Method CTOCD

Effects of a Static Electric Field on Molecular Magnetic Properties Employing the CTOCD Method Shielding Polarizabilities of CO, H20, and CH4 Compounds... 

Advantage of the CTOCD Method Continuous Transformation of the Origin of the Current Density. The CTOCD method for theoretical determination of hypermagnetizabilities and shielding polarizabilities is reported in detail in ref. (28). In this section we make only a very brief description of the theory involved in the formulation of CrOCZ)-Z>Z r and a1/ -... 

Hartree-Fock theory using the CTOCD method (see Section 2.4) for anthracene, phenanthrene and triphenylene. The magnetizabihties and nuclear shieldings are also calculated in the same approximation and are found to agree well with experimental values. Ferraro and Caputo have used the RPA (TDHF) method in conjunction with the CTOCD gauge transformation and a polarization propagator formahsm to calculate magnetic properties of HF, H2O, NH3 and CH4. 

Induced currents densities in the perylene/bisanthrene family were also calculated [143] (see also [151]) characteristic results are depicted in Fig. 11.11. The respective geometries were optimized by the B3LYP/6-311+G(d,p) method, using Gaussian 03. Current densities were computed by means of coupled HF theory, using the diamagnetic-zero variant of the CTOCD method [143]. 

Basis set size LORG Common origin Geertsen method CTOCD GIAOs... 

Figure 14. Direction of the induced, first-order current density for the CO2 moiecuie, in the molecular plane, obtained with the CTOCD DZ method of Zanasi et ai. Note the outer diamagnetic circulation and the paramag netic vortical circulation near the center of symmetry. (Adapted and reprinted with permission from ref 337. Copyright 1995 American Institute of Physics.)...

Figure 15. Projected direction of the induced, first order, current-density field for benzene, in the molecular plane (d= 0) and in planes parallel with it at distances d= 0.13, 0.26, 0.39, and 0.52 bohr, obtained by the CTOCD DZ method. (Adapted and reprinted with permission from refs 4 and 338. Copyright 2000 Elsevier Science B.V.)...

These two terms are known as the paramagnetic and diamagnetic terms, respectively and / is a molecular orbital in the presence of the magnetic field, p is the classical linear momentum operator and A the vector potential. In the so-called CSGT or CTOCD-DZ or ipsocentric methods [79-82], the second term is effectively put to zero via the special choice of gauge. What ranains eventually, is the paramagnetic term ... 

An even more effective numerical method for calculating the magnetic properties (25), (28), (31), and (34), based on formal annihilation of the paramagnetic contribution to the current density all over the molecular domain (CTOCD-PZ), has been outlined in a series of papers. Extensive numerical tests document the reliability, simplicity, and accuracy of this numerical procedure. To build up the CTCXID-PZ computational scheme it is expedient to define a set of generalized transformation functions theoretical methods which have been examined in detail by Coriani et al. Unlike the DZ procedure, the CTOCD-PZ equations cannot, in general, be solved to obtain closed form expressions. Rather the functions employed to cancel the transverse paramagnetic contribution to current density are evaluated pointwise via conditions imposed on first- and second-order current densities (compare for equations 113 and 115) ... 

For computational purposes (i.e., to get rid of the fields from the very beginning), second- and third-rank current density tensors are defined within the CTOCD-PZ method ... 

---