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## Über dieses Buch

Readers of this volume can take a tour around the research locations in Belgium which are active in theoretical and computational chemistry. Selected researchers from Belgium present research highlights of their work. Originally published in the journal Theoretical Chemistry Accounts, these outstanding contributions are now available in a hardcover print format. This volume will be of benefit in particular to those research groups and libraries that have chosen to have only electronic access to the journal. It also provides valuable content for all researchers in theoretical chemistry.

## Inhaltsverzeichnis

### Preface

Abstract
In Belgium, theoretical chemistry began more than 50 years ago, with an initial focus on quantum chemistry, which gradually developed into a general interest in different domains of theoretical chemistry. In the Florilège des Sciences en Belgique [1], Louis d’Or cites as founding members of quantum chemistry in Belgium: Jean–Claude Lorquet at the Université de Liège, Georges Leroy at the Universite catholique de Louvain (UCL), Georges Verhaegen at Université libre de Bruxelles (ULB), Luc Vanquickenborne at Katholieke Universiteit Leuven (KUL), and Piet van Leuven at Antwerpen (RUCA).
Benoît Champagne, Michael S. Deleuze, Frank De Proft, Tom Leyssens

### Is there an exact potential energy surface?

Abstract
Transition state theory was introduced in the 1930s to account for chemical reactions. Central to this theory is the idea of a potential energy surface (PES). It was assumed that quantum mechanical computation, when it became possible, would yield such surfaces, but for the time being they would have to be constructed empirically. The approach was very successful. Nowadays, quantum mechanical ab initio electronic structure calculations are possible and from their results PESs can be constructed. Such surfaces are now widely used in the explanation of chemical reactions in place of the traditional empirical ones. It is argued here that theoretical basis of such PESs is not quite as clear as is usually assumed and that, from a quantum mechanical perspective, certain puzzles remain.
Brian Sutcliffe

### Self-consistent methods constrained to a fixed number of particles in a given fragment and its relation to the electronegativity equalization method

Abstract
The variational procedure of the Hartree–Fock and Kohn–Sham methods can be modified by adding one or more constraints that fix the number of electrons in a given number of molecular fragments. The corresponding Euler–Lagrange equations lead to a modified Fock matrix, where the contribution from the constraints only depends on the overlap matrix, when using the Mulliken or Hirshfeld atoms-in-molecules method. For all compounds in the test set, the energy shows a quadratic dependence on the fixed charges. This behavior provides a procedure to obtain the atomic electronegativity and hardness parameters in the electronegativity equalization method.
Andrés Cedillo, Dimitri Van Neck, Patrick Bultinck

### Host–guest and guest–guest interactions between xylene isomers confined in the MIL-47(V) pore system

Abstract
The porous MIL-47 material shows a selective adsorption behavior for para-, ortho-, and meta-isomers of xylenes, making the material a serious candidate for separation applications. The origin of the selectivity lies in the differences in interactions (energetic) and confining (entropic). This paper investigates the xylene–framework interactions and the xylene–xylene interactions with quantum mechanical calculations, using a dispersion-corrected density functional and periodic boundary conditions to describe the crystal. First, the strength and geometrical characteristics of the optimal xylene–xylene interactions are quantified by studying the pure and mixed pairs in gas phase. An extended set of initial structures is created and optimized to sample as many relative orientations and distances as possible. Next, the pairs are brought in the pores of MIL-47. The interaction with the terephthalic linkers and other xylenes increases the stacking energy in gas phase (-31.7 kJ/mol per pair) by roughly a factor four in the fully loaded state (-58.3 kJ/mol per xylene). Our decomposition of the adsorption energy shows various trends in the contributing xylene–xylene interactions. The absence of a significant difference in energetics between the isomers indicates that entropic effects must be mainly responsible for the separation behavior.
An Ghysels, Matthias Vandichel, Toon Verstraelen, Monique A. van der Veen, Dirk E. De Vos, Michel Waroquier, Veronique Van Speybroeck

### Laser control in open quantum systems: preliminary analysis toward the Cope rearrangement control in methyl-cyclopentadienylcarboxylate dimer

Abstract
We present a preliminary simulation toward the control of theCope rearrangement of themost stable isomer of methyl-cyclopentadienylcarboxylate dimer. An experimental investigation of the dimerization of methyl-cyclopentadienylcarboxylate has been carried out. It shows that the most stable isomer of the dimer, the Thiele’s ester, is the major product of the dimerization. The simulation takes it as the initial state for the further control of the Cope reaction. The aim of the simulation is to examine the possibility of laser control to form the target product, not detected during the dimerization. The relevant stationary states have been characterized at the DFT B3LYP level, particularly the Cope transition state in which the dimer is connected only by a single bond r1. A minimum energy potential surface has been computed in a two-dimensional subspace of two bounds r2 and r3 which achieve the dimerization and have a very high weight in the reaction path from the Cope TS to the two adducts. Quantum wave packet optimal control simulation has been studied in a one-dimensionalmodel using an active coordinate r_= r3 - r2 which nearly corresponds to the reaction path. The stability of the optimal field against dissipation is examined by a non-Markovian master equation approach, which is perturbative in the system-bath coupling but without limitation on the strength of the field.
G. Dive, R. Robiette, A. Chenel, M. Ndong, C. Meier, M. Desouter-Lecomte

