Coupled Pair Functional Research Articles

ChemInform Abstract: SCF and Electron Correlation Studies on Structures and Harmonic In‐Plane Force Fields of Ethylene, trans‐1,3‐Butadiene, and all‐trans‐1,3,5‐Hexatriene.

Equilibrium structures and in‐plane harmonic force fields of ethylene, trans 1,3‐butadiene, and all‐trans 1,3,5‐hexatriene were investigated with the aid of ab initio Hartree–Fock (SCF) calculations applying basis sets of DZ+P and TZ+P quality. The most interesting parts of the force fields, namely those involving stretching vibrations of the conjugated carbon backbone, were subsequently reevaluated including electron correlation at the coupled pair functional (CPF) level. We demonstrate that electron correlation has a significant influence not only on the degree of bond alternation in the ground state equilibrium structure but simultaneously leads to an increase in absolute value of all off‐diagonal stretch–stretch coupling constants within the carbon backbone.

SCF and electron correlation studies on structures and harmonic in-plane force fields of ethylene, t r a n s 1,3-butadiene, and all-t r a n s 1,3,5-hexatriene

Equilibrium structures and in-plane harmonic force fields of ethylene, trans 1,3-butadiene, and all-trans 1,3,5-hexatriene were investigated with the aid of ab initio Hartree–Fock (SCF) calculations applying basis sets of DZ+P and TZ+P quality. The most interesting parts of the force fields, namely those involving stretching vibrations of the conjugated carbon backbone, were subsequently reevaluated including electron correlation at the coupled pair functional (CPF) level. We demonstrate that electron correlation has a significant influence not only on the degree of bond alternation in the ground state equilibrium structure but simultaneously leads to an increase in absolute value of all off-diagonal stretch–stretch coupling constants within the carbon backbone.

The prediction of nuclear quadrupole moments from a b i n i t i o quantum chemical studies on small molecules. II. The electric field gradients at the 17O, 35Cl, and 2H nuclei in CO, NO+, OH−, H2O, CH2O, HCl, LiCl, and FCl

The electric field gradients (efg’s) at the oxygen and hydrogen nuclei in CO,NO+, OH−, H2O, and CH2O, and at the chlorine, lithium, and hydrogen nuclei in HCl, LiCl, and FCl, calculated using ab initio quantum chemical methods, are reported. Using extended Gaussian basis sets, the efg’s at the oxygen and chlorine nuclei were computed at the self-consistent field (SCF), singles and doubles configuration interaction [CI(SD)], and coupled pair functional (CPF) levels of theory as the expectation values of the efg operator and also as the energy derivatives of the appropriate perturbed Hamiltonian using the finite field method. The efg’s at the hydrogen and lithium nuclei were computed as expectation values. Corrections due to zero point vibrational motions were also calculated. The effect of basis set incompleteness on the calculated efg’s is discussed and, where possible, corrected for. The calculated efg’s, together with the experimental nuclear quadrupole coupling constants, are used to estimate the 17O, 35Cl, and 2H nuclear quadrupole moments, and to test the quality of the correlated wave functions generated by the CI(SD) and CPF methods. The recommended values on the basis of the present calculations are −2.64±0.03, −8.2±0.2, and 0.278 fm2, respectively, for the 17O, 35Cl, and 2H nuclear quadrupole moments.

An a b i n i t i o quantum chemical study of the hydrogen- and ‘‘anti’’-hydrogen-bonded HF/ClF and HF/Cl2 dimers

A b initio electronic structure calculations at the SCF and coupled pair functional (CPF) level have been carried out for the hydrogen- and ‘‘anti’’-hydrogen-bonded isomers of the ClF/HF and Cl2/HF complexes. The stability of each isomer with respect to its constituent monomers has been calculated at the appropriate optimized geometry, paying particular attention to correlation effects, zero point energies, and basis set superposition errors. The differences between the latter quantities for a given pair of isomers, all calculated to be ≲0.5 kcal mol−1, are comparable in magnitude to the difference in stabilities, hence in a quantitative description of bonding in these dimers all these effects must be considered. The dipole moments and the 35Cl and 2H nuclear quadrupole coupling constants for the dimers have also been evaluated and compared with the available experimental data. In agreement with the results of recent molecular beam measurements, in both systems the anti-hydrogen-bonded isomers are found to be the more stable ones.

The prediction of nuclear quadrupole moments fromab initioquantum chemical studies on small molecules. I. The electric field gradients at the 14N and 2H nuclei in N2, NO, NO+, CN, CN−, HCN, HNC, and NH3

Electric field gradients (efg’s) at the nitrogen nuclei in N2, NO+, NO, CN, and CN− and at the nitrogen and hydrogen nuclei in HCN, HNC, and NH3, calculated using ab initio quantum chemical methods, are reported. Employing extensive Gaussian basis sets, the efg’s were computed at the self-consistent field (SCF), singles and doubles configuration interaction [CI(SD)], and coupled pair functional (CPF) levels of theory as the expectation values of the efg operator and also as the energy derivatives of the appropriate perturbed Hamiltonian using the finite field method. Corrections due to zero point vibrational motions were also calculated. The effect of basis set incompleteness on the calculated efg’s, together with the experimental nuclear quadrupole coupling constants, are used to estimate the 14N and 2H nuclear quadrupole moments, and to test the quality of the correlated wave functions generated by the CI(SD) and CPF methods. The recommended values, on the basis of the present calculations, are 2.05±0.02 and 0.29±0.01 fm2, respectively, for the 14N and 2H quadrupole moments.

