Probing molecular conformations with electron momentum spectroscopy: the case of n-butane.

High-resolution (e,2e) measurements of the valence electronic structure and momentum-space electron density distributions of n-butane have been exhaustively reanalyzed in order to cope with the presence of two stable structures in the gas phase, namely the all-staggered and gauche conformers. The measurements are compared to a series of Boltzmann-weighted simulations based on the momentum-space form of Kohn-Sham (B3LYP) orbital densities, and to ionization spectra obtained from high-level [ADC(3)] one-particle Green's Function calculations. Indubitable improvements in the quality of the simulated (e,2e) ionization spectra and electron momentum profiles are seen when the contributions of the gauche form of n-butane are included. Both the one-electron binding energies and momentum distributions consistently image the distortions and topological changes that molecular orbitals undergo due to torsion of the carbon backbone, and thereby exhibit variations which can be traced experimentally. With regard to the intimate relation of (e,2e) cross sections with orbital densities, electron momentum spectroscopy can therefore be viewed as a very powerful, but up to now largely unexploited, conformational probe. The study also emphasizes the influence of thermal agitation in photoionization experiments of all kind.     

Exact Kohn-Sham versus Hartree-Fock in momentum space: Examples of two-fermion systems

The question of how density functional theory (DFT) compares with Hartree-Fock (HF) for the computation of momentum-space properties is addressed in relation to systems for which (near) exact Kohn-Sham (KS) and HF one-electron matrices are known. This makes it possible to objectively compare HF and exact KS and hence to assess the potential of DFT for momentum-space studies. The systems considered are the Moshinsky [Am. J. Phys. 36, 52 (1968)] atom, Hooke's atom, and light two-electron ions, for which expressions for correlated density matrices or momentum densities have been derived in closed form. The results obtained show that it is necessary to make a distinction between true and approximate DFTs.     

Core excitation in O3 localized to one of two symmetry-equivalent chemical bonds: molecular alignment through vibronic coupling

Core excitation from terminal oxygen OT in O3 is shown to be an excitation from a localized core orbital to a localized valence orbital. The valence orbital is localized to one of the two equivalent chemical bonds. We experimentally demonstrate this with the Auger-Doppler effect which is observable when O3 is core excited to the highly dissociative OT1s(-1)7a1 1 state. Auger electrons emitted from the atomic oxygen fragment carry information about the molecular orientation relative to the electromagnetic-field vector at the moment of excitation. The data together with analytical functions for the electron-peak profiles give clear evidence that the preferred molecular orientation for excitation only depends on the orientation of one bond, not on the total molecular orientation. The localization of the valence orbital "7a1" is caused by mixing of the valence orbital "5b2" through vibronic coupling of antisymmetric stretching mode with b2 symmetry. To the best of our knowledge, it is the first discussion of the localization of a core excitation of O3. This result explains the success of the widely used assumption of localized core excitation in adsorbates and large molecules.     

Exact non-additive kinetic potentials in realistic chemical systems

In methods based on frozen-density embedding theory or subsystem formulation of density functional theory, the non-additive kinetic potential (v(t) (nad)(r)) needs to be approximated. Since v(t) (nad)(r) is defined as a bifunctional, the common strategies rely on approximating v(t) (nad)[ρ(A),ρ(B)](r). In this work, the exact potentials (not bifunctionals) are constructed for chemically relevant pairs of electron densities (ρ(A) and ρ(B)) representing: dissociating molecules, two parts of a molecule linked by a covalent bond, or valence and core electrons. The method used is applicable only for particular case, where ρ(A) is a one-electron or spin-compensated two-electron density, for which the analytic relation between the density and potential exists. The sum ρ(A) + ρ(B) is, however, not limited to such restrictions. Kohn-Sham molecular densities are used for this purpose. The constructed potentials are analyzed to identify the properties which must be taken into account when constructing approximations to the corresponding bifunctional. It is comprehensively shown that the full von Weizsa?cker component is indispensable in order to approximate adequately the non-additive kinetic potential for such pairs of densities.     

