G tensor rotational

Likewise the electronic contribution to the rotational g tensor is proportional to the paramagnetic part of the magnetizability... 

In the derivation of quantum mechanical expressions for the rotational g tensor e nuclei are usually treated as classical rotating point charges, Z e, located at Rk- Their contribution to the g tensor is then given as... 

In practical applications of the expressions for the rotational g tensor, equations (2), (4), (5), or (6), the nuclear masses in the nmment of inertia tensor I are generally approximated with atomic masses and is approximated with the center of atomic masses. This introduces a correction term to the moment of inertia tensor which is actually closely related to the nuclear contribution to the rotational g tensor [3,11,38]. Going to second order of perturbation theory for the electronic contributions one would obtain a further correction term to the moment of inertia tensor which is similar to the electronic contribution to the rotational g tensor [3,4]. 

All together one would obtain an effeetive moment of inertia tensor which includes the rotational g tensor again. This correction is normally ignored for polyatomic molecules, but allows to estimate the rotational g factor of diatomic molecules from field-free rotation-vibration spectra [5,10,11]. 

The nuclear contribution, equation (2) to the rotational g tensor is trivially calculated from the nuclear coordinates and atomic masses. The calculation of the electronic contribution, equation (5), requires in principle the calculation of all excited states of appropriate symmetry and the corresponding... 

Before one can compare different correlated methods and their results for the rotational g tensor, one should discuss the quality of the employed basis set. Therefore, I have performed also calculations with rotational London orbitals for all the molecules at the SCF and the level of theory and compare... 

Table 5. H2O the rotational g tensor calculated with different ab initio methods and two basis sets. The nuclear contributions to the rotational g factor are = 0.9802 and = 0.9995...

Table 7. NH3 the rotational g tensor calculated with different ab initio methods and two...

The first observation one can make is that the correlation effects for the rotational g tensor in HF, H2O, and NH3 are in general small, 1.5-3.5%, and negative, i.e., correlation reduces the values of the rotational g tensor and therefore the amount of coupling between the electronic and rotational motion. Methane is an exception in that respect, because correlation increases the value of the g factor and because some methods, MPn and CCSD, predict much larger correlation corrections. 

The valence CAS calculations overestimate the correlation corrections dramatically and predict rotational g tensor components which are much too small for all molecules. In CH4 it predicts even the wrong sign for the correlation correction. Similarly, MP2 is not able to reproduce the sign or size of the correlation correction. For HF and the in-plane component in H2O, the MP2 contribution is too small and for all the other molecules or tensor components the MP2 contribution is much too large and has even the wrong sign. 

Fig. 2. H2O the gi (top) and goop (bottom) components of the rotational g tensor as a function of ab initio methods for two basis sets.

The components of the rotational g tensor of hydrogen fluoride, water, ammonia and methane have been calculated at their equilibrium geometries with different correlated ab initio methods and two large basis sets. 

On the other hand, the results of MP2 and valence CAS calculations are not useful. MP2 predicts correlation correction which are not only much too large but have also the wrong sign for most g tensor components studied here. In the remaining cases the correlation correction is either much too large (CH4) or much too small (HF and H2O gip). The valence CAS calculations similarly overestimate the correlation effects and predict in general much too small g tensor components. SOPPA and SOPPA(CCSD) performs thus clearly better than MP2 or valence CAS calculations for the rotational g tensor in the studied molecules. 

Such a basis set combines well with coupled-cluster wave functions to tend to converge in a consistent and predictable manner towards limits of the basis set and the theory. Calculation of the rotational g tensor and magnetizability involved use of rotational London orbitals [10]. Optimization, first order in derivatives of energy with respect to internuclear distances, yielded all reported geometric stmctures of... 

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