doubles coupled-cluster equations-of-motion (EOM-CCSD) energies using a [3s 2p 1d] atomic natural orbital basis. The EOM-CCSD calculations were done with the code "ACES II". We compare the properties of the potential surface to previous calculations at the trans minimum and also compare the vibrational energies to experimental ones.     

Equation-of-motion coupled-cluster study on exciton states of polyethylene with periodic boundary condition

Equation-of-motion coupled cluster with singles and doubles (EOM-CCSD) method has been applied to exciton states of polyethylene using ab initio crystal Hartree-Fock method with one-dimensional periodic boundary condition. Full transformation of two-electron integrals from atomic-orbital basis to crystal-orbital basis has been performed for EOM-CCSD calculations. In order to make transformed integrals to have correct properties of translational symmetry, a lattice summation scheme has been proposed. The EOM-CCSD excitation energies have been obtained for the lowest singlet and triplet exciton states of polyethylene. The excitation energies converge with system size much faster than oligomer calculations using n-alkanes. Quasiparticle energy-level calculations by second-order many-body perturbation theory and by solving the inverse Dyson equation have also been performed to obtain exciton binding energies. Basis set dependencies on excitation energy, quasiparticle band gap, and exciton binding energy have been investigated. At the 6-31+G level, the excitation energy of the lowest singlet-exciton state and its binding energy are calculated to be 8.1 and 3.2 eV, respectively. The calculated excitation energy is well comparable with the corresponding experimental value, 7.6 eV.     

Solvent effects on the electronic transitions of p-nitroaniline: a QM/EFP study

Solvatochromic shifts of the electronic states of a chromophore can be used as a measure of solute-solvent interactions. The shifts of the electronic states of a model organic chromophore, p-nitroaniline (pNA), embedded in solvents with different polarities (water, 1,4-dioxane, and cyclohexane) are studied using a hybrid quantum mechanics/molecular-mechanics-type technique in which the chromophore is described by the configuration interaction singles with perturbative doubles (CIS(D)) method while the solvent is treated by the effective fragment potential (EFP) method. This newly developed CIS(D)/EFP scheme includes the quantum-mechanical coupling of the Coulomb and polarization terms; however, short-range dispersion and exchange-repulsion terms of EFP are not included in the quantum Hamiltonian. The CIS(D)/EFP model is benchmarked against the more accurate equation of motion coupled cluster with singles and doubles (EOM-CCSD)/EFP method on a set of small pNA-water clusters. CIS(D)/EFP accurately predicts the red solvatochromic shift of the charge-transfer π → π* state of pNA in polar water. The shift is underestimated in less polar dioxane and cyclohexane probably because of the omission of the explicit quantum-mechanical treatment of the short-range terms. Different solvation of singlet and triplet states of pNA results in different probabilities of intersystem crossing (ISC) and internal conversion (IC) pathways of energy relaxation in solvents of different polarity. Computed singlet-triplet splittings in water and dioxane qualitatively explain the active ISC channel in dioxane and predict almost no conversion to the triplet manifold in water, in agreement with experimental findings.     

Fifth-order constant denominator perturbation therory within a localized bond model: Contributions from single and double excitations

A Fifth-order constant denominator perturbation treatment of all single and double excitations occuring in the third-order perturbation wave function is presented for the perturbation configuration interaction using localized orbitals (PCILO ) method. Contributions from triple and quadruple excitations which decay back to singles and doubles at third order are automatically included in this theory. This method is computationally very fast, with an execution speed proportional to N³, Where N is the number of orbitals present. A [2,1] Padé approximate involving only singles and doubles contributions through to fifth order is shown to be remarkably accurate.     

