Ab Initio Electron Densities Research Articles

Hybrid exchange-correlation functional determined from thermochemical data and ab initio potentials

Multiplicative potentials, appropriate for adding to the non-multiplicative fractional orbital exchange term in the Kohn–Sham equations, are determined from correlated ab initio electron densities. The potentials are examined graphically and are used in conjunction with conventional thermochemical data to determine a new hybrid exchange-correlation functional, denoted B97-2. Calculations using B97-2 are compared with those from (a) the B97-1 functional [J. Chem. Phys. 109, 6264 (1998)], which has the same functional form and fraction of orbital exchange, but was fitted to just thermochemical data; and (b) the widely used B3LYP functional [J. Chem. Phys. 98, 5648 (1993)]. B97-2 atomization energies are close to those from B97-1; total electronic energies and ionization potentials are less accurate, but remain an improvement over B3LYP. Molecular structures from all three functionals are comparable. Static isotropic polarizabilities improve from B3LYP to B97-1 to B97-2; the B97-2 functional underestimates experimental values, which is consistent with the neglect of zero-point vibrational corrections. NMR shielding constants—determined as the conventional second derivative of the electronic energy—improve from B3LYP to B97-1 to B97-2. Shieldings determined directly from these DFT electron densities using the recently proposed MKS approach [Chem. Phys. Lett. 337, 341 (2001)] are two to three times more accurate than the conventional shieldings, and exhibit an analogous improvement across the three functionals. Classical reaction barriers for sixteen chemical reactions improve significantly from B3LYP to B97-1 to B97-2. The introduction of multiplicative potentials into semi-empirical hybrid functional development therefore appears beneficial.

Role of the Hydrogen Bonds in Nitroanilines Aggregation: Charge Density Study of 2-Methyl-5-nitroaniline

The electron charge distribution of 2-Methyl-5-nitroaniline has been studied from high-resolution single-crystal X-ray data at 100 K, and ab initio calculations which include X-ray structure factors computed from a superposition of ab initio molecular electron densities. Using the Hansen and Coppens' rigid pseudoatom multipolar model refinements were performed on both the experimental and the theoretical X-ray data sets from which, molecular atomic charges and dipolar moments were obtained. To understand the nature and the magnitude of the intermolecular interactions, the Atoms in Molecules theory was used to investigate the topology of the electron density of the in-crystal, both experimental interacting as well as theoretical noninteracting, and in-vacuum molecules. A meticulous analysis of the topological properties of the experimental charge density and of its Laplacian indicates, contrary to expectations, a two center character of the N−H···O synthons that induce the known polar chain formation in nitroanilines and the presence of a Cmethyl-H···O interaction further strengthening the chains. It also shows the attractive nature of the rather strong C−H···O interactions that help the head-to-tail arrangement of the chains. They build two intermolecular six membered hydrogen bonded rings, embracing a N−H···O interaction, that originate centrosymmetric dimers which impair the macroscopic second harmonic generation of the title compound. The authenticity of a previously proposed closed shell Caryl-H···π interaction between adjacent chains has been confirmed. The latter has not been observed in m-nitroaniline, 2-methyl-4-aniline or other related compounds with chains built from similar N−H···O synthons and assembled head-to-head. Crystallization causes a molecular electric dipolar moment higher than that of the free molecule, the latter being coincident with the experimental value in solution, and with the one calculated from the refinement of the theoretical X-ray data. It also induces changes in the charge density distribution and its topology, and an enhancement of the intramolecular conjugation that can be related to a molecular aggregation mechanism ruled by the N−H···O synthon. These findings strongly point to the existence of cooperative effects.

