Configuration Interaction Singles And Doubles Research Articles

Dependence of the multipole moments, static polarizabilities, and static hyperpolarizabilities of the hydrogen molecule on the H-H separation in the ground singlet state.

In this work, we provide values for the quadrupole moment Θ, the hexadecapole moment Φ, the dipole polarizability α, the quadrupole polarizability C, the dipole-octopole polarizability E, the second dipole hyperpolarizability γ, and the dipole-dipole-quadrupole hyperpolarizability B for the hydrogen molecule in the ground singlet state, evaluated by finite-field configuration interaction singles and doubles (CISD) and coupled-cluster singles and doubles (CCSD) methods for 26 different H-H separations r, ranging from 0.567 a.u. to 10.0 a.u. Results obtained with various large correlation-consistent basis sets are compared at the vibrationally averaged bond length r0 in the ground state. Results over the full range of r values are presented at the CISD/d-aug-cc-pV6Z level for all of the independent components of the property tensors. In general, our values agree well with previous ab initio results of high accuracy for the ranges of H-H distances that have been treated in common. To our knowledge, for H2 in the ground state, our results are the first to be reported in the literature for Φ for r > 7.0 a.u., γ and B for r > 6.0 a.u., and C and E for any H-H separation outside a narrow range around the potential minimum. Quantum Monte Carlo values of Θ have been given previously for H-H distances out to 10.0 a.u., but the statistical error is relatively large for r > 7.0 a.u. At the larger r values in this work, αxx and αzz show the expected functional forms, to leading order in r-1. As r increases further, Θ and Φ vanish, while α, γ, and the components of B converge to twice the isolated-atom values. Components of C and E diverge as r increases. Vibrationally averaged values of the properties are reported for all of the bound states (vibrational quantum numbers υ = 0-14) with rotational quantum numbers J = 0-3.

Multicomponent Coupled Cluster Singles and Doubles Theory within the Nuclear-Electronic Orbital Framework.

The nuclear-electronic orbital (NEO) method treats all electrons and specified nuclei, typically protons, quantum mechanically on the same level with molecular orbital techniques. This approach directly includes nuclear delocalization, anharmonicity, and zero point energy contributions of the quantum nuclei in the self-consistent-field procedure for solving the time-independent Schrödinger equation. Herein the multicomponent wave function based methods configuration interaction singles and doubles (CISD) and coupled cluster singles and doubles (CCSD) are implemented within the NEO framework and are applied to molecular systems. In contrast to the NEO-HF (Hartree-Fock) and NEO-CISD methods, which produce proton densities that are much too localized, the NEO-CCSD method produces accurate proton densities in reasonable agreement with a grid-based reference. Moreover, the NEO-CCSD method also predicts accurate proton affinities in agreement with experimental measurements for a set of 12 molecules. An advantage of the NEO-CCSD method is its ability to include nuclear quantum effects, such as proton delocalization and zero point energy, during geometry optimizations and nuclear dynamics simulations. The NEO-CCSD method is a promising, parameter free approach for including nuclear quantum effects in high-level electronic structure calculations of molecular systems.

Interplay between Electronic Correlation and Metal-Ligand Delocalization in the Spectroscopy of Transition Metal Compounds: Case Study on a Series of Planar Cu2+ Complexes.

We present a comprehensive theoretical study of the physical phenomena that determine the relative energies of three of the lowest electronic states of each of the square-planar copper complexes [CuCl4]2-, [Cu(NH3)4]2+, and [Cu(H2O)4]2+ and present a detailed analysis of the extent to which truncated configuration interaction (CI) and coupled cluster (CC) theories succeed in predicing the excitation energies. We find that ligand-metal charge transfer (CT) single excitations play a crucial role in the correct determination of the properties of these systems, even though the first impact of these CT on the energetics of these systems appears at fourth-order in perturbation theory. We provide a minimal selected CI space for describing these systems with multireference theories and use a high-order perturbation theory analysis within this space to derive a simple and general physical picture for the LMCT process. We find that coupled cluster singles and doubles (CCSD) energy differences agree very well with near full CI values even though the D1 diagnostics are large, which casts doubt on the usefulness of single-amplitude-based multireference diagnostics. Configuration interaction singles and doubles (CISD) severely underestimates the excitation energies, and the failure is a direct consequence of the size-inconsisency errors in CISD. Finally, we present reference values for the energy differences computed using explicitly correlated CCSD(T) and BCCD(T) theory.

