Quantitative measures of similarity between pharmacologically active compounds

A theoretical measure of molecular similarity based on ab initio computations of electron density derived from molecular orbital wave functions is first applied to a model series (CH₃CH₂CH₃, CH₃OCH₃, and CH₃SCH₃) and then to the rings in a series of prostaglandins and to some histamine H2 antagonists. Comparison in terms of valence electron density seems to be a good basis for structure-activity studies.     

Molecular electronic density fitting using elementary Jacobi rotations under atomic shell approximation

Fitted electron density functions constitute an important step in quantum similarity studies. This fact not only is presented in the published papers concerning quantum similarity measures (QSM), but also can be associated with the success of the developed fitting algorithms. As has been demonstrated in previous work, electronic density can be accurately fitted using the atomic shell approximation (ASA). This methodology expresses electron density functions as a linear combination of spherical functions, with the constraint that expansion coefficients must be positive definite, to preserve the statistical meaning of the density function as a probability distribution. Recently, an algorithm based on the elementary Jacobi rotations (EJR) technique was proven as an efficient electron density fitting procedure. In the preceding studies, the EJR algorithm was employed to fit atomic density functions, and subsequently molecular electron density was built in a promolecular way as a simple sum of atomic densities. Following previously established computational developments, in this paper the fitting methodology is applied to molecular systems. Although the promolecular approach is sufficiently accurate for quantum QSPR studies, some molecular properties, such as electrostatic potentials, cannot be described using such a level of approximation. The purpose of the present contribution is to demonstrate that using the promolecular ASA density function as the starting point, it is possible to fit ASA-type functions easily to the ab initio molecular electron density. A comparative study of promolecular and molecular ASA density functions for a large set of molecules using a fitted 6-311G atomic basis set is presented, and some application examples are also discussed.     

Three-center expansion of electron repulsion integrals with linear combination of atomic electron distributions

A new systematic way of constructing auxiliary basis functions for approximating the evaluation of electron repulsion integrals is proposed and applied to SCF and MCSCF wavefunction calculations. In the approximation, the one-electron density is expanded in terms of a linear combination of atomic electron distributions (LCAD), and the four-center two-electron repulsion integrals are reduced to the three- and two-center quantities. This results in a high-accuracy approximation as well as a large reduction in disk storage and input/output requirement, proportional to N³ rather than N⁴, N being the number of basis functions. Numerical results indicate that the error from the present approximation decreases as the size of molecular basis functions increases and that the LCAD version of MCSCF calculations requires only a fractional amount of the CPU time required in the conventional procedure without loss of accuracy.     

Possible criterion for the balance of basis sets in quantum-chemical calculations

We propose to characterize the width of a basis set (BS) by the number of basis functions falling within one electron of the considered atomic or molecular systems. It is established that for atoms, this value (the electron function endowment, or EFE) undergoes drastic changes as the atomic number of a periodic system element increases. It is shown that widening the BS through the addition of valence and polarizational functions increases the imbalance of the basis sets of various atoms in terms of EFE. A scheme of construction is proposed and an example of a BS balanced according to the EFE value is given. The properties of LiH and HF molecules are calculated by the density functional UB3LYP method with the use of standard and molecular-optimized (relaxed) BSes with segmented and general contraction of the Gaussian functions. It is established that there are uniform dependences for the error of calculating the properties of both molecules from the EFE. We conclude that the accuracy of calculating the equilibrium distance, ionization energy, electron affinity, atomization energy, dipole moment, and frequency of normal vibration increases steadily as the EFE value of a molecule rises.     

Closed‐form analytical solutions for the calculation of the moments of the molecular electron density

Moments of the molecular electron density can be related directly to several experimental observables, but formerly they have only been accurately calculated through methods which lack consistency with standard quantum chemical methods. Here we report analytical solutions to the basic molecular integrals required to compute the moments of the molecular electron charge density over Gaussian basis functions. These are derived and cast into a practical closed form, suitable to interface with modern codes for the calculation of the molecular electronic structure. Illustrative calculations for the hydrogen molecule, at both the Hartree–Fock and the full configuration interaction levels of theory, are shown and discussed in connection with observables linked directly to some of the calculated moments. This revised version was published online in July 2006 with corrections to the Cover Date.     