### Ruthenocene and cyclopentadienyl pyrrolyl ruthenium as precursors for ruthenium atomic layer deposition: a comparative study of dissociation enthalpies

Abstract
RuCp2 (ruthenocene) and RuCpPy (cyclopentadienyl pyrrolyl ruthenium) complexes are used in ruthenium (Ru) atomic layer deposition (ALD) but exhibit a markedly different reactivity with respect to the substrate and co-reactant. In search of an explanation, we report here the results of a comparative study of the heterolytic and homolytic dissociation enthalpy of these two ruthenium complexes, making use of either density functional theory (DFT) or multiconfigurational perturbation theory (CASPT2). While both methods predict distinctly different absolute dissociation enthalpies, they agree on the relative values between both molecules. A reduced heterolytic dissociation enthalpy is obtained for RuCpPy compared to RuCp2, although the difference obtained from CASPT2 (19.9 kcal/mol) is slightly larger than the one obtained with any of the DFT functionals (around 17 kcal/mol). Both methods also agree on the more pronounced stability of the Cp- ligand in RuCpPy than in RuCp2 (by around 9 kcal/ mol with DFT and by 6 kcal/mol with CASPT2).
Quan Manh Phung, Steven Vancoillie, Annelies Delabie, Geoffrey Pourtois, Kristine Pierloot

### The Boron conundrum: the case of cationic clusters $${\rm{B}}^{+}_{n}$$ with n = 2–20

Abstract
We investigate the molecular and electronic structure and thermochemical properties of the cationic boron clusters Bn + with n = 2–20, using both MO and DFT methods. Several functionals are used along with the MP2, G3, G3B3, G4, and CCSD(T)/CBS methods. The latter is the high accuracy reference. While the TPSS, TPSSh, PW91, PB86, and PBE functionals show results comparable to high-accuracy MO methods, both BLYP and B3LYP functionals are not accurate enough for three-dimensional (3D) structures. A negligible difference is observed between the B3LYP, MP2, and CCSD(T) geometries. A transition between 2D and 3D structures occurs for this series at the B16+–B19 + sizes. While smaller clusters Bn + with n ≤ 15 are planar or quasi-planar, a structural competition takes place in the intermediate sizes of B+16–19 . The B20 ? cation has a 3D tubular shape. The standard heats of formation are determined and used to evaluate the cluster stability. The average binding energy tends to increase with increasing size toward a limit. All closed-shell species Bn+ has an aromatic character, but an enhanced stability is found for B5 + and B13 + whose aromaticity and electron delocalization are analyzed using the LOL technique.
Truong Ba Tai, Nguyen Minh Tam, Minh Tho Nguyen

### Quantum chemical study of self-doping PPV oligomers: spin distribution of the radical forms

Abstract
A quantum chemical study was performed on ten different self-doping PPV oligomers. The geometry and the different weak intramolecular interactions were studied. The atomic spin populations were calculated using the FOHI method and related to the calculated EPR parameters. The effects of the removal of methoxy groups, the introduction of nitrogen atoms, and the relocation of the self-doping sidechain on the geometry, the spin distribution, and the EPR parameters have been described.
D. Geldof, A. Krishtal, F. Blockhuys, C. Van Alsenoy

### Electron momentum spectroscopy of metal carbonyls: a reinvestigation of the role of nuclear dynamics

Abstract
The main purpose of this work is to reinvestigate the influence of nuclear dynamics in the electronic ground state of group 6 metal hexacarbonyl compounds [W(CO)6, Cr(CO)6, Mo(CO)6] on electron momentum density profiles obtained from experimental orbital reconstructions employing Electron Momentum Spectroscopy. We call into question the view (Liu et al. in Chem Phys Lett 497:229, 2010) that thermally induced nuclear displacements associated with the first three triply degenerate 1T2g, 1T1u, and 1T2u vibrational eigenmodes can be large enough at or near room temperature (298–310 K) to explain on their own the unexpectedly large electron densities inferred for the frontier orbitals of these compounds at low momenta. In this purpose, we resort to an analysis of populations over these three vibrational eigenmodes, according to a description of vibrational excitations employing Maxwell– Boltzmann statistical thermodynamics. Comparison is made with Born–Oppenheimer Molecular Dynamical (BOMD) simulations over the potential energy surface associated with the electronic ground state. The role of nuclear dynamics in the final ionized state, in the form of Jahn–Teller distortions, is also tentatively investigated.
Balázs Hajgató, Filippo Morini, Michael S. Deleuze