Second- and third-order triples and quadruples corrections to coupled-cluster singles and doubles in the ground and excited states

Second- and third-order perturbation corrections to equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) incorporating excited configurations in the space of triples [EOM-CCSD(2)T and (3)T] or in the space of triples and quadruples [EOM-CCSD(2)TQ] have been implemented. Their ground-state counterparts--third-order corrections to coupled-cluster singles and doubles (CCSD) in the space of triples [CCSD(3)T] or in the space of triples and quadruples [CCSD(3)TQ]--have also been implemented and assessed. It has been shown that a straightforward application of the Rayleigh-Schrodinger perturbation theory leads to perturbation corrections to total energies of excited states that lack the correct size dependence. Approximations have been introduced to the perturbation corrections to arrive at EOM-CCSD(2)T, (3)T, and (2)TQ that provide size-intensive excitation energies at a noniterative O(n(7)), O(n(8)), and O(n(9)) cost (n is the number of orbitals) and CCSD(3)T and (3)TQ size-extensive total energies at a noniterative O(n(8)) and O(n(10)) cost. All the implementations are parallel executable, applicable to open and closed shells, and take into account spin and real Abelian point-group symmetries. For excited states, they form a systematically more accurate series, CCSD1 eV) and the ground-state wave function has single-determinant character. In other cases, however, the corrections tend to overestimate the triples and quadruples effects, the origin of which is discussed. For ground states, the third-order corrections lead to a rather small improvement over the highly effective second-order corrections [CCSD(2)T and (2)TQ], which is a manifestation of the staircase convergence of perturbation series.     

Theoretical investigations of molecules composed only of fluorine,oxygen and nitrogen: determination of the equilibrium structures of FOOF, (NO)2 and FNNF and the transition state structure for FNNF cis-trans isomerization

The deficiencies of common ab initio methods for the reliable prediction of the equilibrium structures of compounds composed of only the fluorine, oxygen and nitrogen atoms are investigated. Specifically, the importance of using large one-particle basis sets with multiple sets of polarization functions has been studied. Additionally, the need for a set of f basis functions was investigated. Several different single reference electron correlation methods have been tested in order to determine whether it is possible for a single reference based method to be routinely used on such chemical systems. These electron correlation methods include second order Møller-Plesset perturbation theory (MP2), singles and doubles configuration interaction (CISD), the coupled pair functional (CPF) approach and singles and doubles coupled cluster (CCSD) theory. The molecular systems studied include difluoroperoxide (FOOF), the cis form of the NO dimer, cis and trans difluorodiazene (FNNF) and the transition state to interconversion of the cis and trans isomers of FNNF. To the best of our knowledge, this is the first time that the cis-trans isomerization transition state has been reported. At the highest level of theory employed, the equilibrium structures of cis and trans FNNF agree very well with the experimental structures. However, the barrier to interconversion is predicted to be 65 kcal/mole, which is substantially higher than the experimental activation energy of 32 kcal/mole. Potential sources of error are discussed. A new diagnostic method for determining a priori the reliability of single reference based electron correlation methods is suggested and discussed.Contribution CCQC No. 36     

Improved description of the orbital relaxation effect by practical use of the self‐energy

The self‐energy shift in the orbital relaxation (OR) term of the polarization propagator complete through the second‐order is presented. In combination with the optimal damping parameter in the OR term, the modified propagator produces the excitation energy of the coupled‐cluster with singles and doubles (CCSD) accuracy. The self‐energy shift requires the floating‐point operation of , where N refers to the magnitude of the molecular size. Because the second‐order polarization propagator requires the floating‐point operation of , the additional computational effort to construct the self‐energy is negligibly small. Numerical results are shown for several molecules including glycine, 2,3,5,6‐tetrafluorobenzene, and naphthalene, and promising agreements with those of CCSD are confirmed within less than 0.2 eV. The basis set dependence is also tested for the water molecule using aug‐cc‐pV NZ (N = D–7), where this newly developed approach mimics the behavior of the CCSD values. The self‐energy shifting for the second‐order response matrix in combination with the use of a dumping parameter is efficiently implemented for calculations of medium‐sized molecular systems, including glycine and naphthalene. The developed approach provides CCSD‐like accuracy at a more affordable computational expense. © 2014 Wiley Periodicals, Inc.     