The core structure, recombination energy and Peierls energy for dislocations in Al

Abstract In the framework of the Peierls model generalized to two dimensions the dissociation of a dislocation in the {111} plane of a fcc lattice into two Shockley partials is studied by a variational procedure. Each partial is made up by a distribution of infinitesimal dislocations with a density obtained by a superposition of three closely spaced Lorentz peaks of adjustable height, width and separation. The atomic misfit energy in the glide plane is obtained from the γ surface represented by a two-dimensional Fourier series showing the symmetry of the {111} plane. The procedure is applied to Al for which a set of γ values in the {111} plane has been obtained by Hartford et al. using ab-initio electron density functional theory. The dissociation width of the edge dislocation is found to be 0.74 nm, which almost agrees with the experimental value of about 0.8 nm. The screw dislocation is not split in the usual way but rather shows a widely extended core with some edge components. The energy to compress t...

The core structure of dislocations. Peierls model vs. atomic simulations in Pd

When the Peierls model for dislocations is properly generalised to 2D, it is possible to obtain a realistic description of dislocation cores with planar extension. This is an attractive alternative to large-scale atomic simulations. Instead of balancing the acting forces by numerically solving the Peierls integral equation, it is of advantage to use a variational procedure for the energy. The atomic misfit energy can be obtained from the γ-surface as determined by ab initio electron density functional methods. Such even a better description may be obtained than by simulations, which must use empirical interatomic potentials. In Pd where calculations of the γ-surface and atomic simulations are available, the core structure has been determined with the generalised Peierls model and the agreement with the atomic simulations is excellent. Problems connected with determining the Peierls energy will be discussed.

The core structure of dissociated dislocations in NiAl

With the Peierls model generalised to 2D, the core structure of dislocations with Burgers vector a[111] in NiAl is determined. The results are compared with atomic computer simulations from the literature using an empirical EAM interatomic potential. When in the generalised Peierls model the elastic constants and the γ-surface resulting from this potential are used, the results show close agreement. This shows that the generalised Peierls model offers an attractive alternative to the large computational effort required by atomic simulations. When the γ-surface is available from ab initio electron density functional theory, the generalised Peierls model will even give more realistic results than simulations which must rely on empirical potentials.

Reaction of Metcar Ti8C12 with Halogen-Containing Addends

Ab initio electron density functional method in the discrete-variational scheme was used to perform self-consistent calculations of the electronic structure of Ti8C12Cl2 and Ti8C12(CHCl3), i.e., the adducts of reaction between the Ti8C12 metallocarbohedrene and halogen-containing addends (Cl2 and CHCl3 molecules). The electronic states, charge distributions, and chemical bonds of the obtained adducts were analyzed. The results were compared with calculations of the Ti8C12Cl complex that can be treated as a model of the destruction stage of the addends. General conditions for the interaction of halogenated addends with metcars in the molecular and crystalline states are discussed based on the data obtained.

The Electronic Structure of Mixed Metcars Ti7MC12 (M = Y, Zr, Nb,..., Ag)

The electronic structures of a series of mixed metallocarbohedrenes (metcars) Ti7MC12formed as a result of replacement of the titanium atom in the Ti8C12metcar by 4dtransition metal ions (M = Y, Zr, Nb, ..., Ag) are established using the ab initioelectron density functional method in the discrete-variational scheme. The dependences of electronic structure, charge distributions, and chemical bonds in the Ti7MC12metcars on the cluster symmetry (Thor Td) and position of the 4datom in a molecular cage are discussed. The electronic states of 4datoms in molecular titanium carbide (Ti8C12metcar) are compared with those in crystal titanium carbide (cubic TiC phase with rock salt structure). The effect of doping of the Ti8C12metcar with 4datoms on its reactivity is studied.