Outstanding performance of configuration interaction singles and doubles using exact exchange Kohn-Sham orbitals in real-space numerical grid method.

To assess the performance of multi-configuration methods using exact exchange Kohn-Sham (KS) orbitals, we implemented configuration interaction singles and doubles (CISD) in a real-space numerical grid code. We obtained KS orbitals with the exchange-only optimized effective potential under the Krieger-Li-Iafrate (KLI) approximation. Thanks to the distinctive features of KLI orbitals against Hartree-Fock (HF), such as bound virtual orbitals with compact shapes and orbital energy gaps similar to excitation energies; KLI-CISD for small molecules shows much faster convergence as a function of simulation box size and active space (i.e., the number of virtual orbitals) than HF-CISD. The former also gives more accurate excitation energies with a few dominant configurations than the latter, even with many more configurations. The systematic control of basis set errors is straightforward in grid bases. Therefore, grid-based multi-configuration methods using exact exchange KS orbitals provide a promising new way to make accurate electronic structure calculations.

Revisiting the symmetry breaking in the X̃(2)Σu (+) state of BNB.

In agreement with our previous work [A. Kalemos, J. Chem. Phys. 138, 224302 (2013)], we established the centrosymmetric nature of the ground BNB state by means of the Restricted Coupled Cluster Singles and Doubles + Perturbative Triples (RCCSD(T)) computational method. We have also studied the symmetry adapted or broken behavior at the Configuration Interaction Singles and Doubles (CISD), CISD + Davidson Correction (CISD + Q), and RCCSD(T) computational levels based on various solutions of the Restricted Hartree-Fock (RHF) equations. Our theoretical conclusions are in agreement with the experimental results concerning the structure of the titled species.

Hole-particle characterization of coupled-cluster singles and doubles and related models

The hole-particle analysis introduced in the paper [J. Chem. Phys. 124, 224109 (2006)] is fully described and extended for coupled-cluster models of practical importance. Based on operator renormalization of the conventional amplitudes t(ai) and t(ab,ij), we present a simplified method for estimating the hole-particle density matrices for coupled-cluster singles and doubles (CCSD). With this procedure we convert the first-order density matrix of the configuration interaction (CI) singles and doubles (CISD) model, which lacks size consistency, into an approximately size-consistent expression. This permits us to correctly estimate specific indices for CCSD, including the hole and particle occupation numbers for each atom, the total occupation of holes/particles, and the entropylike measure for effective unpaired geminals. Our calculations for simple diatomic and triatomic systems indicate reasonable agreement with the full CI values. For CCSD and CISD we derive special types of two-center indices, which are similar to the charge transfer analysis of excited states previously given within the CIS model. These new quantities, termed charge transfer correlation indices, reveal the concealed effects of atomic influence on electronic redistribution due to electron correlation.

Electron correlation effects in N2 and CO studied by X-ray scattering and CISD calculations

Total X-ray scattering intensities σee(q) for N2 and CO have been measured as a function of momentum transfer using the energy dispersive method. Novel procedures to extract accurate σee(q), which eliminate effects of polarization, inelastic scattering, anomalous dispersion, and molecular vibration, have been proposed. A simplified theoretical treatment based on configuration interaction singles and doubles (CISD) calculations has been suggested. This procedure makes it possible to apply combined theoretical and experimental X-ray scattering studies to larger molecules. The inclusion of f and g functions is crucial, and the σee(q) calculated with the cc-pVQZ[5s4p3d2f1g] basis set almost reproduces the data based on more elaborate MR-CISD calculations within the experimentally most relevant region of up to q ≈ 3 au. In contrast to experimental electron scattering data, the X-ray scattering intensities agree well with the computed results.

