Atomic unit system

The atomic units system (au system) is a system of units meant to simplify the equations of molecular and atomic quantum mechanics. The units of the au system are combinations of the fundamental units of mass (mass of the electron), charge (charge of the electron), and of Planck s constant. By setting these three quantities to unity one gets simpler equations. Si in the usual SI system, Schrodinger equation takes the form ... 

All equations are written in the atomic unit systems in which the mass of the electron and Planck s constant are equal to one. The speed of light, c is approximately 137 in this unit system. We consider magnetic fields that can he represented hy a vector potential A that is the sum of the vector potential for the homogenous external magnetic field... 

The definitions of the first and second order magnetic perturbation operators are given helow. In the nonrelativistic formalism these operators are two-component operators, in the Kutzelnigg formalism all operators are to he multiplied hy the four-component matrix. All operators are given in the atomic unit system and we do not apply QED corrections so that the free electron g-factor is precisely equal to 2. 

To make the formulae more simple, the atomic unit system is used everywhere in this chapter, unless otherwise specified. The Boltzmann constant is assumed to be equal to unity. 

It is also interesting to estimate the maximum value of the frequency factor in the case of purely quantum nuclear motion. This can be done with the help of the formula W 2nV2Sp, where V2 exp(—2yR) is the exchange matrix element, S is the Franck-Condon factor, p 1 jco is the density of the vibrational levels, and co 1000 cm-1 is the characteristic vibrational frequency of the nuclei. In the atomic unit system, the multiplier 2np has the order 103 and the atomic unit of frequency is 4.13 x 1016s-1 consequently, in the usual unit system, the frequency factor is of the order 4 x 1019Ss-1. The frequency factor reaches its maximum value when S 1. Thus, in the case of purely quantum nuclear motion, the maximum value of the frequency factor is also 1019-102°s-1. 

The oscillating part of the secondary electron spectrum fine structure in the expression obtained is determined by two interference terms resulting from scattering of secondary electrorrs of final and intermediate states (the latter are due to the second-order process only). Here intensities of oscillating terms are determined by the amplitudes and intensities of electron transitions in the atom ionized. In this section we make estimations of these values within the framework of the simple hydrogen like model using the atomic unit system as in the preceding section. This section s content is based on papers [20,22,29-31,33,35,37,45-47]. 

Unit conversion among magnetic properties depends on the dimensions used for the magnetic field, B. In the Gaussian and atomic units systems, electric fields and magnetic fields have the same dimensions, since the Lorentz force law is F (E -I- V X B/c). For these, Eq. [34] is valid for the conversion from atomic to Gaussian units. For S.I. units, where F = q(E -1- v x B), the conversion factor, F, is slightly different from Eq. [34] ... 

In this book we have used two systems of units. The first is the SI system, which we use in the early chapters of the book and in particular for electromagnetic quantities. Factors of c therefore always represent the speed of light and never a conversion factor for magnetic units. The second is the Hartree atomic units system, defined by b = e = me = 1. In these units, c 137. Many physics texts use the system b = e = c = 1, since they are dealing with particles of different masses. Our concern is principally with the electron and chemistry, and the size of relativistic effects, which are measured by c, so Hartree atomic units are more appropriate. However, to keep the connection with SI units and to track quantities that involve the charge, the mass, or spin, the symbols ft, e, and m = me are retained in much of the development, whereas l/4 reo is usually omitted for clarity. 

The Is function shows a peak at around 0.529 A this is known as the Bohr radius Aq and is the basic unit of distance used in the atomic units system discussed in Appendices 9 and 10. The same value was derived by Bohr as the radius for the orbit of the electron based on a classical physics analysis of the electrostatic interaction between the electron and nucleus in a hydrogen atom. 

Adoption of the atomic unit system simplifies the Schrddinger equation for the H atom to... 

The atomic units system is built around the H atom problem, and so it is no surprise that the potential energy should be -1 Ha. 

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