Molecular surfaces from the promolecule: A comparison with Hartree–Fock ab initio electron density surfaces

A new molecular surface, the promolecule electron density isosurface arising from the superposition of spherical atomic electron density functions, is compared and contrasted with the Hartree–Fock ab initio electron density isosurface, the fused-sphere van der Waals (CPK) surface, and the smooth Connolly surface. From application to a number of small to medium-sized molecules, including several amino acids, the promolecule surface is shown to be very similar to the Hartree–Fock electron density isosurface but, in contrast, is trivial to calculate. The promolecule electron density surface constructed with a contracted hydrogen atom provides remarkably reliable, and consistent, estimates of ab initio surface areas (typically within 0.5%) and volumes (routinely overestimated by less than 4%). Differences between ab initio and promolecule surfaces are explored visually by mapping the deformation density on the promolecule surface. To highlight the usefulness of the promolecule surface, a promolecule 0.002 au isosurface of the small protein crambin is shown. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 933–942, 2000

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.

Anisotropy Effects in Methyl Chloride Ionization by Metastable Neon Atoms at Thermal Energies

Quasiclassical trajectory calculations have been carried out for the Penning ionization reaction Ne*(3P2,0) + CH3Cl → CH3Cl+(X, A, B) + Ne + e-. The calculations have been performed, within the rigid rotor approximation, for the translational energy range of 0.04−0.2 eV. The interaction potential of the colliding Ne*−CH3Cl system has been semiempirically estimated. The ionization probability has been determined, within the assumption that ionization occurs at the turning point, using a model which takes into account both geometry of the intermediate complex and ab initio electron density distribution of the orbitals involved on ionization. Calculations carried out for different rotational states (j = 0, 7, 14, 21, and 28, being j = 14 the most populated rotational level at 300 K) manifest the influence of CH3Cl rotation on partial (that is for specific X, A, B electronic states of CH3Cl+) and total ionization. Results averaged for the populated rotational levels at 300 K show that total ionization cross section decreases with translational energy. The branching ratio to X and A states also decreases, while that to the B state increases. These results fairly reproduce previous experimental results on the energy dependence total ionization cross section and branching ratios for the production of CH3Cl+, CH2Cl+, and CH3+ ions.

Molecular surfaces from the promolecule: A comparison with Hartree-Fockab initio electron density surfaces

A new molecular surface, the promolecule electron density isosurface arising from the superposition of spherical atomic electron density functions, is compared and contrasted with the Hartree–Fock ab initio electron density isosurface, the fused-sphere van der Waals (CPK) surface, and the smooth Connolly surface. From application to a number of small to medium-sized molecules, including several amino acids, the promolecule surface is shown to be very similar to the Hartree–Fock electron density isosurface but, in contrast, is trivial to calculate. The promolecule electron density surface constructed with a contracted hydrogen atom provides remarkably reliable, and consistent, estimates of ab initio surface areas (typically within 0.5%) and volumes (routinely overestimated by less than 4%). Differences between ab initio and promolecule surfaces are explored visually by mapping the deformation density on the promolecule surface. To highlight the usefulness of the promolecule surface, a promolecule 0.002 au isosurface of the small protein crambin is shown. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 933–942, 2000

A fuzzy-set approach to functional-group comparisons based on an asymmetric similarity measure

A new, fuzzy-set framework for molecular similarity analysis is proposed. Recent advances in the computation of ab initio quality fuzzy electron densities of molecular fragments, pharmacophoric moieties, and functional groups of both small and macromolecular systems have motivated the search for new approaches to the evaluation of molecular similarity. Fuzzy-set methods appear especially suitable for the task for two reasons: the inherent fuzziness of electron densities due to Heisenberg's quantum mechanical uncertainty relation, and the fuzzy range of possible local molecular conformations which may correlate with a given chemical or biochemical function. In this contribution, a new, asymmetric similarity measure is proposed for local molecular moieties, such as functional groups or pharmacophores, based on a fuzzy-set description of electron densities and a fuzzy-set adaptation of earlier scaling–nesting similarity measures. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 503–514, 1999