Variational optimization of effective atom centered potentials for molecular properties

In plane wave based electronic structure calculations the interaction of core and valence electrons is usually represented by atomic effective core potentials. They are constructed in such a way that the shape of the atomic valence orbitals outside a certain core radius is reproduced correctly with respect to the corresponding all-electron calculations. Here we present a method which, in conjunction with density functional perturbation theory, allows to optimize effective core potentials in order to reproduce ground-state molecular properties from arbitrarily accurate reference calculations within standard density functional calculations. We demonstrate the wide range of possible applications in theoretical chemistry of such optimized effective core potentials (OECPs) by means of two examples. We first use OECPs to tackle the link atom problem in quantum mechanics/molecular mechanics (QM/MM) schemes proposing a fully automatized procedure for the design of link OECPs, which are designed in such a way that they minimally perturb the electronic structure in the QM region. In the second application, we use OECPs in two sample molecules (water and acetic acid) such as to reproduce electronic densities and derived molecular properties of hybrid (B3LYP) quality within general gradient approximated (BLYP) density functional calculations.     

Geometry of simple molecules: nonbonded interactions, not bonding orbitals, and primarily determine observed geometries.

The forces responsible for the observed geometries of the YX(3) (Y = N or P; X = H, F, or Cl) molecules were studied through ab initio computations at the HF-SCF/6-31G level. The calculated molecular orbitals were grouped as contributing primarily to (a) the covalent bonds, (b) the terminal atom nonbonding electrons (for X = F or Cl), and (c) the central atom nonbonding electrons. This grouping was accomplished through 3-D plotting and an atomic population analysis of the molecular orbitals. The molecules were then moved through a X-Y-X angular range from 90 degrees to 119 degrees, in four or five degree increments. Single-point calculations were done at each increment, so as to quantify the energy changes in the molecular orbital groups as a function of geometry. These calculations show that the nonbonding electrons are much more sensitive to geometry change than are the bonding orbitals, particularly in the trihalide compounds. The molecular orbitals representing the nonbonding electrons on the terminal atoms (both valence and core electrons) contribute to the spreading forces, as they favor a wider X-Y-X angle. The contracting forces, which favor a smaller X-Y-X angle, consist of the orbitals comprising the nonbonding electrons on the central atom (again, both valence and core electrons). The observed geometry is seen as the balance point between these two sets of forces. A simple interaction-distance model of spreading and contracting forces supports this hypothesis. Highly linear trends are obtained for both the nitrogen trihalides (R(2) = 0.981) and phosphorus trihalides (R(2) = 0.992) when the opposing forces are plotted against each other. These results suggest that a revision of the popular conceptual models (hybridization and VSEPR) of molecular geometry might be appropriate.     

The Influence of Two‐Dimensional Organization on Peptide Conformation

Molecular crowding plays a significant role in regulating molecular conformation in cellular environments. It is also likely to be important wherever high molecular densities are required, for example in surface‐phase studies, in which molecular densities generally far exceed those observed in solution. Using on‐surface circular dichroism (CD) spectroscopy, we have investigated the structure of a synthetic peptide assembled into a highly packed monolayer. The immobilized peptide undergoes a structural transition between α‐helical and random coil conformation upon changes in pH and ionic concentration, but critically the threshold for conformational change is altered dramatically by molecular crowding within the peptide monolayer. This study highlights the often overlooked role molecular crowding plays in regulating molecular structure and function in surface‐phase studies of biological molecules.     

XeCu covalent bonding in XeCuF and XeCuCl, characterized by fourier transform microwave spectroscopy supported by quantum chemical calculations

XeCu covalent bonding has been found in the complexes XeCuF and XeCuCl. The molecules were characterized by Fourier transform microwave spectroscopy, supported by MP2 ab initio calculations. The complexes were prepared by laser ablation of Cu in the presence of Xe and SF(6) or Cl(2) and stabilized in supersonic jets of Ar. The rotational constants and centrifugal distortion constants show the XeCu bonds to be short and rigid. The (131)Xe, Cu, and Cl nuclear quadrupole coupling constants indicate major redistributions of the electron densities of Xe and CuF or CuCl on complex formation which cannot be accounted for by simple electrostatic effects. The MP2 calculations corroborate the XeCu bond lengths and predict XeCu dissociation energies approximately 50-60 kJ mol(-)(1). The latter cannot be accounted for in terms of induction energies. The MP2 calculations also predict valence molecular orbitals with significant shared electron density between Xe and Cu and negative local energy densities at the XeCu bond critical points. All evidence is consistent with XeCu covalent bonding.     

