Michał Jaszuński

Intraatomic correlation effects for the He–He dispersion and exchange–dispersion energies using explicitly correlated Gaussian geminals

The coupling of the intermolecular interaction with the intramolecular correlation effects is considered using the coupled cluster (CC) formalism. The CC equations for the dispersion energy are presented and their relation to the double perturbation theory is analyzed. An approximate scheme based on partial decoupling of the CC equations is applied for the He–He interaction. Numerical results are obtained using explicitly correlated Gaussian geminal basis set. They confirm the importance of the intraatomic (apparent) correlation effects and agree very well with the experimentally derived potential.

An ab initio study of the non-linear optical properties of the He atom and the H2 molecule

Using the steady state formulation of the time-dependent Schrodinger equation a systematic examination has been undertaken of the frequency dependent dipole polarizabilities and third order susceptibilities for the helium atom and the hydrogen molecule. Full configuration interaction wavefunctions determined using large basis sets were employed. For both systems the calculated dipole polarizabilities are in excellent agreement with the best known results. For the calculated non-linear susceptibilities-the frequency dependent hyperpolarizability and the coefficient of the third harmonic generation-the results are estimated to be accurate to within a few per cent.

A multiconfigurational linear response study of N2

Abstract The multiconfigurationai time-dependent Hartree-Fock (MCTDHF) method (which is the correct linear response for a multiconfigurational wavefunction) has been applied in a study of the linear response properties of N 2 . The excitation energies, transition moments, static and dynamic dipole polarizabilities, magnetic susceptibility and nitrogen atom NMR shielding constant were analyzed. Several CGTO basis sets were used. With the largest CGTO basis set (124 functions) our TDHF results appear to be close to the Hartree-Fock response limits. For most of the low-lying excitation energies the MCTDHF calculation, which takes into account some valence shell correlation effects, yields results significantly improved with respect to TDHF. We present also the results for some higher lying excitations of particular interest for experimentalists, i.e. 1 Σ u + excitations 23–35 eV, the 1 Π u , excitation observed at ≈23 eV, and a 1 Π g transition observed at 31.4 eV. An analysis of the computed electric and magnetic properties indicates that they are strongly dependent on correlation corrections. The calculations of magnetic properties are the first to explicitly include correlation effects for a system this large.

Frequency-dependent hyperpolarizability of hydrogen fluoride

Abstract The response of a multiconfiguration self-consistent field wavefunction to a homogeneous periodic field is used to study the dipole hyperpolarizability of FH. All the tensor components are obtained for the second harmonic generation process for the ruby laser frequency and vibrational averaging is performed. Various contributions, which have been only estimated until now, were thus explicitly calculated. The final result, −7.8 au, is in agreement with previous theoretical estimates, but in disagreement with the experimental value.

Time-dependent Hartree-Fock calculations of dispersion energy

A new method of computing intermolecular dispersion energies, starting from the SCF wavefunctions of the separate systems, is discussed and illustrated. The method is based on the use of generalized frequency-dependent polarizabilities, calculated using TDHF (time-dependent Hartree-Fock) theory, and all ‘self-consistency’ effects are thus accounted for in the final expressions for the dispersion energy. No multipole expansions are required. The method is shown to be computationally efficient in test calculations of the dispersion interactions between helium atoms and between hydrogen fluoride molecules.

Ab initio study of magnetochiral birefringence

The magnetically induced axial birefringence of six closed-shell chiral molecules (methyloxirane, C3H6O, fluoro- and methylcyclopropanone, C3H3OF and C4H6O, carvone, C10H14O, limonene, C10H16, and proline, C5H9NO2) is determined at the Hartree–Fock wave-function level by evaluating the frequency dependent quadratic response functions entering the molecular property expression, according to Barron and Vrbancich [Mol. Phys. 51, 715 (1984)]. Both the magnetic dipole and the electric quadrupole contributions are taken into account and their relative importance is discussed. A proof of the origin independence of the magnetochiral birefringence is presented for the exact wave function and the dependence on the origin is investigated in finite basis set calculations at the Hartree–Fock level. For carvone, limonene, and proline the results are compared with recent experimental data obtained by two different experimental groups, which are in disagreement with respect to the magnitude of the magnetochiral effect. A...

