Electron orbital dipole moment

Quantitative similarities of molecules can easily be recognized if it is possible to define quantities for molecular parts which are additive as well as transferable. Such quantities can be derived from transferable molecular orbitals because any one-electron property, such as dipole moment, quadrupole moment, kinetic energy, is a sum of the corresponding contributions from all molecular orbitals in a system, if such orbitals are chosen mutually orthogonal. Thus, for each transferable orthogonal molecular orbital there exists, e.g., a transferable orbital dipole moment. Since chemists appreciate additive decompositions of... 

One-electron electric dipole moment integral over orbitals p and q. 

Table 11. CCSD results for the total Verdet constant at w = 0.11391 a.u. in the case of hydrogen fluoride. Results labeled as Unrelaxed refer to the use of the unrelaxed (one-electron) magnetic dipole moment operator together with the usual magnetic-field independent basis sets. Results labeled Relaxed include additional contributions due to orbital relaxation in the presence of the magnetic field. Results labeled LAO are those obtained when using GIAOs/LAOs ...

The s electrons are spherically distributed about the chorine nucleus, and the px and py electrons lie in a disc perpendicular to the z axis with the Cl nucleus at its center. Now let us suppose instead that the chlorine atom has full sp3 hybridization and uses one of these hybrid orbitals to form the bond. The remaining three pairs of electrons will lie in the three equivalent hybrid orbitals, which have approximately the shape shown in Fig. 3-17. It is easily seen that electrons in such an orbital are much more concentrated below the xy plane than above it, and hence there will be an orbital dipole moment which can be represented by a vector of magnitude v pointing along the axis of the orbital. There is, then, a dipole moment contribution in the bond direction of — v cos 71°, or a total from the three such orbitals of — 3v cos 71°, namely ... 

The atomic unit (AU) of dipole moment is that of a proton and electron separated by a distance equal to the first Bohr orbit, oq. Similarly, the au of polarizability is Oq [125]. Express and o for NH3 using both the cgs/esu and SI approach. 

Quantum chemical descriptors such as atomic charges, HOMO and LUMO energies, HOMO and LUMO orbital energy differences, atom-atom polarizabilities, super-delocalizabilities, molecular polarizabilities, dipole moments, and energies sucb as the beat of formation, ionization potential, electron affinity, and energy of protonation are applicable in QSAR/QSPR studies. A review is given by Karelson et al. [45]. 

The measurements are predicted computationally with orbital-based techniques that can compute transition dipole moments (and thus intensities) for transitions between electronic states. VCD is particularly difficult to predict due to the fact that the Born-Oppenheimer approximation is not valid for this property. Thus, there is a choice between using the wave functions computed with the Born-Oppenheimer approximation giving limited accuracy, or very computationally intensive exact computations. Further technical difficulties are encountered due to the gauge dependence of many techniques (dependence on the coordinate system origin). 

State averaging gives a wave function that describes the first few electronic states equally well. This is done by computing several states at once with the same orbitals. It also keeps the wave functions strictly orthogonal. This is necessary to accurately compute the transition dipole moments. 

In addition to total energy and gradient, HyperChem can use quantum mechanical methods to calculate several other properties. The properties include the dipole moment, total electron density, total spin density, electrostatic potential, heats of formation, orbital energy levels, vibrational normal modes and frequencies, infrared spectrum intensities, and ultraviolet-visible spectrum frequencies and intensities. The HyperChem log file includes energy, gradient, and dipole values, while HIN files store atomic charge values. 

For a quantum mechanical calculation, the single point calculation leads to a wave function for the molecular system and considerably more information than just the energy and gradient are available. In principle, any expectation value might be computed. You can get plots of the individual orbitals, the total (or spin) electron density and the electrostatic field around the molecule. You can see the orbital energies in the status line when you plot an orbital. Finally, the log file contains additional information including the dipole moment of the molecule. The level of detail may be controlled by the PrintLevel entry in the chem.ini file. 

To understand the origins of dispersion forces, let us consider two Bohr atoms, each of which consists of an electron orbiting around a nucleus comprised of a proton, having a radius ao, often referred to as the first Bohr radius . It is obvious that a Bohr atom has no permanent dipole moment. However, the Bohr atom can be considered to have an instantaneous dipole moment given by... 

Compare the dipole moment and the electrostatic potential map for the ground state of acetone to those of the n to pistar state of acetone. Which molecule is more polar Rationalize the differences by appealing to the shape of the orbitals (in ground-state acetone) whose electron populations are changed by excitation. 

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