Information distance analysis of molecular electron densities

The information‐theoretic basis of the Hirshfeld partitioning of the molecular electronic density into the densities of the “stockholder” atoms‐in‐molecules (AIM) is summarized. It is argued that these AIM densities minimize both the directed divergence (Kullback–Leibler) and divergence (Kullback) measures of the entropy deficiency between the AIM and their free atom analogs of the promolecule. The local equalization of the information distance densities of the Hirshfeld components, at the local value of the corresponding global entropy deficiency density, is outlined and several approximate relations are established between the alternative local measures of the missing information and the familiar function of a difference between the molecular and promolecule densities. Various global (of the system as a whole) and atomic measures of the entropy deficiency or the displacements relative to the isoelectronic promolecule, defined for densities or probabilities (shape functions) in both the local resolution and the Hirshfeld AIM discretization, are introduced and tested. This analysis is performed also for the valence electron (frozen‐core) approximation. Illustrative results for representative linear molecules, including diatomics, triatomics, and tetraatomics, are reported. They are interpreted as complementary characteristics of changes in the net AIM charge distribution and of the displacements in the information content of the electron distributions of bonded atoms. These numerical results confirm the overall similarity of the stockholder AIM to their free atom analogs and reflect the information displacements due to the AIM polarization and charge transfer in molecules. They also demonstrate the semiquantitative nature of the approximate relations established between the entropy deficiency densities and the related functions involving the density difference function. This development extends the range of interpretations based on the density difference diagrams into probing the associated information displacements in a molecule accompanying the formation of the chemical bonds. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

On the theoretical foundation of Walsh's rules of molecular geometry in terms of the Hellmann–Feynman theorem

A new interpretation of the ordinate in a Walsh diagram for a polyatomic molecule is suggested in terms of the Hellmann–Feynman theorem. This makes use of the fact that in a single-configurational MO wave function the total one-electron density is the sum of individual densities in the occupied orbitals. Walsh-type diagrams have been constructed for three different molecules, water, ammonia and hydrogen peroxide. In H₂O and NH₃ calculation of the force, and thus of the energy, in terms of the valence angle, is made on the assumption that the central (heavy) atom is kept fixed while each of the lighter atoms moves in a plane containing the principal symmetry axis and the relevant bond, in a totally symmetric fashion; for H₂O₂ the two oxygen atoms are kept fixed. The angular correlation diagrams obtained reproduce the general features of those obtained by plotting Hartree–Fock MO energies as functions of the valence angles. The conclusion emerges that the force formulation provides a satisfactory pictorial basis for understanding molecular geometry in terms of the balance between the electron–nucleus attractive forces resulting from the charge densities in the occupied MO'S , and the nuclear repulsive forces. However, in the absence of highly accurate charge distributions such an approach is unsuitable for the quantitative prediction of molecular quantities such as valence angles, force constants or energy barriers.     

Variable-energy photoelectron spectroscopy of substituted rhenium and manganese pentacarbonyls: molecular orbital assignments and the interatomic resonant effect