Influence of intermolecular interactions on multipole-refined electron densities

This work examines the effect of intermolecular interactions on molecular properties derived from simulated X-ray diffraction data. Model X-ray data are computed from a superposition of ab initio molecular electron densities in the crystal, as well as from periodic crystal Hartree-Fock electron densities, for the hydrogen-bonded systems ice VIII, formamide and urea, as well as the weakly bound acetylene. The effects of intermolecular interactions on the electron density are illustrated at both infinite and finite data resolution, and it is concluded that multipole models are capable of quantitative retrieval of the interaction density, despite the known shortcomings of the radial functions in the model. Multipole refinement reveals considerable enhancement of the molecular dipole moment for hydrogen-bonded crystals, and negligible change in molecular second moments. Electric field gradients at H nuclei are significantly reduced in magnitude upon hydrogen bonding, and this change is also faithfully represented by the rigid pseudoatom model.

Holographic electron density shape theorem and its role in drug design and toxicological risk assessment.

Each complete, boundaryless molecular electron density is fully determined by any nonzero volume piece of the electron density cloud. This inherent feature of molecules, called the "holographic" property of molecular electron densities, provides a strong foundation for the local, quantum chemical shape analysis of various functional groups, pharmacophores, and other local molecular moieties. A proof is presented for the relevant molecular shape theorem, the "holographic electron density shape theorem", and the role of this theorem in quantum chemical, quantitative shape-activity relations (QShAR) is discussed. The quantum chemical methods of molecular shape analysis can be extended to ab initio quality electron densities of macromolecules, such as proteins, as well as to local molecular moieties, such as functional groups or pharmacophores, based on the transferability and additivity of local, fuzzy density fragments and the associated local density matrixes within the framework of the ADMA (Adjustable Density Matrix Assembler) approach. In addition to new results on chemical bonding and the development of macromolecular force methods, the new methodologies are also applicable to QShAR studies in computer-aided drug discovery and in toxicological risk assessment.

One - determinantal pure state versus ensemble Kohn-Sham solutions in the case of strong electron correlation: CH 2 and C 2

The possibility that the Kohn-Sham (KS) solution for a noninteracting auxiliary electron system is not the conventional one-determinantal pure state but a few-determinantal ensemble has been investigated. The KS solutions (the exchange-correlation potential v xc and the orbitals) have not been approximated by local-density or density-gradient approximations but have been constructed from an accurate ab initio electron density. The lowest singlet states of the CH2 and C2 molecules have been selected for this investigation since for these cases the ground-state wave function Ψ is nondegenerate but has an essentially multideterminantal character (electron correlation is strong). For C2 the dependence of the type of KS solution on the bond distance R(C–C) has been studied at the QZ level. For the shortest distance considered, R(C–C)=1.8 a.u., a pure-state KS solution has been obtained. For the equilibrium distance R e(C–C)=2.348 a.u. and at larger distances ensemble solutions have been obtained with widely varying weights of the individual determinants, depending on the bond distance. For CH2 the dependence of the type of KS solution on the basis has been studied: calculation in the triple zeta (TZ) basis for the KS orbitals yields an ensemble solution, while the pure-state KS solution has been obtained in the quadruple zeta (QZ) basis. The form of the KS orbitals has been compared with that of the natural orbitals (NOs). It has been shown for the model example of the stretched H2 molecule as well as for CH2 and C2, that the KS orbitals of the pure state may be rather different from the corresponding NOs, while the occupied KS orbitals of the ensemble solution can be considered as plausible approximations to the corresponding NOs.

Learnings from exchange-correlation potentials

Exchange-correlation potentials V xc( r) can be obtained (within an additive constant) from high-quality ab initio electron densities of atoms and small molecules. These potentials show qualitative features not captured by popular density functionals, and highlight unappreciated aspects of electron densities and density functionals. While V xcs generally scale with ρ 1/3 except at very long or short range, the proportionality is more similar to that of hydrogenic systems than to that of the homogeneous electron gas. The Fermi–Amaldi long-range approximation works well into the valence region. The size and location of the large feature at the valence–core transition is system-dependent. This qualitative information can guide the search for improved density functionals.

