Atomic axial tensor

Lazzeretti and coworkers175 calculated nuclear electric and electromagnetic shielding tensors for 1 and oxirane. These properties are related to atomic polar tensors and atomic axial tensors used by infrared and VCD spectroscopists. The authors demonstrated that they could obtain fairly accurate sum rules for atomic polar tensors and atomic axial tensors with relatively little computational effort. 

The tensors are termed atomic axial tensors (AATs) 7 and are the electronic and nuclear components. Here, (dpG/dXXa)0 is the same derivative which occurred already in Equation (2.86). The electronic AAT, 7 is the overlap integral with the derivative (dif/G/dHp)0. The latter is defined via... 

Cheeseman JR, Frisch MJ, Devlin FJ etal (1996) Ab initio calculation of atomic axial tensors and vibrational rotational strengths using density functional theory. Chem Phys Lett 252 211-220... 

In practice, the electric and magnetic dipole transition moments are usually expressed as summations of atomic properties, namely the atomic polar tensor (APT), Pgp, and atomic axial tensor (AAT), respectively. In the... 

R. D. Amos, K. J. Jalkanen, and P. J. Stephens, /. Phys. Chem., 92,5573 (1988). Alternative Formalism for die Calculation of Atomic Polar Tensors and Atomic Axial Tensors. 

Before proceeding with some more details regarding the evaluation of the magnetic dipole moment gradient (the atomic axial tensor, Mj in the context of a nonadiabatic wavefunction, let us first note that it is from a computational point of view advantageous to derive equations with respect to Cartesian displacements of a nucleus A rather than with respect to the normal modes. These two different representations of the nuclear motion are related by a linear transformation... 

We note that the atomic axial tensor cannot be expressed directly as an energy derivative since it involves the overlap over two perturbed wavefunctions. However, the perturbed wavefunctions can be obtained as the dot product of the solution vectors N defined by the linear response function in Eq. 2.26 for a magnetic field and nuclear displacement perturbation, respectively. It is important here to note that some care needs to be exercised in the way the orbital rotations, in the language of Section 2.1.1, are defined [253, 254]. 

The Raman (Eq. 2) and ROA (Eq. 3) invariants require the evaluation of the first-order derivatives of three polarizability tensors (Bo/O/f, ), (6A/6R ), and (0G /07 ia)- A review by Buckingham [34] defines all these polarizabilities. The dipole strength and rotational strength entering into the IR (Eq. 4) and VCD (Eq. 5) intensities require the calculation of the atomic polar tensors (APTs, Pm = and of the atomic axial tensors (AATs,... 

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