High-resolution variable-energy photoelectron spectra of M(CO)5X [M = Re, X = Re(CO)5, Cl, Br, and I; and M = Mn, X = Mn(CO)5 and Br] are reported. Tunable synchrotron radiation is used to distinguish the Re 5d and Br 4p orbital based peaks for the controversial Re(CO)5Br. Our results provide firm molecular orbital assignments for all of these molecules. The valence orbital in the ordering of ionization energies for M(CO)5Cl (M = Mn and Re) and Mn(CO)5Br is a 1(M-X) > e(X) > b2(M) > e(M); but for M(CO)5I (M = Mn and Re) and Re(CO)5Br the ordering is a1(M-X) > e(M) > b2(M) > e(X). The crossover of the HOMO in the Re molecules due to the change in the halogen electronegativities occurs at Re(CO)5Br. The metal np-->nd resonance is observed for all of these molecules. For molecules like M2(CO)10 (M = Re and Mn) and Mn(CO)5Br, the observation of this np-->nd resonance is useful in assigning the metal nd based orbitals in their valence level spectra. However, for molecules like Re(CO)5X (X = Br and Cl), a np-->nd type resonance is observed on bands arising from both Re 5d and halogen mp based orbitals. This new resonant effect on the ligand-based orbitals is shown to be mainly due to the interatomic resonant effect. The core and valence level chemical shifts of these compounds are treated using Jolly's approach to confirm the assignments for the valence level spectra of some of these molecules. The high-resolution inner valence and core level spectra of these compounds are reported. Broadening of Re 4f, Br 3d, and I 4d core level spectra is discussed. The Auger peaks are observed in the high-resolution, high-intensity Br 3d of Re(CO)5Br and I 4d of Re(CO)5I spectra.     

Resonance energies of large conjugated hydrocarbons by a statistical method

We developed a theoretical method for studying the aromatic stability of large molecules, molecules having a dozen and more fused benzene rings. Such molecules have so far often been outside the domain of theoretical studies. Combining the statistical approach and a particular graph theoretical analysis, it is possible to derive the expressions for molecular resonance energy for molecules of any size. The basis of the method is enumeration of conjugated circuits in random Kekulé valence structures. The method has been applied to evaluation of the resonance energies of conjugated hydrocarbons having about a dozen fused benzene rings. The approach consists of (1) construction of random Kekulé valence structures, (2) enumeration of conjugated circuits within the generated random valence structures, and (3) application of standard statistical analysis to a sufficiently large sample of structures. The construction of random valence forms is nontrivial, and some problems in generating random structures are discussed. The random Kekulé valence structures allow one not only to obtain the expression for molecular resonance energies (RE ) and numerical estimates for RE , but also they provide the basis for discussion of local molecular features, such as ring characterization and Pauling bond orders.     

Variationally optimized basis orbitals for biological molecules

Numerical atomic basis orbitals are variationally optimized for biological molecules such as proteins, polysaccharides, and deoxyribonucleic acid within a density functional theory. Based on a statistical treatment of results of a fully variational optimization of basis orbitals (full optimized basis orbitals) for 43 biological model molecules, simple sets of preoptimized basis orbitals classified under the local chemical environment (simple preoptimized basis orbitals) are constructed for hydrogen, carbon, nitrogen, oxygen, phosphorous, and sulfur atoms, each of which contains double valence plus polarization basis function. For a wide variety of molecules we show that the simple preoptimized orbitals provide well convergent energy and physical quantities comparable to those calculated by the full optimized orbitals, which demonstrates that the simple preoptimized orbitals possess substantial transferability for biological molecules.     

To What Extent are “Atoms in Molecules” Structures of Hydrocarbons Reproducible from the Promolecule Electron Densities?

The “atoms in molecules” structures of 225 unsubstituted hydrocarbons are derived from both the optimized and the promolecule electron densities. A comparative analysis demonstrates that the molecular graphs derived from these two types of electron densities at the same geometry are equivalent for almost 90 % of the hydrocarbons containing the same number and types of critical points. For the remaining 10 % of molecules, it is demonstrated that by inducing small perturbations, through the variation of the used basis set or slight changes in the used geometry, the emerging molecular graphs from both densities are also equivalent. Interestingly, the (3, ?1) critical point between two “non‐bonded” hydrogen atoms, which triggered “H?H bonding” controversy is also observed in the promolecule densities of certain hydrocarbons. Evidently, the topology of the electron density is not dictated by chemical bonds or strong interactions and deformations induced by the interactions of atoms in molecules have a quite marginal role, virtually null, in shaping the general traits of the topology of molecular electron densities of the studied hydrocarbons, whereas the key factor is the underlying atomic densities.     

Can QTAIM topological parameters be a measure of hydrogen bonding strength?

