A new intrinsic localization algorithm is suggested based on a recently developed mathematical measure of localization. No external criteria are used to define a priori bonds, lone pairs, and core orbitals. It is shown that the method similarly to Edmiston–Ruedenberg’s localization prefers the well established chemical concept of σ–π separation, while on the other hand, works as economically as Boys’ procedure. For the application of the new localization algorithm, no additional quantities are to be calculated, the knowledge of atomic overlap intergrals is sufficient. This feature allows a unique formulation of the theory, adaptable for both ab initio and semiempirical methods, even in those cases where the exact form of the atomic basis functions is not defined (like in the EHT and PPP calculations). The implementation of the procedure in already existing program systems is particularly easy. For illustrative examples, we compare the Edmiston–Ruedenberg and Boys localized orbitals with those calculated by the method suggested here, within both the CNDO/2 and ab initio frameworks (using STO-3G and 6-31G** basis sets) for several molecules (CO, H2CO, B2H6, and N2O4). Some similarities concerning the localization procedures of von Niessen as well as Magnasco and Perico are also discussed.

New developments of the adjustable density matrix assembler (ADMA) approach to macromolecular quantum chemistry are described, based on the original fuzzy density matrix fragmentation scheme combined with an approach of using point charges to approximate the effects of additional, distant parts of a given macromolecule in the quantum chemical calculation of each fragment. The ADMA approach divides a macromolecule (the target molecule) into fuzzy fragments, for which conventional quantum chemical calculations are performed using moderate-sized “parent molecules” which contain both the fragment and all the local interactions of the fuzzy fragment with its surroundings within a preselected distance. For any such distance criterion, that is, for any size limit for the parent molecules, the computational time scales linearly with the size of the macromolecule. As demonstrated in earlier papers, in the original, linear-scaling ADMA approach, the accuracy is fully controlled by this distance, and with a large enough distance criterion nearly exact results are obtained when compared with the conventional Hartree−Fock method. In the new field-adapted ADMA method the same accuracy can be achieved using a smaller distance criterion for the parent molecules if in each parent molecule calculation point charges are also used to represent distant parts of the macromolecule. This allows one to use smaller parent molecules and faster overall calculations resulting in the same overall accuracy that can be achieved only with larger parent molecules in the original ADMA method. Specifically, in the quantum chemical calculations determining the fragment density matrices, each parent molecule is placed within a point-charge field representing the rest of the macromolecule. Consequently, not only the short-range interactions within the actual parent molecule, but also the approximate effects of longer-range electrostatic interactions present in the rest of the macromolecule, are included in the new fragment density matrices. With a number of test calculations of small oligopeptides and proteins, it is shown that the inclusion of partial charges is an efficient tool to obtain results of a uniform accuracy for all these test cases, and that this approach can be used to reduce the need to include longer-range interactions by explicit quantum chemical calculation for much larger parent molecules for the fragments. With a large increase in accuracy and the decrease in computational demand, the field-adapted ADMA approach is now able to describe efficiently very large biomolecular systems at the ab initio quality level.

A new method is presented for the construction of ab initio quality approximate electronic charge distributions for large molecules from charge distributions of small molecular fragments. This method is reminiscent to building structures using Lego blocks. The electronic density distribution calculated using the method is quantitatively shown to be very similar to that calculated for entire molecules using conventional ab initio packages with standard basis sets such as 6-31G**, while requiring only a fraction of the computational time. The pre-calculated fuzzy electron distributions of base molecular fragments, stored in a data bank, are merged (rotated, translated, and subsequently added together) to calculate these approximate charge distributions for the molecule. The method requires only the Cartesian coordinates

We describe new developments of an earlier linear scaling algorithm for ab initio quality macromolecular property calculations based on the adjustable density matrix assembler (ADMA) approach. In this approach, a large molecule is divided into fuzzy fragments, for which quantum chemical calculations can easily be done using moderate-size "parent molecules" that contain all the local interactions within a selected distance. If greater accuracy is required, a larger distance is chosen. With the present extension of this approximation, properties of the large molecules, like the electron density, the electrostatic potential, dipole moments, partial charges, and the Hartree-Fock energy are calculated. The accuracy of the method is demonstrated with test cases of medium size by comparing the ADMA results with direct quantum chemical calculations.

The electrostatic potential around a molecule is often used to describe reactions, binding, and catalysis mechanisms or to serve as a descriptor in structure-activity relationships and molecular similarity studies. Often, very accurate descriptions of this property are needed that traditionally can be obtained, at least for small molecules, by quantum chemical calculations. The aim of this paper is to extend ab initio-quality quantum chemical accuracy to larger molecules such as proteins. The additive fuzzy density fragmentation (AFDF) principle and the adjustable density matrix assembler (ADMA) method are used to divide large molecules into fuzzy fragments, for which quantum chemical calculations can be done directly using smaller, "custommade" parent molecules including all the local interactions within a preset distance limit. In the next step, the obtained density matrices of electron density fragments are combined to approximate the global density matrix and the electron density of the whole molecules. These ADMA electron densities are then used to calculate ab inito-quality electrostatic potentials of the large molecules. The accuracy of the method is analyzed in detail by two test cases of a penta-and a hexapetide, and the efficiency of the technique is demonstrated by the calculation of the electrostatic potential of the protein crambin.

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