Approximate molecular orbital theory: the ese mo formalism.: III. Parametrization for all- or valence-electron calculation using accurate STF bases for molecules containing 1st, 2nd,and 3rd row atoms. SO2 results

The key components of a completely theoretical parametrization of the essential-structural-elements molecular orbital (ESE MO) formalism using Slater-type AO basis in the LCAO SCF procedure are discussed. Special attention is paid to the problem of separability into core and valence parts of the total molecular wavefunction, including the case where valence functions strongly overlap neighbouring core orbitals. The use of Huzinaga and Cantu effective hamiltonian is proposed. The parametrization is tested in relation to the SO₂ molecules. The role of sulphur 3d functions in bonding as predicted by the present ESE MO calculations and ab initio calculations are compared. The present parametrization appears to adequately handle both the core/valence separation, and the diffuse higher valence sulphur 3d functions in this system.     

The definition of core electrons

The traditional separation of electrons in molecules into core and valence types is often based on molecular orbital energies. This method is known to lead in some cases to large relative errors in correlated calculations. Instead, we propose a method based on the definition of molecular core character using separation of basis functions into core and valence types. This gives size-consistency to separation of electrons in molecules into core and valence types.     

Topological and orbital-based mechanisms of the electronic stabilization of bis(diisopropylamino)cyclopropenylidene

Previous analysis of the topology of the electron density of bis(dimethylamino)cyclopropenylidene as a model of the stable bis(diisopropylamino)cyclopropenylidene revealed mechanisms of induction/back-polarization, sigma-aromaticity, and sigma-pi polarization to be responsible for the electronic stabilization of the divalent carbon C2 upon amino substitution on the 3MR. This work presents new data from molecular orbital calculations and a full analysis of the operative natural bond orbitals and their interactions. The discrepancies between these orbital-based stabilization mechanisms and the physical stabilization based upon the quantum theory of atoms in molecules are uncovered through the separation of electron localization and delocalization indices into contributions from orbitals of sigma- and pi-symmetry, as well as calculated nucleus-independent chemical shifts that determine the degree of sigma- and pi-delocalization/aromaticity. Graphical representations of functions of the electron density mapped onto various pi-orbital isosurfaces serve to better visualize the underlying differences between mathematical orbital space and the real space of the electron density. This work also provides new insight into the topological-based mechanism through investigation of the changes in the virial of the electronic forces acting on the interatomic surfaces--forces that govern the bonding and stabilization within a molecule.     

Morphological changes in SBS block copolymers caused by oil extension as determined by absolute small angle x-ray scattering

A series of SBS block copolymers diluted with different amounts (0–60 wt%) of three different kinds of oil were investigated: 1) lithene PM (a low molecular weight polybutadiene); 2) a paraffinic mineral oil with its electron density close to that of the polybutadiene (PB) phase; 3) a highly aromatic mineral oil with an electron density close to the polystyrene (PS) phase. All the oils seem to go into the polybutadiene matrix. Paraffinic oil and lithene form a homogeneous phase with PB; the aromatic oil at low concentrations mixes with the PB phase with a high level of inhomogeneity, while at higher concentration partial phase separation occurs. In the undiluted polymer, styrene forms cylinders in hexagonal packing. The distance between cylinders (about 43 nm) is not significantly changed upon dilution up to 33 wt%. Previously proposed changes in the morphology of PS domains at larger oil contents can be related to observed changes in the long period, in the segment length distributions, and in the homogeneities of the phase (density fluctuations). The electron density difference obtained for pure SBS is lower than the theoretical one calculated from the densities of pure PS and pure PB. Dilution by paraffinic oil improves the phase separation.     

Ab initio quality one-electron properties of large molecules: development and testing of molecular tailoring approach

The development of a linear-scaling method, viz. "molecular tailoring approach" with an emphasis on accurate computation of one-electron properties of large molecules is reported. This method is based on fragmenting the reference macromolecule into a number of small, overlapping molecules of similar size. The density matrix (DM) of the parent molecule is synthesized from the individual fragment DMs, computed separately at the Hartree-Fock (HF) level, and is used for property evaluation. In effect, this method reduces the O(N(3)) scaling order within HF theory to an n.O(N'(3)) one, where n is the number of fragments and N', the average number of basis functions in the fragment molecules. An algorithm and a program in FORTRAN 90 have been developed for an automated fragmentation of large molecular systems. One-electron properties such as the molecular electrostatic potential, molecular electron density along with their topography, as well as the dipole moment are computed using this approach for medium and large test chemical systems of varying nature (tocopherol, a model polypeptide and a silicious zeolite). The results are compared qualitatively and quantitatively with the corresponding actual ones for some cases. This method is also extended to obtain MP2 level DMs and electronic properties of large systems and found to be equally successful.     