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

AbstractTotal X‐ray scattering intensity σee(q) is very sensitive to electron correlation effects. In this study σee(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. σee(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

Ab Initio Calculations on Hydroaromatics: Hydrogen Abstraction and Dissociation Reaction Pathways

Three hydrogen abstraction reactions on cyclohexene, cyclohexadiene, and propene involving hydrogen radicals, and five bond dissociation reactions on cyclohexene, cyclohexene-3-yl, 1,3-cyclohexadiene, 1,3-cyclohexadiene-5-yl, and propene were studied using ab initio quantum chemical methods. The aim was to indicate possible reaction pathways for aromatization processes during oil and gas generation as well as coalification in natural processes. 3-21G and DZP basis sets were used for the unrestricted Hartree−Fock (UHF), restricted Hartree−Fock (RHF), second-order Moller−Plesset perturbation (MP2), and singles and doubles configuration interaction (SDCI) calculational methods. SDCI with size consistency corrections yielded a barrier of 9, 8, and 11 kcal/mol for hydrogen abstraction on cyclohexene, 1,3-cyclohexadiene, and propene, respectively. Near degeneracy causes UHF-based calculational methods to predict incorrectly energies for the open shell molecules. Two observations distinguish the transition state...

Vibrational structure of theO 1sionization spectrum ofCO2

The dynamical localization of the $\mathrm{O} 1s$ core holes in the ${\mathrm{CO}}_{2}$ molecule is studied ab initio beyond the linear vibronic coupling model. The vibrational structure of the $\mathrm{O} 1s$ x-ray photoelectron spectrum (XPS) has been calculated employing accurate potential energy surfaces of the ground and ionized diabatic electronic states obtained at the self-consistent field and singles and doubles configuration-interaction (SDCI) methods. A very good agreement of the SDCI computed vibrational structure of the $\mathrm{O} 1s$ XPS with the respective experimental high-resolution spectrum has been obtained. The anharmonicity of the ionic state potential-energy surface induced mostly by the ground-state surface anharmonicity plays a crucial role in the proper description of the vibrational line intensities. The linear model is discussed in detail. The linear model based on the vibronic coupling constants obtained from the geometry change in the ionized state relative to the ground-state reference configuration has been shown to contain a hidden renormalization of the coupling constants. This improves the agreement of the calculated intensities of the vibrational lines in the spectrum with the experiment, compared to the case of the strict linear model. The limitations of this renormalized linear model are discussed. Electron relaxation and correlation considerably affect the vibrational line intensities. The popular equivalent core approximation is tested for ${\mathrm{CO}}_{2}$. The calculation of the $\mathrm{O} 1s$ XPS performed at the SDCI level with and without this approximation is shown to provide almost identical results on the vibrational intensities.

Size-extensive calculations of static structure factors from the coupled cluster singles and doubles model

The x-ray incoherent scattering factor S(q), which is also called the static structure factor, is very sensitive to electron correlation. In this study a method for calculating S(q) based on coupled cluster singles and doubles (CCSD) approach is developed and the computed S(q) of H2O, CH3OH, CH3CN, C6H6, and C6H12 are compared with experimental results. It is shown that the CCSD method improves theoretical S(q) of large molecules significantly compared with those by configuration interaction singles and doubles (CISD) previously employed.

X-ray and electron scattering intensities of molecules calculated using density functional theory

The elastic and total intensities for x-ray and high-energy electron scattering from the ten-electron hydride series has been calculated from Kohn–Sham orbitals using the BLYP, B3LYP and LSDA functionals, and compared to the previous Hartree–Fock and singles and doubles configuration interaction (SDCI) results of Wang [J. Wang, A. N. Tripathi, and V. H. Smith, Jr., J. Chem. Phys. 101, 4842 (1994)] in the same basis. In those cases where density functional theory (DFT) provides a significantly better electron density than Hartree–Fock, the pair density and hence total scattering intensity for x-rays is also better reproduced, especially in the low s region. The asymptotic behavior of the scattering curves from the DFT methods is poorer than Hartree–Fock due to the inability of DFT to reliably predict the density at the nucleus, the electron–electron distribution at zero-electron separation, and the second moment of the electron–electron distribution.

