Jan Geertsen

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.

The dipole moment of carbon monoxide

The dipole moment of CO has been calculated with many‐body perturbation theory (MBPT) and coupled cluster (CC) methods using basis sets which have been optimized at the MBPT‐2 level. It is demonstrated that triple excitations as well as g‐type functions in the basis set are crucial to obtain satisfactory agreement with experiment. The most reliable prediction (0.125 D) is obtained at the CCSD(T) (coupled cluster including all single, double, and connected triple excitations, perturbatively) level of theory using a 10s9p4d2f1g basis set (160 basis functions). This result is in excellent agreement with the experimental value of 0.122 D.

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 A 1Π 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.

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.

Nuclear magnetic shieldings and spin rotation constants of HF and N2

The paramagnetic contribution to the nuclear magnetic shieldings and the spin rotation constants are calculated using polarization propagator theory. Results are reported both in the first order approximation [equivalent to the coupled Hartree–Fock (CHF) method] and in the second order polarization propagator approximation (SOPPA). It is demonstrated how the constant Cgauge which gives the gauge origin dependence of the total nuclear magnetic shielding in a finite basis set [σ(Rc+d)=σ(Rc)+d⋅Cgauge] can be calculated from the polarization propagator. The magnetic shieldings of H and F in HF are nearly the same in CHF and SOPPA and results from both levels of theory agree well with experiment. For N2, σ(SOPPA)=−72.2 ppm, also in good agreement with the most recent measurement. However, for N2 there is a large correlation effect since σ(CHF)=−106.5 ppm. The computed spin rotation constant for N2 is M(15N)=20 kHz, i.e., about 2 kHz lower than its measured value. This value of M(15N) corresponds to σ(N)=−72.2 ppm.

A solution of the gauge origin problem for the magnetic susceptibility

A polarization propagator based theory for calculation of the diamagnetic part of the magnetic susceptibility is presented. Since the paramagnetic term also may be obtained from the propagator it is thus possible to compute both contributions at the same level of approximation, e.g., in RPA, SOPPA, and CCPPA. Contrary to other commonly used procedures the present method gives a total result for the susceptibility, which—even in a limited basis set—is independent of the origin chosen for the vector potential.

A solution of the gauge-origin problem for the magnetic shielding constant

Abstract It is shown that the diamagnetic contribution to the magnetic shielding constant can be expressed in terms of the polarization propagator. Contrary to the commonly used approach, the suggested method gives a result for the total shielding which is independent of the origin chosen for the vector potential.

Some Aspects of The Coupled Cluster Based Polarization Propagator Method

Publisher Summary This chapter describes a spin-adapted formulation of the coupled cluster singles and doubles (CCSD) method, which is apt for subsequent use in the coupled cluster polarization propagator approximation (CCPPA). A brief review of the perturbative polarization propagator methods is provided. The chapter introduces the CCPPA method by requiring that when using the first iteration of the coupled cluster (CC) coefficients in the CCPPA method one obtains the second order polarization propagator approximation (SOPPA). Thus, the same kind of relation between CCPPA and SOPPA is maintained, as there exists between many body perturbation theory (MBPT) and CCD calculations of ground state correlation energies; in the first iteration of the coupled cluster method the MBPT-based solution is obtained. The chapter also analyzes the extra terms that the iterated CCPPA method introduces relative to SOPPA. Several examples of CCPPA calculations, together with a complete summary of all applications of the method are provided.

Unexpected differential sensitivity of nuclear spin—spin coupling constants to bond stretching in methane

Abstract Accurate coupled-cluster calculations reveal that when one of the CH bonds in the methane molecule is stretched by a small amount from its equilibrium bond length (a) the carbon—proton spin—spin coupling constant involving the nuclei of the stretched bond changes by less than the carbon—proton coupling constant of the three unstretched bonds, and (b) the three proton—proton coupling constants which involve the proton of the stretched bond change by less than the three proton—proton coupling constants which do not involve the proton of the stretched bond. This unexpected differential sensitivity is evidently due to electron correlation as it is absent at the RPA level. It has been observed in an experimental study of carbon—proton coupling in the methane isotopomers. Experimental results in which primary and secondary isotope effects are directly compared suggest that it is a fairly common phenomenon.