A coupled cluster study of the electronic spectroscopy and photochemistry of Cr(CO)6

The transition energies to the low-lying singlet and triplet excited states of Cr(CO)(6) are computed by equation-of-motion coupled cluster singles and doubles (EOM-CCSD) and similarity transformed equation-of-motion coupled cluster singles and doubles (STEOM-CCSD) methods with all-electrons basis sets. Both experimental and optimized geometries are used for the calculations. Calculations with various basis sets, among them one of the largest calculations performed at the EOM-CCSD level, based on atomic natural orbitals with 627 functions, were used to evaluate the basis set influence on computed transition energies. The presence of a shoulder at 3.9 eV in the experimental absorption spectrum, assigned to the (1)A(1g)-->(1)T(2u) transition, which was not reproduced by recent density functional theory (DFT) or multi-state complete active space perturbation theory (MS-CASPT2) is supported by the present STEOM-CCSD calculations with a theoretical value of 3.92 eV. In addition to this weak (1)A(1g)--> a (1)T(2u) absorption, we observe two strong absorptions corresponding to (1)A(1g)--> a (1)T(1u) at 4.37 eV (vs. an experimental value of 4.46 eV) and (1)A(1g)--> b (1)T(1u) at 5.20 eV (vs. an experimental value of 5.53 eV). Both are characterized as metal-to-ligand charge-transfer (MLCT) allowed transitions. The first metal-centered (MC) absorption at 4.37 eV in our best calculation is degenerate with the lowest MLCT absorbing state. The one-dimensional potential energy curves associated to the low-lying singlet MLCT and MC states as a function of the chromium axial carbonyl bond distance q(a) = [Cr-CO(axial)] show that an avoided crossing exists between the a (1)T(1g) (MC) and a (1)T(1u) (MLCT) states near 1.92 A, which is very close to the equilibrium Cr-CO distance. Moreover, the MC state seems to be dissociative for the CO loss. These two important features could explain the ultra-fast dissociation of CO (100 fs) observed in recent low intensity laser probed gas phase experiments.     

Electronic structure and vertical excitation spectrum of methylene amidogen CH2N

Ab initio electronic structure calculations are reported for five electronic states of the methylene amidogen radical. Structure parameters for the ground electronic state are predicted by RHF and D -MBPT (4) calculations. Vertical excitation energies were determined using four different theoretical chemical models: complete active space (CAS ) MCSCF , CAS /MCSCF plus singles and doubles Cl, fourth-order many-body perturbation theory SDQ -MBPT (4), and coupled-cluster theory.     

The structures,binding energies and vibrational frequencies of Ca3 and Ca4 — An application of the CCSD(T) method

Summary The Ca₃ and Ca₄ metallic clusters have been investigated using state-of-the-artab initio quantum mechanical methods. Large atomic natural orbital basis sets have been used in conjunction with the singles and doubles coupled-cluster (CCSD) method, a coupled-cluster method that includes a perturbational estimate of connected triple excitations, denoted CCSD(T), and the multireference configuration interaction (MRCI) method. The equilibrium geometries, binding energies and harmonic vibrational frequencies have been determined with each of the methods so that the accuracy of the coupled-cluster methods may be assessed. Since the CCSD(T) method reproduces the MRCI results very well, cubic and quartic force fields of Ca₃ and Ca₄ have been determined using this approach and used to evaluate the fundamental vibrational frequencies. The infrared intensities of both thee mode of Ca₃ and thet ₂ mode of Ca₄ are found to be small. The results obtained in this study are compared and contrasted with those from our earlier studies on small Be and Mg clusters.Dedicated to Prof. Klaus Ruedenberg on the occasion of his 70th birthday     

New procedure to evaluate aromaticity at the density functional theory,Hartree–Fock,and post‐self‐consistent field levels

The spatial exchange interaction, arising from the exchange‐type two‐electron integrals ( ) between two different groups P and Q, is another driving force for the delocalization of π‐electrons besides orbital charge‐transfer and exchange interactions. We have developed a new combination program for restricted geometry optimization, in which all of the orbital and spatial interactions among isolated groups were excluded from the localized geometry of a conjugated molecule. This was achieved by deleting particular Fock elements and the 15 types of exchange‐type two‐electron integrals, ensuring that the corresponding π‐electrons are completely localized within their respective groups and the π‐orbitals are fully localized. The extra stabilization energy (ESE) of benzene is ?36.3 kcal/mol (B3LYP/6‐31G*), and the level of density functional theory, Hartree–Fock, and post‐self‐consistent field (Møller–Plesset 2, configuration interaction singles and doubles, and singles and doubles coupled‐cluster) and the basis sets have slight effect on the ESE. Based on the comparisons between our procedure, Morokuma's energy decomposition analysis and the block‐localized wave function method, it was confirmed that our program calculates reliable results. The nonaromaticity of acyclic polyenes and antiaromaticity of cyclobutadiene and planar cyclooctatetraene were also estimated. Comparison of the C? C single bond lengths in the ground state with its π‐localized geometries showed that shortening of the single bonds in acyclic polyenes and butadiyne should be attributed to different hybridization, demonstrating that the effect of π‐delocalization on single bonds is so small as to be negligible. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Theoretical study of the first transition row oxides and sulfides

