Dipole moment convergence

As examples of molecular properties we will look at how the dipole moment and harmonic vibrational frequencies converge as a function of level of theory. 

The experimental value for the dipole moment is 1.847 D, and the calculated value at different levels of theory is shown in Table 11.10. The dipole moment may be considered as the response of the wave function (and energy) to the presence of an 

12 H2O dipole moment (Debye) as a function of DFT functional and basis set the  

Basis SVWN BLYP BPW91 B3LYP B3PW91 

The HF dipole moment is too large, which is quite general, as the HF wave function overestimates the ionic contribution. The MP2 procedure recovers the large majority of the correlation effect, hut the convergence, with the ang-cc-pVXZ basis sets is not 

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Classical Valence Bond 11.3 Dipole Moment Convergence 270... 

The analysis above illustrates why dipole-based expressions like Eqs. [28] usually give better results. With base field strengths of 0.001 au and dipole moments converged to 10 , the errors in p are already down to 1 au, while the 7 error is 10 au. Convergence of 10 in the dipole moment is needed to lower the 7 error to 1 au. 

Total Energy Convergence Dipole Moment Convergence... 

The HF level as usual overestimates the polarity, in this case leading to an incorrect direction of the dipole moment. The MP perturbation series oscillates, and it is clear that the MP4 result is far from converged. The CCSD(T) method apparently recovers the most important part of the electron correlation, as compared to the full CCSDT result. However, even with the aug-cc-pV5Z basis sets, there is still a discrepancy of 0.01 D relative to the experimental value. 

The charge distribution of the molecule can be represented either as atom centred charges or as a multipole expansion. For a neutral molecule, the lowest-order approximation considers only the dipole moment. This may be quite a poor approximation, and fails completely for symmetric molecules which do not have a dipole moment. For obtaining converged results it is often necessarily to extend the expansion up to order 6 or more, i.e. including dipole, quadrupole, octupole, etc. moments. 

In spite of the fact that we have introduced the factor of exp(—) in equation (47), our analytical expression for the dipole moment does not have a qualitatively correct asymptotic behaviour for the bond lengths r,—> 00. The function does not converge to the dipole moment of the NH2 fragment if we remove a hydrogen atom. However, neither does it diverge The calculated dipole moment values at large r, are around 2-3 D depending on which dissociation path we use. Obviously, the asymptotic behaviour of the dipole moment is of no importance for the simulations carried out in the present work we are only concerned with molecular states well below dissociation. 

State. The latter is verified by the population dynamics in frame (ii) around t = 0. Subsequently, the pulse continues to invert the bare state system, which is typical for RAP. Just like the ground state the excited p-state exhibits no permanent dipole moment. Therefore, both (/ )(t) and V) t) converge back to zero as the system is steered adiabatically toward state 2). This indicates the successive loss of selectivity among the dressed states, which is in fact observed in frame (ii) for f > 0. By the end of the pulse, both dressed states are again fully equalized. 

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