Jens Oddershede

Transition moments and dynamic polarizabilities in a second order polarization propagator approach

We have formulated a polarization propagator approach which yields excitation energies, transition moments, and dynamic polarizabilities which are consistent through second order in the electronic repulsion. Certain terms are proven to be missing in our previous second order calculations of transition moments and dynamic polarizabilities and in the equation‐of‐motion calculations of the same quantities. Numerical calculations on carbon monoxide are performed. The calculations show that the major difference between the polarizability (and some transition moments) in the RPA and in the second order polarization propagator approximation is due to these terms. The total effect of all correction terms has been to improve considerably the agreement between theoretical and experimental estimates of the excitation properties for carbon monoxide.

Polarization Propagator Calculations

Publisher Summary The polarization propagator is the double-time Greens function that describes the propagation of a density disturbance through an interacting system. The focus of this chapter is to show how the polarization propagator can be used advantageously in practical calculations of excitation properties of atomic, molecular, and metallic systems. The approximate polarization propagator through any order in electronic repulsion is symmetric under a transformation E → –E, that is, it can be represented in a spectral form. This is not the case for the corresponding particle-hole propagator for which only the positive energy spectrum is treated consistently through the required order. This deficiency of the particle-hole propagator has very little influence on the (positive) excitation energies, whereas the transition moments are rather poor in methods where the E→ – E symmetry of the propagator is not preserved. The particle-hole propagator can be compared directly with the diagrammatic perturbation calculation of the proper particle-hole self-energy. The chapter also discusses the second-order response properties and sum rules, and the ground-state correlation energies.

Full four‐component relativistic calculations of NMR shielding and indirect spin–spin coupling tensors in hydrogen halides

Various methods for the inclusion of relativistic effects in the calculation of NMR parameters are discussed. Benchmark values for the NMR shieldings and indirect nuclear spin–spin coupling tensors for the hydrogen halides are calculated using the four‐component relativistic random phase approximation method. Apart from recovering the well‐known trend of increasing hydrogen isotropic shielding going from HF to HI, we also find a large effect on the anisotropy that decreases along this series. Inclusion of spin‐orbit coupling in a nonrelativistic formalism suffices to recover both effects on the hydrogen shieldings but fails to reproduce the much larger effect on the halogen shieldings. This effect can be explained by considering the relativistic mass‐velocity operator that contains correction terms to the nonrelativistic magnetic field operators. We recommend routine inclusion of the one‐electron spin‐orbit correction in calculations of hydrogen shieldings for hydrogens bonded to heavy atoms. For the heavy nucleus shielding one should include an additional mass‐velocity correction. The relativistic effect on the indirect nuclear spin–spin coupling tensor is large and affects mainly the isotropic values; the effect on the anisotropy is small.u2003©1999 John Wiley & Sons, Inc.u2003J Comput Chem 20: 1262–1273, 1999

A new implementation of the second‐order polarization propagator approximation (SOPPA): The excitation spectra of benzene and naphthalene

We present a new implementation of the second‐order polarization propagator approximation (SOPPA) using a direct linear transformation approach, in which the SOPPA equations are solved iteratively. This approach has two important advantages over its predecessors. First, the direct linear transformation allows for more efficient calculations for large two particle–two hole excitation manifolds. Second, the operation count for SOPPA is lowered by one order, to N5. As an application of the new implementation, we calculate the excitation energies and oscillator strengths of the lowest singlet and triplet transitions for benzene and naphthalene. The results compare well with experiment and CASPT2 values, calculated with identical basis sets and molecular geometries. This indicates that SOPPA can provide reliable values for excitation energies and response properties for relatively large molecular systems.

Second-order polarization propagator calculations of indirect nuclear spin-spin coupling tensors in the water molecule

Abstract The contribution to indirect nuclear spin-spin coupling tensors provided by the Fermi contact, the spin-dipolar, the Fermi contact/spin-dipolar crossterm, and the paramagnetic spin-orbit interactions are investigated in a zeroth-, first- (the same as the coupled Hartree-Fock method), and second-order polarization propagator approach. Numerical applications to the water molecule show that the second-order results for both the HO and the HH coupling constants are in good agreement with experimental data - especially if vibrational corrections and the diamagnetic spin-orbit contributions are taken into account. We find that the correlation corrections beyond coupled Hartree-Fock are important. We also report how the second-order results are influenced by neglect of some of the most time-consuming steps in the calculation.

