Density functionals connection methods

In particular, reactions involving transition-metals have attracted a lot of interest recently because of the connection to catalytic and enzymatic processes. Unfortunately, the proper computational description of such reactions is one of the great challenges of today s theoretical chemistry and the question for the general applicability of density functional methods in the field is an area of active research. We chose to provide a single but - as we think - representative example to illustrate the difficulties one has to face in theoretical studies of transition-metal reactivity. 

Adamo, C., Barone, V., 1998a, Implementation and Validation of the Lacks-Gordon Exchange Functional in Conventional Density Functional and Adiabatic Connection Methods , J. Comput. Chem., 19, 418. 

Adamo, C., di Matteo, A., Barone, V., 1999, From Classical Density Functionals to Adiabatic Connection Methods. The State of the Art , Adv. Quantum Chem., 36, 45. 

From the early advances in the quantum-chemical description of molecular electron densities [1-9] to modem approaches to the fundamental connections between experimental electron density analysis, such as crystallography [10-13] and density functional theories of electron densities [14-43], patterns of electron densities based on the theory of catastrophes and related methods [44-52], and to advances in combining theoretical and experimental conditions on electron densities [53-68], local approximations have played an important role. Considering either the formal charges in atomic regions or the representation of local electron densities in the structure refinement process, some degree of approximate transferability of at least some of the local structural features has been assumed. 

It is instructive, however, in order to establish the connection between the usual methods in quantum chemistry - based on molecular orbitals - and the local-scaling transformation version of density functional theory, to discuss Cioslowski s work in some detail. 

Simply to look at the literature is to convince yourself of the importance that density functional theory (DFT) methods have attained in molecular calculations. But there is among the molecular physics community, it seems to me, a widespread sense of unease about their undoubted successes. To many it seems quite indecent that such a cheap and cheerful approach (to employ Peter Atkins s wonderful phrase) should work at all, let alone often work very well indeed. I think that no-one in the com-mimity any longer seriously doubts the Hohenberg-Kohn theo-rem(s) and anxiety about this is not the source of the unease. As Roy reminded us at the last meeting, the N— representability problem is still imsolved. This remains true and, even though the problem seems to be circumvented in DFT, it is done so by making use of a model system. He pointed out that the connection between the model system and the actual system remains obscure and in practice DFT, however successful, still appears to contain empirical elements And I think that is the source of our present unease. 

The electronic coupling of donor and acceptor sites, connected via a t-stack, can either be treated by carrying out a calculation on the complete system or by employing a divide-and-conquer (DC) strategy. With the Hartree-Fock (HF) method or a method based on density functional theory (DFT), full treatment of a d-a system is feasible for relatively small systems. Whereas such calculations can be performed for models consisting of up to about ten WCPs, they are essentially inaccessible even for dimers when one attempts to combine them with MD simulations. Semiempirical quantum chemical methods require considerably less effort than HF or DFT methods also, one can afford application to larger models. However, standard semiempirical methods, e.g., AMI or PM3, considerably underestimate the electronic couplings between r-stacked donor and acceptor sites and, therefore, a special parameterization has to be invoked (see below). 

The gas-phase basicity (GB) of 3-thio-5-oxo 1, 5-thio-3-oxo 2, and 3,5-dithio 4 derivatives of 2,7-dimethyl-[l,2,4]-triazepine (Figure 1) has been measured by means of Fourier transform ion cyclotron resonance (FTICR) mass spectrometry and complemented with theoretical calculations. The experimental FTICR results are discussed in Section 13.14.4.1.l(i). The structures and vibrational frequencies of all stable protonated tautomers and all transition states connecting them have been obtained by means of the B3LPY density functional method, together with 6-31G basis set expansion. The final energies were obtained at the B3LYP/6-311 + G(3df,-2p) level (2002JPC7383). 

The flexible helix modeled here is best described by the entire array of conformations it can assume. A comprehensive picture of this array is provided by the three-dimensional spatial probability density function Wn(r) of all possible end-to-end vectors (25, 35). This function is equal to the probability per unit volume in space that the flexible chain terminates at vector position relative to the chain origin 0,as reference. An approximate picture of this distribution function is provided by the three flexible single-stranded B-DNA chains of 128 residues in Figure 5(a). The conformations of these molecules are chosen at random by Monte Carlo methods (35, 36) from the conformations accessible to the duplex model. The three molecules are drawn in a common coordinate system defined by the initial virtual bond of each strand. For clarity, the sugar and base moieties are omitted and the segments are represented by the virtual bonds connecting successive phosphorus atoms. 

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