Static structure factor and electron correlation effects studied by inelastic x-ray scattering spectroscopy

Inelastic x-ray scattering spectra of methanol, acetonitrile, benzene, and cyclohexane have been measured with 2 eV resolution for momentum transfer q between 0.69 and 2.77 a.u. using synchrotron radiation from the photon factory (PF) storage ring. By utilizing the Bethe sum rule, the spectra were brought onto an absolute scale, so that the static structure factor S(q) has been obtained. S(q) of these molecules has also been calculated at the single reference configuration interaction (CI) with several types of basis sets. A new formula is proposed to carry out spherical averaging accurately. It is concluded that the CI singles and doubles (CISD) treatment is necessary to predict correct S(q), and that an inclusion of polarization function influences S(q) significantly at this level. An addition of f functions also improves the agreement with the experiments. S(q)’s based on CISD wave functions are in good agreement with the experimental ones, in particular at large q.

The prediction of molecular equilibrium structures by the standard electronic wave functions

A systematic investigation has been carried out of the accuracy of molecular equilibrium structures of 19 small closed-shell molecules containing first-row atoms as predicted by the following standard electronic ab initio models: Hartree–Fock (HF) theory, Mo/ller–Plesset theory to second, third, and fourth orders (MP2, MP3, and MP4), coupled-cluster singles and doubles (CCSD) theory; CCSD theory with perturbational triples corrections [CCSD(T)], and the configuration-interaction singles and doubles (CISD) model. For all models, calculations were carried out using the correlation-consistent polarized valence double-zeta (cc-pVDZ) basis, the correlation-consistent polarized valence triple-zeta (cc-pVTZ) basis, and the correlation-consistent polarized valence quadruple-zeta (cc-pVQZ) basis. Improvements in the basis sets shorten the bond distances at all levels. Going from cc-pVDZ to cc-pVTZ, bond distances are on the average reduced by 0.8 pm at the Hartree–Fock level and by 1.6 pm at the correlated levels. From cc-pVTZ to cc-pVQZ, the contractions are about ten times smaller and the cc-pVTZ basis set appears to yield bond distances close to the basis-set limit for all models. The models HF, MP2, and CCSD(T) give improved accuracy at increased computational cost. The accuracy of the Mo/ller–Plesset series oscillates, with MP3 being considerably less accurate than MP2 and MP4. The MP2 geometries are remarkably accurate, being only very slightly improved upon at the MP4 level for the cc-pVQZ basis. The CCSD equilibrium structures are only moderately accurate, being intermediate between MP2 and MP3. The accuracy of the CCSD(T) model, in contrast, is high and comparable to that observed in most experimental studies and it has been used to challenge the experimentally determined equilibrium structure of HNO. The CISD wave function provides structures of low quality.

Local weak pairs spectral and pseudospectral singles and doubles configuration interaction

A new approximate correlation method has been developed by application of the local weak pairs approximation of Sæbo/ and Pulay to pseudospectral singles and doubles configuration interaction (SDCI) as developed by Martinez and Carter. The combination of the localization and pseudospectral approximations attacks both the problems of two-electron integral storage on disk and CI vector storage in memory that, respectively, hinder nondirect local spectral and nonlocal pseudospectral SDCI calculations individually and provides a scaling advantage over even direct local spectral SDCI calculations. The reproduction of total energies to within a kcal/mol leads to speed increases with respect to nonlocal calculations that grow larger with increasing molecular size: little or no savings for ethane and a factor of 1.1–1.6 for larger molecules studied (glyoxal, glycine, C6H2, and C8H2). The prediction of conformational energy differences with the new method appears quite promising, since energy difference predictions accurate to within a kcal/mol of the exact energy differences are obtained even when the single-point total energies are individually many kcal/mol in error. The speed increases for energy difference predictions of both local spectral and pseudospectral SDCI also grow with molecular size: from a factor of 4 in ethane and glyoxal to a factor of 6 in glycine. Additionally, when compared to the exact spectral result, the fastest local pseudospectral prediction of the conformational energy difference in glyoxal is in error by 0.2 kcal/mol and saves a factor of 10 in CPU time, indicating the prospects of combining local correlation and pseudospectral methods.