An analysis and implementation of a general coupled cluster approach to excitation energies with application to the B2 molecule

A general scheme is presented for the calculation of excitation energies using the standard coupled cluster hierarchy and a simple implementation is described for the higher standard models. An error analysis is performed to find to what order excitation energies in different coupled cluster models are correct. The analysis includes both the standard coupled cluster hierarchy as well as the approximate models and considers excitations to states that are dominated by one, two, and three electron replacements compared to the reference state. Calculations are presented up to the quadruple excitation level for the open shell B2 molecule using an excited closed shell state as reference state to emphasize the usefulness of the order analysis. The coupled cluster excitation energies are compared to full configuration interaction results.

Frequency dependent hyperpolarizabilities of polyynes

Ab initio calculations have been performed for the static and dynamic polarizability and hyperpolarizability for a series of polyynes C2nH2 using self‐consistent field (SCF) (n=1–6) and multiconfiguration self‐consistent field (MCSCF) (n=1–4) wave functions. We have considered the longitudinal component of the static hyperpolarizability and the same component of the dynamic hyperpolarizability measured in electric‐field induced second harmonic generation γESHG=γ(−2ω;ω,ω,0). The frequency dependence of the polarizability and hyperpolarizability has been rationalized in terms of the coefficients in expansions in ω2. The static hyperpolarizabilities vary smoothly with the chain length and satisfy γ(C2nH2)=γ (C2H2)×nX, where X≊3.0. The dynamic hyperpolarizability satisfies a similar relation where X increases slowly with ω.

Magnetic susceptibility of the BH molecule

The coupled Hartree-Fock (CHF) perturbation approach and its extension to multiconfiguration wavefunctions (MC CHF scheme) were used to calculate the magnetic susceptibility of the BH molecule. The results obtained for an SCF and two pair-excitation MC SCF functions confirm the paramagnetism of the BH molecule and indicate a rather weak dependence of the computed molecular susceptibility on the correlation effects.

Density-Functional and Coupled-Cluster Singles-and-Doubles Calculations of the Nuclear Shielding and Indirect Nuclear Spin-Spin Coupling Constants of o-Benzyne.

Density-functional theory (DFT) and coupled-cluster singles-and-doubles (CCSD) theory are applied to compute the nuclear magnetic resonance (NMR) shielding and indirect nuclear spin-spin coupling constants of o-benzyne, whose biradical nature makes it difficult to study both experimentally and theoretically. Because of near-equilibrium triplet instabilities that follow from its biradical character, the calculated DFT NMR properties of o-benzyne are unusually sensitive to details of the exchange-correlation functional. However, this sensitivity is greatly reduced if these properties are calculated at the equilibrium of the chosen functional. A strong correlation is demonstrated between the quality of the calculated indirect spin-spin coupling constants and the quality of the calculated lowest triplet excitation energy in o-benzyne. Orbital-unrelaxed coupled-cluster theory should be less affected by such instabilities, and the CCSD NMR properties were only calculated at the experimental equilibrium geometry. For the shielding constants, the results in best agreement with experimental results are obtained with CCSD theory and with the Keal-Tozer KT1 and KT2 functionals. For the triply bonded carbon atoms, these models yield an isotropic shielding of 1.3, -3.3, and -1.2 ppm, respectively, compared with the experimentally observed shielding of 3.7 ppm for incarcerated o-benzyne. For the indirect spin-spin coupling constants, the CCSD model and the Perdew-Burke-Ernzerhof functional both yield reliable results; for the most interesting spin-spin coupling constant, (1)J (C⋮C), we obtain 210 and 209 Hz with these two models, respectively, somewhat above the recently reported experimental value of 177.9 ± 0.7 Hz for o-benzyne inside a molecular container, suggesting large incarceration effects.