Spherical tensor gradient operator method for integral rotation: a simple, efficient, and extendable alternative to Slater-Koster tables

We present a novel alternative to the use of Slater-Koster tables for the efficient rotation and gradient evaluation of two-center integrals used in tight-binding Hamiltonian models. The method recasts the problem into an exact, yet implicit, basis representation through which the properties of the spherical tensor gradient operator are exploited. These properties provide a factor of 3 to 4 speedup in the evaluation of the integral gradients and afford a compact code structure that easily extends to high angular momentum without loss in efficiency. Thus, the present work is important in improving the performance of tight-binding models in molecular dynamics simulations and has particular use for methods that require the evaluation of two-center integrals that involve high angular momentum basis functions. These advances have a potential impact for the design of new tight-binding models that incorporate polarization or transition metal basis functions and methods based on electron density fitting of molecular fragments.     

Cumulative atomic multipole representation of the molecular charge distribution and its basis set dependence

A simple procedure to decompose the theoretical molecular charge distribution into cumulative atomic multipoles supplementing any population analysis scheme has been described and tested for a number of molecules in extended basis sets. This approach may be applied to describe local charge distributions in neutral as well as charged systems and also leads to a simplified point-charge model conserving the local anisotropy of the atomic charge distribution in molecules. Such an approach may be useful in estimating intermolecular interactions, representing the molecular environment in solvent effect or enzyme catalytic activity studies, evaluation of molecular electrostatic potentials or tracing the quality of basis set functions.     

Use of promolecular ASA density functions as a general algorithm to obtain starting MO in SCF calculations

Atomic shell approximation (ASA) constitutes a way to fit first‐order density functions to a linear combination of spherical functions. The ASA fitting method makes use of positive definite expansion coefficients to ensure appropriate probability distribution features. The ASA electron density is sufficiently accurate for the practical implementation of quantum similarity measures, as was proved in previous published work. Here, a new application of the ASA density formalism is analyzed, and employed to obtain an initial guess of the density matrix for SCF procedures. The number of cycles needed to assess the convergence criterion in electronic energy calculations appears comparable to or less than those obtained by other means. Several molecular structures of different classes, including organic systems and metal complexes, were chosen as representative test cases. In addition, an ASA basis set for atoms Sc‐Kr fitted to an ab initio 6‐311G basis set is also presented. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Electron transfer dynamics

This paper surveys the current ‘state-of-art’ of the theoretical understanding of electron transfer dynamics in donor-acceptor systems, which provide the conceptual and technical basis for solar energy conversion via optical and optoelectronic molecular devices and for the primary charge separation in photo-synthesis.     

Extracting atoms from molecular electron densities via integral equations

The observation that a molecular electron density is close to the superposition of its constituent atoms leads naturally to the idea of modeling a density by a sum of nuclear-centered, spherically symmetric functions. The functions that are optimal in a least-squares sense are known as Stewart atoms. Previous attempts to construct Stewart atoms by expanding them in an auxiliary basis have been thwarted by slow convergence with respect to the size of the auxiliary basis used. We present a method for constructing Stewart atoms via convolution integrals which bypasses the need for an auxiliary basis, and is able to produce highly accurate approximations to Stewart atoms.     

Subshell fitting of relativistic atomic core electron densities for use in QTAIM analyses of ECP-based wave functions

Scalar-relativistic, all-electron density functional theory (DFT) calculations were done for free, neutral atoms of all elements of the periodic table using the universal Gaussian basis set. Each core, closed-subshell contribution to a total atomic electron density distribution was separately fitted to a spherical electron density function: a linear combination of s-type Gaussian functions. The resulting core subshell electron densities are useful for systematically and compactly approximating total core electron densities of atoms in molecules, for any atomic core defined in terms of closed subshells. When used to augment the electron density from a wave function based on a calculation using effective core potentials (ECPs) in the Hamiltonian, the atomic core electron densities are sufficient to restore the otherwise-absent electron density maxima at the nuclear positions and eliminate spurious critical points in the neighborhood of the atom, thus enabling quantum theory of atoms in molecules (QTAIM) analyses to be done in the neighborhoods of atoms for which ECPs were used. Comparison of results from QTAIM analyses with all-electron, relativistic and nonrelativistic molecular wave functions validates the use of the atomic core electron densities for augmenting electron densities from ECP-based wave functions. For an atom in a molecule for which a small-core or medium-core ECPs is used, simply representing the core using a simplistic, tightly localized electron density function is actually sufficient to obtain a correct electron density topology and perform QTAIM analyses to obtain at least semiquantitatively meaningful results, but this is often not true when a large-core ECP is used. Comparison of QTAIM results from augmenting ECP-based molecular wave functions with the realistic atomic core electron densities presented here versus augmenting with the limiting case of tight core densities may be useful for diagnosing the reliability of large-core ECP models in particular cases. For molecules containing atoms of any elements of the periodic table, the production of extended wave function files that include the appropriate atomic core densities for ECP-based calculations, and the use of these wave functions for QTAIM analyses, has been automated.     