Ab initio calculations on first-row transition metal porphyrins Part 2. Ground state spin multiplicities, calculated ionisation potentials and electron affinities and their relation to catalytic activity

This article continues the discussion of ab initio calculations on chromium(III)-chloro-, manganese(III)-chloro-, iron(III)-chloro-, cobalt(III)-chloro-, cobalt(II)-, nickel(II)-, copper(II)- and zinc(II)-porphyrin. Restricted Hartree Fock (RHF) and Singles and Doubles Configuration Interaction (SDCI) results were obtained with the quantum chemical program system GAMESS-UK. The SDCI calculations were used to confirm the high spin multiplicities found with RHF for the electronic ground states of the metal porphyrins. The metal, nitrogen and chlorine atoms were described with the Split Valence 3-21G basis set; the carbon and hydrogen atoms with STO3G. The largest SDCI calculation dealt with 14.6 million Configuration State Functions. The electron distribution of singly charged porphyrins (cations and anions) show that the Highest Occupied Molecular Orbitals (HOMOs) of each porphyrin are delocalised, doubly occupied orbitals from the porphyrin ring moiety. The HOMOs donate the first electron, even though there are singly occupied orbitals present in the system. Acceptance of the first electron takes place in an orbital dominated by metal Atomic Orbital components. The partially occupied d-like orbitals present in the porphyrins take little part in this process and tend to preserve their identities. The energy differences of the charged porphyrins may give an indication of their ionisation potentials and electron affinities. A relation is apparent between the spin multiplicity of the ground states of the porphyrins discussed here and the activity of the porphyrin in the catalytic decomposition of cyclohexyl peroxide: all porphyrins with a quartet or higher spin ground state may be found among the active catalysts.

Compact Variational Wave Functions Incorporating Limited Triple and Quadruple Substitutions

We have investigated a number of configuration interaction (CI) wave functions which incorporate the dominant effects of triple and quadruple substitutions. If we employ natural orbitals from a CI singles and doubles (CISD) procedure, then the orbitals may be conveniently partitioned into subspaces of varying importance, and electron configurations may be classified according to how they occupy each of the subspaces. We employ a CI model space containing all single and double substitutions and also those classes of triply and quadruply substituted configurations deemed most important on the basis of natural orbital populations. This a priori selection scheme recovers a large fraction of the energy of a CI including all triples and quadruples (CISDTQ) at a drastically reduced computational expense, and it represents a more “black-box” alternative to traditional multireference CI approaches. Implications for nonvariational approaches are also discussed.

A study of the X 2Σ+ and A 2Π states of MgAr + and MgKr +

The ground 2 Σ + and lowest excited 2 Π states of MgAr + and MgKr + are studied using the singles and doubles configuration-interaction (SDCI) approach, in conjuction with large basis sets. The effect of Mg core correlation and core polarization are accounted of using the core-polarization potential (CPP) approach. Franc-Condon factors, oscillator strengths, radiative lifetimes, dissociation energies, bond lenghts, and excitation energies are reported. The computed results are in good agreement with the available experimental data.

