Atomic units values

Quantity Atomic unit Value in SI units Symbol (name)... 

All values are in atomic units. Values given in parentheses are experimental uncertainty. 

Besides the expressions for a surface derived from the van der Waals surface (see also the CPK model in Section 2.11.2.4), another model has been established to generate molecular surfaces. It is based on the molecular distribution of electronic density. The definition of a Limiting value of the electronic density, the so-called isovalue, results in a boundary layer (isoplane) [187]. Each point on this surface has an identical electronic density value. A typical standard value is about 0.002 au (atomic unit) to represent electronic density surfaces. 

Quantum mechanics is primarily concerned with atomic particles electrons, protons and neutrons. When the properties of such particles (e.g. mass, charge, etc.) are expressed in macroscopic units then the value must usually be multiplied or divided by several powers of 10. It is preferable to use a set of units that enables the results of a calculation to he reported as easily manageable values. One way to achieve this would be to multiply eacli number by an appropriate power of 10. However, further simplification can be achieved by recognising that it is often necessary to carry quantities such as the mass of the electron or electronic charge all the way through a calculation. These quantities are thus also incorporated into the atomic units. The atomic units of length, mass and energy are as follows ... 

Here, k is a factor which converts to units (kcal/mol in this case where the distances are in A and the polarisabilities in A ). G, and Gj are constants chosen to reproduce the well depths for like-with-like interactions. The atomic polarisability values are obtained from an examination of appropriate molecular experimental data (such as measurements of molar refractivity). 

Note that these equations do not contain the constants that are typically included in introductory texts, such as the vacuum permitivity constant. Theoreticians, and thus software developers, work with a system of units called atomic units. Within this unit system, many of the fundamental constants are defined as having a value of 1. Atomic units will be used throughout this book unless otherwise specified. 

The system of atomic units was developed to simplify mathematical equations by setting many fundamental constants equal to 1. This is a means for theorists to save on pencil lead and thus possible errors. It also reduces the amount of computer time necessary to perform chemical computations, which can be considerable. The third advantage is that any changes in the measured values of physical constants do not affect the theoretical results. Some theorists work entirely in atomic units, but many researchers convert the theoretical results into more familiar unit systems. Table 2.1 gives some conversion factors for atomic units. 

The value is in hartrees. The number of cycles it took the SCF calculation to converge is also given on this line (refer to Appendix A for a discussion of the iterative nature of the SCF method). When we discuss energies in this work, we will generally use hartrees (atomic units) when we discuss energy differences, kcal-moT will often be a more convenient unit (especially when comparing calculation predictions to experimental results). 

Old and new values for-structure variables, in atomic units (bohrs and radians]... 

Gaussian computes isotropic hyperfine coupling constants as part of the population analysis, given in the section labeled "Fermi contact analysis the values are in atomic-units. It is necessary to convert these values to other units in order to compare with experiment we will be converting from atomic units to MHz, using the following expressions ri6ltYg ... 

Table 0.1 shows such atomic units . The accepted values of the SI constants are themselves subject to minor experimental improvements, so authors generally report (he results of molecular modelling calculations as (e.g.) R = 50aa and give the conversion factor to SI somewhere in their paper, usually as a footnote. 

Name Value Derivative information (Atomic Units) i... 

In the nonrelativistic limit (at c = 10 °) the band contribution to the total energy does not depend on the SDW polarization. This is apparent from Table 2 in which the numerical values of Eb for a four-atom unit cell are listed. The table also gives the values of the Fermi energy Ep and the density of states at the Fermi level N Ef). 

Table 3 Unrestricted Hartree-Fock energies (Hartrees) for Ceo and C70 and their muon adducts, muon in atomic units (and MHz) after quartet spin state annihilation. The value of the total spin operator, < >, is also given after quartet spin state...

Once available, and supplemented by the nuclear contribution, the EFG tensor can be diagonalized. The numerically largest element (in atomic units) defines the value of q which is in turn used to calculate the quadrupole splitting parameter... 

Here, we have removed the factor 1 /47ieo because in atomic units (a.u.) its value is unity. We have also used the short-hand notation Ex r) = ZxIi x2 for the nuclear electric field. Furthermore, we use the following two identities to arrive at the above expression ... 

The units we use in daily life, such as kilogram (or pound) and meter (or inch) are tailored to the human scale. In the world of quantum mechanics, however, these units would lead to inconvenient numbers. For example, the mass of the electron is 9.1095 X J0 31 kg and the radius of the first circular orbit of the hydrogen atom in Bohr s theory, the Bohr radius, is 5.2918 X 10 11 m. Atomic units, usually abbreviated as au, are introduced to eliminate the need to work with these awkward numbers, which result from the arbitrary units of our macroscopic world. The atomic unit of length is equal to the length of the Bohr radius, that is, 5.2918 X 10 n m, and is called the bohr. Thus 1 bohr = 5.2918 X 10"11 m. The atomic unit of mass is the rest mass of the electron, and the atomic unit of charge is the charge of an electron. Atomic units for these and some other quantities and their values in SI units are summarized in the accompanying table. 

The energy eigenvalue e depends only on the principal quantum number its value is given (in atomic units see Appendix C) by... 

Atomic unit (base units) SI value Name (symbol)... 

Table 17.1 Parameters for a simple treatment of jellium unless stated otherwise, the values are given in atomic units.

Predicted ionic radii r, experimental ionic radii n, central charge Q and RF potential Ok in atomic units. Electrostatic free energies of solvation, 8pel, in kcal/mol. Experimental values from reference [16]. Electrostatic potential for anions from reference [19]. For all calculations done, the effective dielectric constant reported in [16] was used. 

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