G factor rotational

Of values in the right column of Table 1, the specified parameters are coefficients of z in formulae 45, 46 and 47, pertaining to vibrational and rotational g factors and adiabatic corrections respectively, with atomic centres B = Ga and A = H for this particular compound. Apart from the value of that was constrained to zero in the ultimate fit because preliminary fits indicated that its standard error much exceeded its magnitude, values of other parameters beyond cg, and Wg in their respective series, and also all and are not... 

For comparison with our results in table 3, which presents values of 20 adjusted parameters with 15 parameters constrained to define the rotational g factor, Dulick et alii [115] required also 20 adjusted parameters, with a constrained parameter T> for the equilibrium binding energy for a function of potential energy having a modified Morse form. The latter parameter is specified as... 

That effective hamiltonian according to formula 29, with neglect of W"(R), appears to be the most comprehensive and practical currently available for spectral reduction when one seeks to take into account all three principal extramechanical terms, namely radial functions for rotational and vibrational g factors and adiabatic corrections. The form of this effective hamiltonian differs slightly from that used by van Vleck [9], who failed to recognise a connection between the electronic contribution to the rotational g factor and rotational nonadiabatic terms [150,56]. There exists nevertheless a clear evolution from the advance in van Vleck s [9] elaboration of Dunham s [5] innovative derivation of vibration-rotational energies into the present effective hamiltonian in formula 29 through the work of Herman [60,66]. The notation g for two radial functions pertaining to extra-mechanical effects in formula 29 alludes to that connection between... 

Although the relation between the vibrational g factor and the derivative of electric dipolar moment, equation (10), is formally equivalent to the relation between the rotational g factor and this dipolar moment, equation (9), there arises an important distinction. The derivative of the electrical dipolar moment involves the linear response of the ground-state wave function and thus a non-adiabatic expression for a sum over excited states similar to electronic contributions to the g factors. The vibrational g factor can hence not be partitioned in the same as was the rotational g factor into a contribution that depends only on the ground-state wave function and irreducible non-adiabatic contribution. Nevertheless g "(R) is treated as such. A detailed expression for ( ) in terms of quantum-mechanical operators and a sum over excited states, similar to equations (11) and (12), is not yet reported. 

The rotational g factor is the ratio of the rotational magnetic dipole moment of a molecule to its molecular rotational angular momentum [1-5]. Experimentally the rotational g factor was originally determined by measuring the rotational magnetic... 

However, until today no systematic comparison of methods based on MpUer-Plesset perturbation (MP) and Coupled Cluster theory, the SOPPA or multiconfigurational linear response theory has been presented. The present study is a first attempt to remedy this situation. Calculations of the rotational g factor of HF, H2O, NH3 and CH4 were carried out at the level of Hartree-Fock (SCF) and multiconfigurational Hartree-Fock (MCSCF) linear response theory, the SOPPA and SOPPA(CCSD) [40], MpUer-Plesset perturbation theory to second (MP2), third (MP3) and fourth order without the triples contributions (MP4SDQ) and finally coupled cluster singles and doubles theory. The same basis sets and geometries were employed in all calculations for a given molecule. The results obtained with the different methods are therefore for the first time direct comparable and consistent conclusions about the performance of the different methods can be made. 

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]. 

Table 4. HF the rotational g factor calculated with different ab initio methods and two basis sets. The nuclear contribution to the rotational g factor is 0.9731...

Fig. 5. CH4 the rotational g factor as a function of ab initio methods for two basis sets.

I want to express my great gratitude to my teacher Jens Oddershede who was and still is an important source of inspiration. The first project he assigned to me was the calculation of the rotational g factor of NH3 [22]. I decided therefore to close... 

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