External Electric And Magnetic Fields

Very occasionally, we might need to add more than one perturbation foj-example, if we wanted to study a molecule subject to external electric and magnetic fields, we might write something like... 

Having considered the general expressions for first- and second-order molecular properties, we now restrict ourselves to properties associated with the application of static uniform external electric and magnetic fields. For such perturbations, the Hamiltonian operator may be written in the manner (in atomic units)... 

The expressions in the first two lines can be used to determine the change in temperature, generalized pressure, and volume of a system maintained under adiabatic conditions when an external electric and magnetic field is applied, but we shall not pursue these matters in detail. 

The weakly relativistic limit of the Hamiltonian (2.20) for fermions in external electric and magnetic fields can be derived with standard techniques, either by direct expansion or by a low order Foldy-Wouthuysen transformation. One obtains... 

The determination of a property density at some point in a molecule by the total distribution of particles in the system is essential to the definition of atomic contributions to the electric and magnetic properties of a system. The densities for properties resulting from the molecule being placed in an external field must describe how the perturbed motion of the electron at r depends upon the field strength everywhere inside the molecule, a point that has been emphasized by others (Maaskant and Oosterhoff 1964). This requirement is met by the definition of an atomic property as determined by the theory of atoms in molecules. Property densities for a molecule in the presence of external electric and magnetic fields have been defined and discussed by Jameson and Buckingham (1980) and the present introduction follows their presentation. 

Recent calculations predict that carbon tubules of different diameters and helicities have striking variations in electronic transport, from metallic to semiconducting (4-7). Also, such tubules ate expected to shield guest atoms from external electric and magnetic fields (8). Besides tubular structures, other low-energy configurations... 

The birefringence in external electric and magnetic fields (the Kerr and Cotton-Mouton effects) can be explained by the anisotropy of the properties of the medium that is due to either the orientation of anisotropic molecules in the external field (the Langevin-Bom mechanism) or the deformation of the electric or magnetic susceptibilities by this field, i.e., to hyperpolarizabilities (Voight mechanism). The former mechanism is effective for molecules that are anisotropic in the absence of the field and... 

In this communication we have presented a 2D fully numerical mesh solution method in its various applications to atoms and simple diatomic molecules in strong external electric and magnetic fields. Specifically these are calculations of atoms with Z < 10 and their positive ions in strong magnetic fields and the comprehensive investigation of the electronic structure of the ground states of the Li and C atoms... 

Ions are produced by electron impact (from a heated filament) on a neutral sample at low pressure (10-7 torr). The ions enter the ICR cell under the influence of external electric and magnetic fields, which constrain them to move in circular orbits with a cyclotron frequency applied magnetic field H ... 

The standard approach of quantum mechanics considers molecules as a collection of positively charged nuclei fixed in space and negatively charged electrons, the latter with spin. Most molecular properties then arise from the introduction of external electric and magnetic fields as well as nuclear spins, possibly coupled to displacements of the nuclei. These properties therefore fall... 

We shall limit attention to molecular properties arising from the introduction of external electric and magnetic fields through minimal coupling (118). In the next section we will consider specific fields for the moment we will focus on the general forms. The introduction of external fields leads to perturbation operators on the form... 

The generic form of the perturbation part of the total Hamiltonian is expressed by (20). In this section we consider specific forms of the perturbation operators Hx appearing in this expression. Note that these operators are time-independent any time-dependence of the perturbation is expressed by the exponentials appearing in the Fourier transform of V(t). We will consider the perturbation operators arising from nuclear spins as well as external electric and magnetic fields. 

The ab initio computation of molecular properties - including those associated with time-dependent external electric and magnetic fields - has advanced significantly in the last several decades, yielding accurate models for linear, quadratic, and higher-order response functions. When electron correlation effects play a pivotal... 

---