Characterization of the X̃ 1A′ state of isocyanic acid

Characteristics of the ground electronic state of HNCO have been investigated theoretically in a series of eight ab initio analyses involving qualitative features of the electronic structure, the barrier to linearity, the NH(3Σ−)+CO fragmentation energy, the H–NCO bond dissociation energy, heats of formation of isomers of HNCO, fundamental vibrational frequencies and anharmonic force fields, the rovibrational spectrum of DNCO, and the precise Re structure of isocyanic acid. Sundry state-of-the-art electronic structure methods were employed in the study, including restricted and unrestricted Hartree–Fock (RHF and UHF), complete-active-space self-consistent-field (CASSCF), configuration interaction singles and doubles (CISD), Mo/ller–Plesset perturbation theory through fourth and occasionally fifth order (MP2–MP5), coupled-cluster singles and doubles (CCSD), and CCSD augmented by a perturbative contribution from connected triple excitations [CCSD(T)]. The one-particle basis sets ranged in quality from (9s5p1d/4s2p1d) to (13s8p3d2f/6s5p3d2f ) on the heavy atoms and from (4s1p/2s1p) to (6s2p1d/4s2p1d) on hydrogen. Several revisions of thermochemical data are proposed, in particular, a larger barrier to linearity of 5.7(3) kcal mol−1, an enhanced bond energy of 85.4(10) kcal mol−1 for D0(NH–CO), and more reliable relative energies for the isomers of HNCO, viz., γe(HOCN)=25.5(10), γe(HCNO)=70(2), and γe(HONC)=84.5(15) kcal mol−1. In addition, the experimental value D0(H–NCO)=113.0(2) kcal mol−1 is confirmed. These results lead to several new proposals for heats of formation (ΔH°f,0, kcal mol−1): HNCO(−26.1), HOCN(−0.7), HCNO(+43.0), HONC (+57.6), and NCO(+35.3). A complete quartic force field has been constructed for HNCO by combining RHF third- and fourth-derivative predictions with CCSD quadratic force constants subjected to the scaled quantum mechanical (SQM) optimization scheme. This force field yields a set of ωi and χij vibrational constants which gives the following fundamental frequencies (with total anharmonicities in parentheses): ν1=3534(−186), ν2=2268(−45), ν3=1330(−9), ν4=778(−50), ν5=576(+9), and ν6=657(+21) cm−1, thus reproducing the observed band origins to 4 cm−1 or less. For DNCO the theoretical force field reveals misassignments of the low-frequency bending vibrations and predicts ν4(a′)=727, ν5(a′)=458, and ν6(a″)=633 cm−1. Finally, the theoretical vibration–rotation interaction constants (αi) for five isotopic species of HNCO have been used in conjunction with empirical rotational constants and the Kraitchman equations to determine re(N–H)=1.0030(20) Å, re(N–C)=1.2145(6) Å, re(C–O)=1.1634(4) Å, θe(H–N–C)=123.34(20)°, and θe(N–C–O)=172.22(20)°.

A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent-field higher-derivative methods. Linear polyatomic molecules

The inclusion of the anharmonicity of molecular vibrations is an important aspect of the goal of making highly accurate theoreticalpredictions of the spectroscopic properties of molecules. Recently developed analytic third derivative methods for selfconsistent-field(SCF) wavefunctions have made it possible to determine the complete cubic and quartic force fields of polyatomic molecules, thus allowing the treatment of anharmonic effects. Here we continue our systematic evaluation of the performance of such theoretical methods by studying several linear molecules which are well characterized experimentally, viz., HCN, DCN, CO 2, N 2O, OCS, C 2H 2, and C 2D 2. A number of anharmonic molecular properties have been determined, including vibration-rotation interaction constants, vibrational anharmonic constants, fundamental vibrational frequencies, sextic centrifugal distortion constants, rotational constants which include zero-point vibrational corrections, and vibrational and rotational l-type doubling constants. These anharmonic molecular constants are not as well converged with respect to basis set enlargement as those which were previously determined for asymmetric top molecules, apparently because all the molecules considered here contain multiple bonds. However, the reported anharmonic constants at the SCF level of theory are still in reasonably good agreement with the corresponding experimental constants. Significant improvements in accuracy are achieved by incorporating electron correlation at the configuration interaction singles and doubles (CISD) level of theory. Standard spectroscopic perturbationtheory methods are used in this study, which are directly and immediately applicable to larger molecular systems than those studied here.