The block-localized wave function (BLW) method, which is the simplest variant of ab initio valence bond (VB) theory, together with the quantum theory of atoms in molecules (QTAIM) approach, have been used to probe the intramolecular hydrogen bonding interactions in a series of representative systems of resonance-assisted hydrogen bonds (RAHBs). RAHB is characteristic of the cooperativity between the π-electron delocalization and hydrogen bonding interactions and is identified in many biological systems. While the deactivation of the π resonance in these RAHB systems by the use of the BLW method is expected to considerably weaken the hydrogen bonding strength, little change on the topological properties of electron densities at hydrogen bond critical points (HBCPs) is observed. This raises a question of whether the QTAIM topological parameters can be an effective measure of hydrogen bond strength.     

The merits of the frozen-density embedding scheme to model solvatochromic shifts

We investigate the usefulness of a frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] for the calculation of solvatochromic shifts. The frozen-density calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: (i) calculations for much larger systems are feasible, since the time-consuming time-dependent density functional theory (TDDFT) part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. (ii) Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low charge-transfer excitations which are an artifact of the adiabatic local-density approximation or generalized gradient approximation exchange-correlation kernels currently used. The performance of the frozen-density embedding method is tested for the well-studied solvatochromic properties of the n-->pi(*) excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics (MD) and Car-Parrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozen-density embedding yields estimated solvent shifts in the range of 0.20-0.26 eV, in good agreement with experimental values of between 0.19 and 0.21 eV.     

Binary (e,2e) spectroscopic study of carbonyl sulfide and the momentum-space chemistry of CO2, CS2 and OCS

The valence-shell binding energy spectra (8–44 eV) and molecular orbital momentum distributions of OCS have been studied by non-coplanar symmetric binary (e,2e) spectroscopy. Existing theoretical binding energy spectra calculated using the many-body 2ph-TDA Green's function (GF) method and using the symmetry-adapted cluster (SAC) on method are compared with the experiment. Intense many-body structure in the measured and calculated binding energy spectra indicates the general breakdown of the independent particle ionization picture. Experimental momentum distributions are compared with those calculated using ab initio SCF wavefunctions of minimal basis set quality and of near Hartree—Fock quality. Excellent agreement between the experimental momentum distributions and those calculated by the near Hartree—Fock wavefunction is obtained for the three innermost valence orbitals: 8σ, 7σ and 6σ. The correct order of the close lying outer-valence 2π and 9σ orbitals is unambiguously identified from the shapes of the measured momentum distributions. Momentum and position contour density maps computed from theoretical wavefunctions of near Hartree—Fock quality are used to interpret the shapes and atomic characters of the observed momentum distributions. The momentum densities of the outermost-valence antibonding π orbitals and of the outermost-valence bonding σ orbitals of the linear triatomic group: CO₂, CS₂ and OCS are compared respectively with each other. The associated chemical trends are discussed within the existing framework of momentum-space chemical principles.     

Covalent bond orders and atomic anisotropies from iterated stockholder atoms

Iterated stockholder atoms are produced by dividing molecular electron densities into sums of overlapping, near-spherical atomic densities. It is shown that there exists a good correlation between the overlap of the densities of two atoms and the order of the covalent bond between the atoms (as given by simple valence rules). Furthermore, iterated stockholder atoms minimise a functional of the charge density, and this functional can be expressed as a sum of atomic contributions, which are related to the deviation of the atomic densities from spherical symmetry. Since iterated stockholder atoms can be obtained uniquely from the electron density, this work gives an orbital-free method for predicting bond orders and atomic anisotropies from experimental or theoretical charge density data.     

Study of molecular interactions between lipids and proteins using dynamic surface tension measurements: a review

Molecular interactions between small molecules and proteins, such as binding of lipids to proteins, are of fundamental importance in various biological processes. A recently-developed method based on dynamic surface tension measurement is efficient and versatile in detecting such molecular interactions: Axisymmetric Drop Shape Analysis (ADSA) provides a tool for measuring the surface tension (γ) response to surface area changes. Through the analysis of the γ response pattern, surface competitive adsorption between small organic molecules and protein molecules can be detected. Surface squeeze-out of small molecules by proteins can also be observed. Molecular binding of lipids to proteins manifests itself in a modification of the γ response which is not compatible with a simple superposition of the two individual patterns. The specific binding can be studied in terms of dose effects and specificity.