Embedding frozen density

Fig. 26 Left. A benzaldehyde dimer at 5 A separation. Right. CD of the dimer computed with TDDFT for the dimer supermolecule, and using a coupled TDDFT frozen-density embedding subsystem approach [266], Figures courtesy of Dr. J. Neugebauer...

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]. 

The frozen density-embedding (FDE) formalism [52] developed by Wesolowski and Warshel [52-54] has been applied to a plethora of chemical problems, for instance, solvent effects on different types of spectroscopy [55-57], magnetic properties [58-62], excited states [55, 63-66], charge transfer states [49, 67, 68]. Computationally, FDE is available for molecular systems in ADF [51, 69], Dalton [70, 71], Q-Chem [72, 73], and Turbomole [74-76] packages, as well as for molecular periodic systems in CP2K [77, 78] and fully periodic systems (although in different flavors) in CASTEP [79, 80], Quantum Espresso [81-83], and Abinit [84, 85]. 

Genova A, Krishtal A, Ceresoli D, PavaneUo M (2013) Frozen Density Embedding Project of Quantum Espresso, http //qe-forge.org/gf/project/fde... 

The Merits of the Frozen-Density Embedding Scheme to Model Solvato-chromic Shifts. 

Hofener S, Visscher L (2012) Calculation of electronic excitations using wave-function in wave-function frozen-density embedding. J Chem Phys 137 204120... 

Fux S et al (2010) Accurate frozen-density embedding potentials as a first step towards a subsystem description of covalent bonds. J Chem Phys 132 164101... 

Neugebauer J et al (2005) The merits of the frozen-density embedding scheme to model solvatochromic shifts. J Chem Phys 122 094115... 

Neugebauer J et al (2005) Modeling solvent effects on electron-spin-resonance hyperfine couplings by frozen-density embedding. J Chem Phys 123 114101... 

Autschbach and co-workers have presented a method for a subsystem-based calculation of indirect nuclear spin-spin coupling tensors. This approach was based on the frozen-density embedding scheme within density-functional theory and was an extension of a previously reported subsystem-based approach for the calculation of nuclear magnetic resonance shielding tensors. The method was particularly useful for the inclusion of environmental effects in the calculation of nuclear spin-spin coupling constants. According to this method, the computationally expensive response calculation had to be performed only for the subsystem of interest. As an example, the authors have demonstrated the results for methylmercury halides which exhibited an exceptionally large shift of the V(Hg,C) upon coordination of dimethylsulfoxide solvent molecules. 

Cortona embedded a DFT calculation in an orbital-free DFT background for ionic crystals [183], which necessitates evaluation of kinetic energy density fiinctionals (KEDFs). Wesolowski and Warshel [184] had similar ideas to Cortona, except they used a frozen density background to examine a solute in solution and examined the effect of varying the KEDF. Stefanovich and Truong also implemented Cortona s method with a frozen density background and applied it to, for example, water adsorption on NaCl(OOl) [185]. 

Figure 8-26 The structure of the 994-residue Ca2+-ATPase of the endoplasmic reticulum of rabbit muscle at 0.8-nm resolution. (A) Predicted topology diagram organized to correspond to the electron density map prepared by electron crystallography of frozen-hydrated tubular crystals. The number of amino acid residues in each connecting loop is marked. (B) The electron density map with the predicted structure embedded. The relationships of the helices in (B) to those in (A) are not unambiguous. The helices marked B, D, E, and F in (B) may form the Ca2+ channel. The large cytoplasmic loops, which are black in (A), were not fitted. From Zhang et al.553 Courtesy of David L. Stokes.

Fig. 23. The KSCED embedding potential (Eq. 53 at the LDA level) generated by the frozen electron density of cytosine in the guanine-cytosine complex. The lines are drawn in the plane of the molecules at —0.1, 0.0, 0.2, 0.4 and 0.7 atomic units.

Cyt/and domain I to the Rieske ISP assignment of domains III and IV to the remaining two subunits was less definitive. However, projection maps were determined more recently by Bron, Lacap e, Breyton and Mosser for the C. reinhardtii Cyt-bff comple using frozen-hydrated crystals. The combination of the projection maps obtained from the ice-embedded and the negative-stained crystals allowed the authors to correlate their results with the atomic model of the Cyt-6c, complex and to localize Cyt to domain III and subunit IV to domain IV. The 8-A resolution map reveals a ring of densities surrounding a deep groove, marked G" in Fig. 7 (B), which appears to be separated by domains III and IV domains I and IV appear more closely connected. 

The AIM chemical potentials defined by the partial functional derivatives of equation (35), calculated for the fixed external potential and the frozen embedding densities pp a r) of the remaining subsystems, are equalized only when the subsystems are mutually open [4,5], This is the case in the global equilibrium state considered in the preceding section. In what follows we shall denote such open subsystem condition by the vertical broken fines in the symbolic representation of the molecular system as a whole, Mg = (a fi y. ..), in the global (g, intersubsystem) equilibrium of the ground-state of an externally open system ... 

In the embedding formalism introduced by Wesolowski and Warshel [3], the total electron density is partitioned into two components. One of them is not optimized (frozen) and the other is subject to optimization. The optimized component is treated in a Kohn-Sham-like way, i.e., by means of a reference system of non-interacting electrons. The multiplicative potential in one-electron equations for embedded orbitals, Eq. (1) or Eqs. (20) and (21) of Ref. [3], differs from the Kohn-Sham... 

P2 is derived from the Kohn-Sham calculations for the isolated embedding subsystem (the cation here). In this case the changes of the embedding electron density accompanying the formation of the complex is neglected frozen P2). 

Tables 1-3 show the magnetic dipolar interaction tensor Aij). The KSCED calculations use the supermolecule expansion of the electron density of each subsystem and are performed using either using the frozen embedding electron density of the relaxed one.

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