A quantitative analysis of light‐driven charge transfer processes using voronoi partitioning of time dependent DFT‐derived electron densities

An analytical method is presented that provides quantitative insight into light‐driven electron density rearrangement using the output of standard time‐dependent density functional theory (TD‐DFT) computations on molecular compounds. Using final and initial electron densities for photochemical processes, the subtraction of summed electron density in each atom‐centered Voronoi polyhedron yields the electronic charge difference, Q ^VECD. This subtractive method can also be used with Bader, Mulliken and Hirshfeld charges. A validation study shows Q ^VECD to have the most consistent performance across basis sets and good conservation of charge between electronic states. Besides vertical transitions, relaxation processes can be investigated as well. Significant electron transfer is computed for isomerization on the excited state energy surface of azobenzene. A number of linear anilinepyridinium donor‐bridge‐acceptor chromophores was examined using Q ^VECD to unravel the influence of its pi‐conjugated bridge on charge separation. Finally, the usefulness of the presented method as a tool in optimizing charge transfer is shown for a homologous series of organometallic pigments. The presented work allows facile calculation of a novel, relevant quantity describing charge transfer processes at the atomic level. © 2017 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Fourier analysis of the Compton profile: Atoms and molecules

Recent work has shown that the one-dimensional projection of the electron momentum density, the Compton profile, can be usefully interpreted as a position space quantity. This has led to an examination of B(r), the Fourier transform of the momentum density. A number of theoretical results relating to this new observable are given. The wave-mechanical representation with (natural) orbitals is employed, and this forms the basis for the subsequent analysis of B(r). The relationship of B(r) to overlap integrals and more generally to other electron density functions is considered. Atomic wavefunctions for krypton are used to illustrate the potential of this new approach to the analysis of momentum density data. General expressions are derived for atoms and molecules, and the radial and angular dependence of B(r) for various orbitals is displayed. The possibility of extracting accurate bond lengths from B(r) is assessed, and an example is given using some recent theoretical data for the fluorine molecule.     

Methods for constructing Stewart atoms

We compare four methods for generating Stewart atoms, the spherically-symmetric nuclear-centred functions whose sum best fits a given electron density. We find that projecting a molecular density onto an atom-centred basis is a more subtle and difficult problem than is generally recognized and we conclude that new approaches, based on integral equations, may be more satisfactory than traditional projection methods.     

Shaping the density to fit one-electron properties: Constrained RHF calculations on N2, FH,CO, and LiH

The molecular density required to give the correct values for one-electron properties is rarely given by wave functions obtained from variation methods based on the total energy or the eigenvalues. Perhaps if we knew how the density should be shaped in any particular volume to fit a particular property, the whole molecular density might then be properly described to fit the whole volume. The secant-parametrization procedure is used to constrain minimum basis set RHF wave functions for N₂, FH, CO, and LiH to determine the effects of different constraints on RHF wave functions, and to see how constraints improve the quality of small basis set RHF wave functions. One-electron property expectation values, energies, and unweighted and property weighted populations and electron density difference profiles are used to analyze the constrained wavefunctions. With the information from the constrained wave functions it should be possible to select a LCAO -CI basis and states to give the correct density for all properties. This should map onto the constrained wave function in the region of the constraint and at the same time minimize the energy of the total molecular wave function. Such a density would be suitable for the density analyses favored by Bader and Nguyen-Dang [Adv. Quantum Chem. 14 , 113 (1981)], Mezey [Theor. Chim. Acta 54 , 95 (1980); 58 , 309 (1981); 59 , 321 (1981)], and March [Theoretical Chemistry (Royal Society of Chemistry, London, 1981), Vol. 4, p. 158], and show the real atom needed to generate the molecule.