Summary The first transition row oxides and sulfides are studied using several different levels of theory. The calculations show the bonding mechanism in the sulfides and oxides to be very similar. For the oxides, accurate experimental data allow the theoretical methods to be calibrated. The same level of theory is used to study the sulfides where there is far less experimental information. For ScO through MnO and CuO the coupled cluster singles and doubles technique including a perturbational estimate of the connected triple excitations [CCSD(T)] yields spectroscopic constants (_e, _e, andD ₀) in good agreement with experiment. The triple excitations are found to be very important in achieving this accuracy. For FeO to NiO, the self-consistent-field (SCF) approach yields orbitals that are localized on the metal or oxygen. This appears to cause problems for the single reference techniques; this is discussed in detail for NiO. The complete-active-space SCF/internally contracted averaged coupled pair functional approach (CASSCF/ICACPF) works well for FeO to NiO. The calculation of accurate dipole moments is found to be very difficult.     

Calculation of X‐ray scattering intensities by means of the coupled cluster singles and doubles model

Total X‐ray scattering intensity σ_ee(q) is very sensitive to electron correlation effects. In this study σ_ee(q) of N₂, CO, and N₂O have been computed by the coupled cluster singles and doubles (CCSD) method and compared with configuration interaction singles and doubles (CISD) calculations as well as experimental observations. σ_ee(q) curves by CCSD calculations are rather close to those by CISD, but although small, there still exist some discrepancies between calculated and observed values. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1315–1320, 2001     

Resolving an apparent discrepancy between theory and experiment: spin-spin coupling constants for FCCF

Ab initio equation of motion coupled cluster singles and doubles (EOM-CCSD) and second-order polarization propagator approximation (SOPPA) calculations have been performed to evaluate spin-spin coupling constants for FCCF (difluoroethyne). The computed EOM-CCSD value of (3)J(F-F) obtained at the experimental geometry of this molecule supports the previously reported experimental value of 2.1 Hz, thereby resolving an apparent discrepancy between theory and experiment. This coupling constant exhibits a strong dependence on the C-C and C-F distances, and its small positive value results from a sensitive balance of paramagnetic spin-orbit (PSO) and spin-dipole (SD) terms. The three other unique FCCF coupling constants (1)J(C-C), (1)J(C-F), and (2)J(C-F) have also been reported and compared with experimental data. While (1)J(C-F) is in agreement with experiment, the computed value of (2)J(C-F) is larger than our estimate of the experimental coupling constant.     

Configuration interaction calculations on the propane radical cation,C3H 8 +

Summary Proton isotropic hyperfine coupling constants have been calculated for three low-energy nuclear conformations on the ground state potential surface of the propane cation, using a multireference singles and doubles configuration interaction (MR-SDCI) wave function. The lowest point found on the potential surface hadC _2v symmetry and the electronic wave function at this point had²B₂ symmetry. At this point, the largest isotropic coupling constant is calculated to be 88.6 G, which is in fair agreement with the experimental value of 98 G obtained in an SF₆ matrix at 4 K. No support is found for a long-bond ground state of lower symmetry thanC _2v . AnotherC _2v minimum on the ground state potential energy surface was found at which the wave function had² B ₁ symmetry. At this point, two large coupling constants of 198 G and 35 G were calculated. AC _2v stationary point was also found on the ground state potential surface at which the wave function had² A ₁ symmetry. At this point, couplings of 86 G and 25 G were obtained. None of these agree closely with the other experimental result of couplings at both 100–110 G and 50–52.5 G which was obtained in freon matrices. It is suggested that the latter spectra might correspond to a dynamical average of two distorted² A' states inC _s symmetry.