## Publication Abstracts

### Green 1974

Green, S., 1974: Sources of error and expected accuracy in ab initio one-electron operator properties: The molecular dipole moment. Adv. Chem. Phys., **25**, 179-209, doi:10.1002/9780470143773.ch3.

According to quantum theory all information about molecular properties is contained in the molecular wave function. The wave function, which effectively describes the motion of the electrons and nuclei, may be obtained by solving the eigenvalue equation (Schrödinger equation) for the Hamiltonian operator. Unfortunately, exact solutions to this equation have not been obtained for systems with more than one electron; however, a great deal of effort has been expended in finding approximate solutions for atomic and molecular systems. In many cases, ab initio results are now accurate enough to provide chemically significant information. Most calculations to date have been concerned primarily with energy properties, and other information contained in the wave function has often been ignored. In this article attention is directed toward those properties that can be obtained as one-electron operator expectation values. All properties that depend on the charge density distribution, such as the molecular electric multipole moments and the field gradient at the nuclei, fall into this category. Other one-electron operator properties include spin hyperfine constants and the diamagnetic contributions to magnetic susceptibility and shielding at the nuclei. The property for which the most accurate and extensive experimental results are available is the electric dipole moment. A recent series of papers by the author has examined methods for the accurate calculation of diatomic dipole moments. Attention was limited to diatomics because of the greater availability of calculations and accurate experimental values; however, similar results are expected for larger systems. Other one-electron operator properties should be amenable to the same techniques as the dipole moment but have been examined to a lesser extent because of the more limited experimental data.

Experimental techniques for determining dipole moments and their expected accuracy have been discussed elsewhere, and tabulations of experimental values are available. The most accurate measurements rely on the Stark effect. If the species can be studied in a molecular beam spectrometer, accuracy of better than 0.001 D can be obtained and the dependence on vibrational and rotational level is generally determined. Even for unstable free radicals experimental accuracy on the order of 0.01 to 0.05 D is often obtained. The ability of quantum theory to reproduce observed dipole moments has obviously been important in understanding the nature of chemical bonding. However, in view of the availability of accurate experimental values, one might question the practical need for accurate theoretical dipole moments. Of course, the dipole was selected for the opposite reason: to use accurate experimental values to gage the reliability of ab initio techniques. Once the sources of error are well understood other properties, such as the molecular quadrupole moment which is not so easy to determine experimentally, can then be calculated with some degree of confidence. However, dipole calculations are not entirely unnecessary. Not all species are equally amenable to experimental techniques; short-lived states may be particularly troublesome. The CN radical is one example where the answer to several astrophysically interesting questions depended on an unknown dipole moment. For CN, an experimental value was eventually obtained; in the future, ab initio determinations may be cheaper, faster, and as reliable as experimental measurements for obtaining such information. Calculations have also been useful in choosing between disparate experimental determinations. Finally, the dipole moment of a charged species is currently amenable only to ab initio techniques, and these moments are needed, for example, for an understanding of rotationally inelastic scattering of electrons by molecular ions.

The purpose of this article is to compare a number of experimental and theoretical dipole moments in order to draw conclusions about the sources of error and the accuracy that can be expected from different levels of approximation. Attention has been limited to ab initio values obtained within the self-consistent field (SCF) and configuration interaction (CI) approximations. Also, only those SCF calculations that employ a large enough basis set to be near the Hartree-Fock (HF) limit have been included. A general discussion of sources of error and expected accuracy is given in Section II. By comparing a large number of theoretical and experimental values for diatomic molecules it will be shown that rather specific estimates may be given for the dipole moment error that can be expected in ab initio calculations. In particular, both the size and direction of the error in HF dipole moments can be predicted from simple, qualitative ideas of the molecular bonding. This capability is especially important because HF wave functions are now rather readily available, but the HF method can never yield the exact solution. The quantum chemist will now be able to determine the feasibility of obtaining an unknown dipole by ab initio methods based on knowledge of the level of approximation and hence the cost of the calculation necessary to obtain a desired accuracy. In a very real sense the computer should be considered as a tool for determining dipole moments which is competitive with other experimental techniques. If very high accuracy is necessary or if the system has very many electrons, the standard experimental techniques are likely to be preferred; however, for highly reactive and short-lived states, and especially for ionic species, ab initio methods will often be cheaper, faster, and more reliable than experiments. In Section III examples of SCF calculations for polyatomic molecules are presented which indicate that the HF errors for these are analogous to those found for diatomics. Several new calculations have been performed to increase the basis for comparison, and these are presented in Section IV. Section V contains a tabulation of the diatomic results upon which the conclusions have been based, and some concluding remarks are given in Section VI.

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#### BibTeX Citation

@article{gr04010a, author={Green, S.}, title={Sources of error and expected accuracy in ab initio one-electron operator properties: The molecular dipole moment}, year={1974}, journal={Advances in Chemical Physics}, volume={25}, pages={179--209}, doi={10.1002/9780470143773.ch3}, }

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#### RIS Citation

TY - JOUR ID - gr04010a AU - Green, S. PY - 1974 TI - Sources of error and expected accuracy in ab initio one-electron operator properties: The molecular dipole moment JA - Adv. Chem. Phys. JO - Advances in Chemical Physics VL - 25 SP - 179 EP - 209 DO - 10.1002/9780470143773.ch3 ER -

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