Constrained density functional method

Several approaches are available in the literature to generate and evaluate Hamiltonian matrix elements with wavefunctions of charge-localized, diabatic states. They differ in the level of theory used in the calculation and in the way localized electronic structures are created [15, 25, 26, 29-31]. When wavefunction-based quantum-chemical methods are employed, the framework of the generalized Mulliken-Hush method (GMH) [29, 32-34], is particularly successful. So far, it has been used in conjunction with accurate electronic structure methods for small and medium sized systems [35-37]. As an alternative to GMH and other derived methods [38, 39], additional methods have been explored for their applicability in larger systems such as constrained density functional method (CDFT) [25, 37, 40, 41], and fragmentation approaches [42-47], which also include the frozen density embedding (FDE) method [48, 49]. 

M. Levy and J. P. Perdew, The constrained search formulation of density functional theo ry, in Density functional methods in physics, edited by R. M. Dreizler and J. da Providencia, pages 11-30, Plenum, 1985. 

Theoretical chemistry at UBC was further strengthened with the arrival of Delano Chong and Keith Mitchell in 1965 and 1966, respectively. Chong s interests in quantum chemistry have spanned the full range from semiempirical to ab initio molecular orbital methods. His long-standing interests in perturbation methods and constrained variations have figured prominently in his publications. He is probably best known for his attempts to calculate the X-ray and UV photoelectron spectra of molecules, often by means of perturbation corrections to Koopmans theorem.40 More recently he has shifted his focus to coupled pair functional methods and density functional methods, with a special interest in polarizabilities and hyperpolarizabilities.41... 

Constrained optimization procedure for finding transition states and reaction pathways in the framework of gaussian based density functional method the case of isomerization reactions. 

Levy, M., Perdew, J. The Constrained Search Formulation of Density Functional Theory, In Dreizler, R. M., da Providencia, J. (eds.) (1985). Density Functional Methods in Phywzcs, Plenum Press, New York, AM7D/1S7 Senes B.-Physics 123,11-31. 

In the second place, a quite useful characteristic of LS-DFT is that it renders possible to transform an arbitrary wavefunction, say, the Hartree-Fock single Slater determinant into a locally-scaled one associated with a given one-particle density such as the exact one. Thus, one can easily generate a locally-scaled Hartree-Fock wavefunction that yields the exact p. In this sense, one finds much common ground between LS-DFT and those constructive realizations of the constrained-search approach which reformulate the Hartree-Fock method as well as with those developments which pose the optimized potential method as a particular instance of density functional theory [42,43,57-61]. 

Wu, Q., and Van Voorhis, T. Direct optimization method to study constrained systems within density-functional theory. Phys. Rev. A, 72, doi 10.1103/PhysRevA.72.024502 (2005). 

Although the Kohn-Sham method has been the basic procedure in DFT calculations, many exchange-correlation functionals used in conventional DFT calculations have no strict theoretical basis upon which to be used in the Kohn-Sham method. Since the Kohn-Sham method is based on the constrained search formulation, it is proven to be applicable to pure exchange-correlation energy density functionals. 

Several useful methods have been proposed to overcome the variational coUapse problem, and a number of different schemes have been proposed for obtaining SCF wave functions for excited states [10, 16-26]. In recent years, there has been renewed interest in the orthogonality-constrained methods [14, 27] as weU as in the SCF theory for excited states [28-32]. It is clear that an experience accumulated for the HF excited state calculations can be useful to develop similar methods within density functional theory [33-36]. Some of these approaches [10, 18, 19, 23, 24, 26, 30-35] explicitly introduce orthogonality constraints to lower states. Other methods [21, 22, 25] either use this restriction implicitly or locate excited states as higher solutions of nonlinear SCF equations [29]. In latter type of scheme, the excited state SCF wave functions of interest are not necessarily orthogonal to the best SCF functions for a lower state or states of the same symmetry. 

A second class of methods is instead based on the knowledge of the electron density in a theoretical framework similar to that of the DPT. In DPT the effects of the exchange and of the electronic correlation are included by the so-called exchange-correlation (xc) functional, which is obtained by an empirical fit of experimental data or by imposing some physical constrains based on the behavior of some limit model systems [44]. Por the excited states, the TD-DPT [17,18] recently emerged as a very effective tool, since, when coupled to suitable density functionals, it often reaches an accuracy comparable to that of the most sophisticated (but expensive) post-Hartree-Fock methods [45-59], with a much more limited computational cost As a consequence in the last years an increasing number of TD-DPT applications have appeared in the literature, also because this method can be used as a blackbox and is thus also easily accessible to nonspecialists. 

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