The development of new exchange-correlation functionals

A procedure is presented for the possible systematic development of exchange-correlation functionals using ab initio electron densities and accurate total energies. For a training set of first row open- and closed-shell systems, densities are computed and are used to determine asymptotically vanishing exchange-correlation potentials. The new functional is then written as an expansion in products of the density and its gradient, and optimum expansion parameters are determined through a least squares fit involving both these potentials and accurate exchange-correlation energies. Unlike conventional functionals, the potential of the fitted functional approaches a non-zero value asymptotically, and this is achieved by introducing a self-consistently computed system-dependent shift into the fitting procedure. This shift represents the influence of the integer derivative discontinuity in the exact energy. The method has been used to determine a 21 term spin-polarized exchange-correlation functional using Brueckner Doubles or MP2 densities of 20 small systems. For those with open-shells the computed shifts are close to the hardness of the system, while for closed-shells they are considerably smaller than the hardness. These observations are consistent with theoretical requirements. A comparison of the new potential with conventional potentials highlights important differences in the inter-shell and asymptotic regions, while the values of the shifts and highest occupied self-consistent eigenvalues suggest improved asymptotic densities. The mean absolute errors in self-consistent total energies and optimized bond-lengths of systems in the training set are 0.003Eh and 0.01 Å, respectively. Comparable values are obtained for 12 first-row closed-shell systems outside the training set. Compared to conventional functionals, the new functional predicts a significantly improved classical barrier height for the hydrogen abstraction reaction H+H2→H2+H.

Exchange-correlation functionals from ab initio electron densities

We describe a procedure for developing new exchange-correlation functionals. For a training set of selected first-row molecules we compute Zhao, Morrison, Parr exchange-correlation potentials from ab initio Brueckner Doubles or MP2 electron densities, and use them to least-squares refine the functional derivatives of chosen exchange-correlation functional forms. The resulting potentials reproduce the characteristic shell structure in the Zhao, Morrison, Parr potentials, and yield Kohn-Sham orbitals with accurate asymptotic behaviour. For a set of 22 closed-shell first-row molecules we obtain optimised geometries which are comparable to those from the BLYP functional. Total energies are significantly in error unless terms are added to account for the derivative discontinuity in the exact exchange-correlation potential.

Differences between ab initio and density functional electron densities

We analyzed the energy contributions and the spatial distribution differences of several electron densities of atoms and small molecules. The results show the insensitivity of local spin density correlation functionals in respect to differences in the electron densities. On the other hand, significant changes in one-electron and two-electron energy contributions are observed, although both compensate each other. The projection of the differences between these electron densities, referred to as the Hartree-Fock density, shows a qualitative resemblance between multideterminantal and Kohn-Sham wavefunctions. Finally, a comparative analysis of the optimized conformational parameters obtained using several methods shows that the inclusion of the correlation energy in SCF or in post-SCF procedures gives similar results and that the exchange potential is more important than is the correlation potential to improve these conformational parameters. © 1997 John Wiley & Sons, Inc.

Molecular electric moments and electric field gradients from X-ray diffraction data: model studies

Model X-ray data sets, with and without the inclusion of experimental thermal motion parameters, have been computed via Fourier transformation of ab initio molecular electron densities for 12 different molecular crystals. These datasets were then analysed with three different multipole models of varying sophistication and, from the multipole functions, molecular dipole and second moments, as well as electric field gradients (EFG's), at each nuclear site were computed and compared with results obtained from the original ab initio wavefunctions. The results provide valuable insight into the reliability of these properties, extracted in the same way from experimental X-ray data. Not all molecular systems display identical trends, but a general pattern is discernible. Specifically, dipole moments are typically underestimated by a small but significant amount (~ 10–15%), the trace of the second moment tensor is well determined but overestimated by a few per cent and electric field gradients at protons are confirmed to be well within reach of a careful charge density analysis of X-ray diffraction data.