Dynamic polarizabilities and raman intensities of CO, N2, HCl and Cl2

Abstract We have performed first-order (identical to coupled Hartree-Fock) and second-order polarization propagator calculations of the dynamic dipole polarizability tensor for the CO, N 2 , HCl and Cl 2 molecules. The derivatives of the polarizability tensor with respect to the internuclear distance at the equilibrium internuclear separation are compared with related data obtained from non-resonance Raman spectra. In most cases the correlation contributions beyond the coupled Hartree-Fock approximation have a more pronounced effect on the derivatives of the polarizability tensor than on the polarizability tensor itself. At both levels of approximation we found that derivatives of the dynamic polarizability tensor with respect to the internuclear separation increase with 10–15% for variation of the frequency from 0 (static polarizability) to about 28500 cm −1 . The depolarization ratio calculated from the polarizability derivatives shows no variation with frequency in the same frequency range.

A coupled cluster polarization propagator method applied to CH

A new approach to the direct evaluation of excitation energies and transition moments from the polarization propagator is presented. The method, which uses a coupled cluster doubles (CCD) reference state within the framework of perturbative propagator methods, is applied to the lowest singlet and triplet excitations in CH+. Comparison of the coupled cluster doubles polarization propagator approximation (CCDPPA) results with experiments and standard perturbative polarization propagator calculations shows that a significant improvement is obtained with a coupled cluster rather than a Rayleigh–Schrodinger reference state: the singlet excitation energy is improved by about 0.5 eV and the triplet instability of the standard second order approach is removed. The radiative lifetime of the v’=0 level of the Au20091Π state is estimated to be very close to 800 ns. The improved performance of the coupled cluster propagator method over propagator calculations based on Rayleigh–Schrodinger expansion mainly stems from a en...

Spin–spin coupling constants of CO and N2

We have used the second order polarization propagator method to calculate the indirect nuclear spin–spin coupling constants of 13C–17O and 14N–15N. We have calculated all coupling terms and the vibrationally averaged results are for CO: JFC =7.93 Hz, JSD =−3.99 Hz, JPSO =14.95 Hz, JDSO =0.10 Hz, Jtotal(CO) =18.99 Hz and for N2: JFC =0.82 Hz, JSD =−1.57 Hz, JPSO =3.32 Hz, JDSO =0.03 Hz, and Jtotal(N2) =2.60 Hz. Recent measurements of the two coupling constants gave 1J(13C,17O)=16.4±0.1 Hz and 1J(14N,15N)=1.8±0.6 Hz.

Comparison between equation of motion and polarization propagator calculations

Abstract Using common finite basis sets we have compared the equation of motion and the polarization propagator method, both through second order. Calculations

Nuclear spin-spin coupling in the methane isotopomers

Abstract The coupling constants 1 J (C, H) and 2 J (H, H) of the methane molecule have been calculated as functions of bond-length extension and compression in the vicinity of equilibrium geometry. This has facilitated the prediction of the temperature dependences of these couplings. The calculations were carried out using various polarization propagator methods. There is a very large contribution from electron correlation to both couplings. The bond-length dependence is dominated by the Fermi-contact part of the coupling. 1 J (C, H) is calculated to increase by 0.054 Hz upon increasing the temperature of 13 CH 4 from 200 to 400 K. This result is less than the observed value of 0.083 Hz due to the neglect of higher-order terms, including those involving the angle dependence of the coupling. 2 J (H, D) in 12 CH 3 D is calculated to be virtually temperature independent. The calculated total carbon-proton coupling at 300 K is 126.31 Hz, which is only 1 Hz greater than that experimentally observed. The calculated total proton-proton coupling at 300 K is −14.24 Hz, which is numerically greater by about 2 Hz than that calculated from a recent measurement on 12 CH 3 D.