Electronic and Nuclear Contributions

In the second row of Table 1.4, we have listed the corrections to the Hartree-Fock energies that are obtained from CCSD calculations. Clearly, we now have a better description of the atomization process, the error in the calculated AE being only -19.6 kJ/mol (2 %). Still, we are far away from the prescribed target accuracy of 1 kJ/mol. 

To improve on the CCSD description, we go to the next level of coupled-cluster theory, including corrections from triple excitations -see the third row of Table 1.4, where we have listed the triples corrections to the energies as obtained at the CCSD(T) level. The triples corrections to the molecular and atomic energies are almost two orders of magnitude smaller than the singles and doubles corrections. However, for the triples, there is less cancellation between the corrections to the molecule and its atoms than for the doubles. The total triples correction to the AE is therefore only one order of magnitude smaller than the singles and doubles corrections. 

With the triples correction added, the error relative to experiment is still as large as 15 kJ/mol. More importantly, we are now above experiment and it is reasonable to assume that the inclusion of higher-order excitations (in particular quadruples) would increase this discrepancy even further, perhaps by a few kJ/mol (judging from the differences between the doubles and triples corrections). Extending the coupled-cluster expansion to infinite order, we would eventually reach the exact solution to the nonrelativistic clamped-nuclei electronic Schrodinger equation, with an error of a little more than 15 kJ/mol. Clearly, for agreement with experiment, we must also take into account the effects of nuclear motion and relativity. 

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Here d is the total dipole operator, including both electron and nuclear contributions. Consider now the effect of inversion on H. Noting that I operates on the coordinates of the molecule, that P = I and that [HMr, /] = 0, we have [69] that... 

The measured sample s magnetic moment is the net spontaneous or induced moment arising from a vector sum of all the microscopic DM, PM, electronic, and nuclear contributions. Nuclei can have permanent m netic moments, although they are much smaller than electronic moments, HN/lts 10, and have much weaker interactions with each other and with electronic moments. For our purposes, the sample s magnetic... 

In order to elucidate the selection rules for the minimal value / resulting in a nonzero torque, we present the operators Qrm, as earlier, in the form of a sum of the electronic and nuclear contributions, and we assume again that the operator of vibronic interaction is linear in the nuclear displacements. In this approximation, Eq. (228) can be transformed to the following form ... 

When we separate the projectile total energy loss into electronic and nuclear contributions, equation (6) can be written as... 

The total vector potential is the sum of the external, electronic and nuclear contributions... 

Note that yz consists of 4 contributions, exhausting the purely electronic and nuclear contribution on both A and B (i.e. 4 = 2x2) that is, the electron-electron Coulomb energy electron-nucleus attraction (potential) energy, denoted... 

The complete Carter-Handy Hamiltonian [2, 100] expressed in internal coordinates, Rn and 6, which correspond to the bond lengths (for three-atomic molecules n = 1,2) and angle, respectively, is first separated between electronic and nuclear contributions,... 

In Einstein s model, in view of the new electronic and nuclear contributions, this would give us ... 

The electron and nuclear contributions are also sums on the number of atoms contained in the molecule ... 

All values in kHz with the exception of the fluorine intemuclear distance, rpp, which is given in 10 cm. The electronic and nuclear contributions of Mgg( F), g = a,b,c have been tabulated for GeFj [93 Styl]. 

The unidirectionality of the primary charge separation in the RC across the A branch constitutes a central dynamic phenomenon in photosynthesis. This effect was attributed to symmetry breakingl , which may originate from the distinct electronic and nuclear contributions to the elementary ET rates, which in turn modify the experimental lifetimes. 

The exponents e and ric for the electronic and nuclear contributions are usually one or two, and the cutoff parameters Jg and are adjusted to suitable reference data, e.g., IPs. This ansatz for CPPs was adapted to energy-consistent LPPs by Fuentealba et al [42] and proved to be quite successful, e.g., in calculations using 4f-in-core [43] and 5f-in-coreLPPs [11,44], respectively. 

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