Spin functionals, gradients

The three multiplet components of an excited triplet state are degenerate in zeroth order. We have therefore, in principle, the freedom of choosing these in their spherical or Cartesian forms. On the other hand, the spin-orbit split triplet levels will transform according to the irreps of the molecular point group. For a smooth variation of the wave function gradient with respect to the perturbation parameter X, we employ Cartesian triplet spin functions also in the unperturbed case and express them as ket vectors ... 

Both HF and DFT calculations can be performed. Supported DFT functionals include LDA, gradient-corrected, and hybrid functionals. Spin-restricted, unrestricted, and restricted open-shell calculations can be performed. The basis functions used by Crystal are Bloch functions formed from GTO atomic basis functions. Both all-electron and core potential basis sets can be used. 

For a quantum mechanical calculation, the single point calculation leads to a wave function for the molecular system and considerably more information than just the energy and gradient are available. In principle, any expectation value might be computed. You can get plots of the individual orbitals, the total (or spin) electron density and the electrostatic field around the molecule. You can see the orbital energies in the status line when you plot an orbital. Finally, the log file contains additional information including the dipole moment of the molecule. The level of detail may be controlled by the PrintLevel entry in the chem.ini file. 

Hohenberg and Kohn demonstrated that is determined entirely by the (is a functional of) the electron density. In practice, E is usually approximated as an integral involving only the spin densities and possibly their gradients ... 

Fourier transformation to reconstruct the spin-density function of the sample, q(i). The variation of gradients is symbolized by diagonal lines in Figure 1.4. 

The argument of the function F is the reduced density gradient for spin o... 

Helgaker, T., Watson, M., Handy, N. C., 2000, Analytical Calculation of Nuclear Magnetic Resonance Indirect Spin-Spin Coupling Constants at the Generalized Gradient Aproximation and Hybrid Levels of Density Functional Theory , J. Chem. Phys., 113, 9402. 

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