Theoretical spectroscopic parameters for the low-lying states of the second-row transition metal hydrides

Spectroscopic parameters (De,re,μe) are determined for the second-row transition metal hydrides using large valence basis sets in conjunction with relativistic effective core potentials (RECPs). All-electron calculations are also performed for YH and AgH to calibrate the RECP results. Electron correlation is incorporated using singles-plus-doubles configuration interaction (SDCI), the coupled pair functional (CPF) method, and a modified version (MCPF) of CPF. Although similarities exist between the bonding in the first- and second-row transition metal hydrides, the greater overlap of the d orbitals in the second row with the hydrogen 1s orbital, tends to lead to larger dissociation energies and some changes in the relative ordering of the states. For example, the ground state of ZrH is predicted to be a 2Δ state whose bonding involves 4d–5s hybrid orbitals, whereas in TiH the ground state is a 4Φ state with primarily 4s–1s bonding. The bonding in the second-row transition metal hydrides involves a mixture of all three atomic asymptotes, 4dn5s2, 4dn+15s1, and 4dn+2, whereas contribution from the 3dn+2 asymptote is unimportant in the first-row TM hydrides. However, the bonding is generally much simpler to describe in the second-row as compared with the first-row TM hydrides, and the spectroscopic parameters are much less sensitive to the level of correlation treatment.

Theoretical study of the electric dipole moment function of the ClO molecule

The potential energy function and electric dipole moment function (EDMF) are computed for ClO X 2∏ using several different techniques to include electron correlation. The EDMF is used to compute Einstein coefficients, vibrational lifetimes, and dipole moments in higher vibrational levels. Remaining questions concerning the position of the maximum of the EDMF may be resolved through experimental measurement of dipole moments of higher vibrational levels. The band strength of the 1–0 fundamental transition is computed to be 12±2 cm−2 atm−1 in good agreement with three experimental values, but larger than a recent value of 5 cm−2 atm−1 determined from infrared heterodyne spectroscopy. The theoretical methods used include SCF, CASSCF, multireference singles plus doubles configuration interaction (MRCI) and contracted CI, coupled pair functional (CPF), and a modified version of the CPF method. The results obtained using the different methods are critically compared.

Theoretical study of the 7Σ+u state of N2

Theoretical potentials for the 7Σ+u state are reported using both extended Slater and Gaussian basis sets. Electron correlation is included using the interacting correlated fragments (ICF), the singles plus doubles configuration-interaction (SDCI), and the coupled-pair functional (CPF) approaches. Our best potential, corrected for basis set superposition errors, has a well depth of about 21 cm−1 and an re of 7.52 bohr. The inclusion of the nitrogen 2s correlation significantly increases the well depth. These results are in reasonably good agreement with the empirical potential of Ferrante and Stwalley, and support the contention that spin-polarized atomic nitrogen should behave like a classical solid such as Ne. It is shown that the modified Buckingham potential used by Ferrante and Stwalley is consistent with our ab initio potentials if smaller values are used for the dispersion coefficients of nitrogen atom.

Theoretical study of the dipole moments of selected alkaline-earth halides

A b initio calculations at the self-consistent-field (SCF), singles plus doubles configuration-interaction (SDCI), and coupled pair functional (CPF) level are reported for the dipole moments, μe, and dipole derivatives, (∂μ/∂r)re, of the X 2Σ+ ground states of BeF, BeCl, MgF, MgCl, CaF, CaCl, and SrF. For comparison, analogous calculations are performed for the X 1Σ+ state of KCl. The CPF results are found to be in remarkably better agreement with experiment than are the SCF and SDCI results. Apparently higher excitations are required to properly describe the radial extent along the bond axis of the remaining valence electron on the alkaline-earth metal.

Electronic structure and bonding in the ground state of Cu 2

Extended basis set calculations have been performed for the ground state of Cu 2 using CI(SD) and the coupled pair functional (CPF) method, a size-consistent modification of CI(SD). Special emphasis is given to the discussion of (i) basis saturation effects (up to g functions were included), (ii) effects of cluster corrections to achieve size consistency, (iii) relativistic effects, which were included in first order from the Cowan-Griffin operator. The final results are R e = 4.23 au = 2.238 A, D e = 1.84 eV, in close agreement with experimental values of 4.20 au = 2.22 A and 2.05 eV, respectively.

The coupled pair functional (CPF). A size consistent modification of the CI(SD) based on an energy functional

A modification of the CI(SD) energy functional is proposed which leads to size consistency through the use of partial normalization denominators. The method is derived from simple principles: correct description of separated two-electron systems and certain invariance requirements. This approach is connected to CEPA-1. The theoretical framework allows for a simple rationalization of connections between CI(SD), CEPA-1, and the linear version of CP–MET. As demonstrative applications we report comparisons with full CI calculations for BH, NH3, H2O, HF, and Re, De for F2, N2, O2, Cl2, NO, and CO obtained for very large basis sets.