Units conversion Gaussian

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] ... 

Quantity Gaussian (c units) SI units Conversion fiictor (cgs to SI)... 

The electric and magnetic fields appearing in Sections 2.3.1 and 2.3.2 have been described in terms of the SI system of units. The Gaussian system of cgs units has frequently been employed in the theory of liquid crystals when magnetic fields are discussed. Gaussian units are considered by many to be natural units for the calculation and measurement of magnetic field effects in liquid crystals. Since much of the literature contains results in both Gaussian units and SI units, it seems appropriate at this point to make some comments on the conversion from one system of units to the other. A comprehensive account of the points touched upon here may be found in Jackson [132] or Moskowitz [206]. Readers should also be famihar with derived SI units. 

The geometry optimizations of molecular structures were performed using the semi-empirical PM3 Hamiltonian [67,68] and the B3LYP/6-3 lG(d) method. All stationary points were confirmed to be true minima by evaluation of hessian. In order to speed up HE and DFT calculations, the fast multipole method (EMM) [47, 48, 69] has been used as implemented in Gaussian suite of programs [56]. We also used linear scaling approaches for calculations of nonlinear optical properties as implemented in ADF package [58]. All the properties are expressed in atomic units. Conversion factors can be found elsewhere [28-31],... 

This list contains various conversion factors and physical constants used by Gaussian in converting from standard to atomic units. 

In the present book, for magnetism we use the SI unit that is based on the MKS A (meter, kilogram, second, ampere) system. In accordance with that, the tesla (1T = 10" gauss) was presented as the magnetic unit in Chapter 17 (see Fig. 17.10a and b). It is useful to know both the SI and Gaussian systems and be able to convert between them. Thus, when one attempts to solve a magnetics problem, to avoid errors one is well advised to stick to a single convenient unit system. A useful conversion table of... 

So far we have employed gaussian units, which are more common in theoretical discussions. However, experimental results are generally discussed in terms of practical units. Since conversions between different systems of units can sometimes be confusing we include here an example. Consider R. In gaussian units E and are in statvolt/cm (for this is called gauss ), j in... 

Other systems of units and equations in common use in electromagnetic theory, in addition to the SI, are the esu system, the emu system, the Gaussian system, and the system of atomic units. The conversion from SI to these other systems may be understood in the following steps. 

In quadmpole and ion trap spectrometers, it is customary to use the unit resolution definition, which means that each mass can be separated from the next integer mass (500 from 501, 2000 from 2001, etc.). The comparison and conversion between the different resolution definitions is not trivial, considering that they are strongly dependent on peak shape (Gaussian, triangular, trapezoidal, Lorent-zian, etc.).9... 

Useful Conversion Factors and Units (All calculations made in Gaussian cgs units) g = 4.S X 10 state c = 3 X 10 cmsec ... 

Two unit systems are commonly employed in describing NLO properties the SI (MKS) and the Gaussian (cgs) systems. One should note that many equations have a different form when written in these two systems of units, and that conversion between these two systems is frequently cumbersome. One should also be aware that definitions of hyperpolarizabilities and susceptibilities may differ between different authors because of the lack of general agreement whether the complex field amplitude in Eq. (2) should include a factor of 1/2 and whether the multiplying degeneracy factors [such as those in Eq. (3)] should be included in the hyperpolarizabilities. 

Here we use Gaussian units. The conversion to Sl-units is tabulated in Appendix C. 

Table D.2 Conversion factors for common quantities [132, 206]. These allow simple conversions from Gaussian cgs units into standard SI units and vice-versa, c == 2.998 X 10 represents the numerical value of the speed of light in SI units. The abbreviations used are poise (P), gauss (G), oersted (Oe), newton (N), pascal second (Pa s), tesla (T), ampere (A), volt (V), coulomb (C), joule (J). This quantity was formerly known as specific gravity it is the density of the material divided by the (maximum) density of water (given by 1 g cm , equivalent to 1000 kg m ).

Appendix D Unit Systems M 679 TABLE D.2 Conversion between CGS (Gaussian) units and SI units... 

For free space, it is straight-forward to translate between CGS (Gaussian) and SI units, by substituting So —> 1/(477) and fio —> 4tt/c. For dielectric and magnetic materials, conversion between the two quantities is not so easy. For details, see a treatise on electromagnetism. An abbreviated set of conversion factors between CGS and SI units that are relevant to the quantities of interest in this text is given in Table D.2. The convenience of Gaussian units is illustrated by the fact that all quantities presented in Table D.2 can be related to the three fundamental units of the CGS system—cm, g, and s. 

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