Electric fields and field gradients

POLY ATOM programs and elsewhere the less obvious ones are tr, diamagnetic shielding F and FG, the electric field and field gradient at the nucleus x the diamagnetic susceptibility. Z is the internuclear axis. All properties are relative to the carbon atom origin and the values are in the global co-ordinate system and atomic units. 

It has recently become clear that classical electrostatics is much more useful in the description of intermolecular interactions than was previously thought. The key is the use of distributed multipoles, which provide a compact and accurate picture of the charge distribution but do not suffer from the convergence problems associated with the conventional one-centre multipole expansion. The article describes how the electrostatic interaction can be formulated efficiently and simply, by using the best features of both the Cartesian tensor and the spherical tensor formalisms, without the need for inconvenient transformations between molecular and space-fixed coordinate systems, and how related phenomena such as induction and dispersion interactions can be incorporated within the same framework. The formalism also provides a very simple route for the evaluation of electric fields and field gradients. The article shows how the forces and torques needed for molecular dynamics calculations can be evaluated efficiently. The formulae needed for these applications are tabulated. 

In this chapter we will discuss electric properties and start with the electrostatic potential of the charges in a molecule, because it leads straightforwardly to a definition of electric moments. Afterwards, we will look at changes in the electric moments due to external electric fields and finally we will derive expressions for the electric field and field gradients due to the charges in a molecule. 

In the second approach we will use the fact that the moments are defined as derivatives of the energy of a molecule in the presence of an inhomogeneous electric field, Eqs. (4.19), (4.20) and (4.21). In order to apply these definitions we need to find an expression for the energy of a molecule in the presence of an inhomogeneous electric field. Here, we are using perturbation theory as developed in Section 3.2. The first step is thus to define the perturbation Hamiltonian operators and to derive explicit expressions for them in terms of components of the electric field a(Ro) and field gradient tensor a/3(Ro)- The electric field and field gradient enter the molecular Hamiltonian in the form of the scalar potential From Eq. (4.15) we can see... 

The ]V-electron operators p. Ro) and Q Ro) will in the following often be called the electric dipole operator and the electric quadrupole operator, respectively. Although we are working within the Born-Oppenheimer approximation we have included the interaction of the electric field and field gradient with the nuclear charges in the molecular Hamiltonian in Eq. (2.101). This interaction then leads to nuclear contributions to the perturbation Hamiltonian operators. The operators and... 

Based on the expansions, one can express the polarizabilities and hyperpolarizabilities as first and higher derivatives of the field-dependent moments ft , ) and , ) with respect to the components of the electric field and field gradient ... 

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