Abstract
An electrophilicity scale for radicals in solution is reported using the electrophilicity index, an important quantity in conceptual density functional theory. Five different solvents were chosen, for which the static dielectric constant covers the entire range of nonpolar to polar solvents: n-hexane (er = 1.8819), dichloromethane (er = 8.9300), 2-propanol (er = 19.2640), acetonitrile (er = 35.6880) and water (er = 78.3553). The calculations in solution were carried out within the polarizable continuum model through the Integral Equation Formalism (IEFPCM) approach. For water, also conductor-like screening model (COSMO) calculations are reported. The electronic chemical potential remains almost constant when going from gas phase to solution. However, large decreases in chemical hardness can be observed, resulting in more electrophilic radicals compared to the gas phase, and even influencing the overall order of the previously established gas-phase scale. Both solvation models (COSMO and IEF-PCM) lead to essentially the same results.
Freija De Vleeschouwer, Paul Geerlings, Frank De Proft

### S5 graphs as model systems for icosahedral Jahn–Teller problems

Abstract
The degeneracy of the eigenvalues of the adjacency matrix of graphs may be broken by non-uniform changes of the edge weights. This symmetry breaking is the graph-theoretical equivalent of the molecular Jahn–Teller effect (Ceulemans et al. in Proc Roy Soc 468:971–989, 2012). It is investigated for three representative graphs, which all have the symmetric group on 5 elements, S5, as automorphism group: the complete graph K5, with 5 nodes, the Petersen graph, with 10 nodes, and an extended K5 graph with 20 nodes. The spectra of these graphs contain fourfold, fivefold, and sixfold degenerate manifolds, respectively, and provide model systems for the study of the Jahn–Teller effect in icosahedral molecules. The S5 symmetries of the distortion modes of the quintuplet in the Petersen graph yield a resolution of the product multiplicity in the corresponding H⊗(g +2h) icosahedral Jahn–Teller problem. In the extended Petersen graph with 20 nodes, a selection rule prevents the Jahn–Teller splitting of the sextuplet into two conjugate icosahedral triplets.
A. Ceulemans, E. Lijnen, P. W. Fowler, R. B. Mallion, T. Pisanski

### Mechanism of ketone hydrosilylation using NHC–Cu(I) catalysts: a computational study

Abstract
The plausibility of the catalytic cycle suggested for the hydrosilylation of ketones by (NHC) copper( I) hydrides has been investigated by a theoretical DFT study. Model systems yield the necessary insight into the intrinsic reactivity of the system. Computations show the activation of the copper fluoride pre-catalyst, as well as both steps of the catalytic cycle to involve a 4-center metathesis transition state as suggested in the literature. These results show the reaction to be favored by the formation of van der Waals complexes resembling the transition states. Stabilizing electrostatic interactions between those atoms involved in the bond-breaking and bondforming processes induces the formation of these latter. Both steps of the actual catalytic cycle show a free energy barrier of about 14.5 kcal/mol for the largest NHC ligands, with respect to the isolated reactants, hereby confirming the plausibility of the suggested cycle. The large overall exothermicity of the catalytic cycle of about 35 kcal/mol is in agreement with experimental observations.
Thomas Vergote, Thomas Gathy, Fady Nahra, Olivier Riant, Daniel Peeters, Tom Leyssens

### From atoms to biomolecules: a fruitful perspective

Abstract
We present a summary of the research activities of the “Quantum Chemistry and Atomic Physics” theoretical group of the “Chimie Quantique et Photophysique” Laboratory at Université Libre de Bruxelles. We emphasize the links between the three orientations of the group: theoretical atomic spectroscopy, structure, and molecular dynamics and list the perspectives of our collaboration.
E. Cauët, T. Carette, C. Lauzin, J. G. Li, J. Loreau, M. Delsaut, C. Nazé, S. Verdebout, S. Vranckx, M. Godefroid, J. Liévin, N. Vaeck

### Stabilization of merocyanine by protonation, charge, and external electric fields and effects on the isomerization of spiropyran: a computational study

Abstract
Protonation, charging, and field effects on the thermal isomerization of a nitrospiropyran (SP) modified by a thiolated etheroxide chain into merocyanine (MC) are computationally studied at the DFT level. The ring opening leads to cis-MC conformers that then isomerize to the more stable trans forms. While the closed neutral spiropyran is more stable than the conjugated open forms, the merocyanine conformers are significantly stabilized by protonation, electron attachment, and ionization. For protonation on the pyran oxygen atom and electron attachment, the MC conformers are more stable than SP, and unlike for the neutral species, the ring opening is spontaneous at room temperature. Moreover, for the pyran oxygen-protonated form, the ring opening to the cis-merocyanine becomes barrierless. On the other hand, barriers comparable to the neutral remain along the thermal pathway to the cis-merocyanine conformer for ionization or electron attachment, and the barrier for isomerization is significantly higher for the N-protonated SP form. External field effects on the neutral reaction path show that ring opening to the cismerocyanine is favored when the field reduces the electron density on the pyran part, as also induced by the local field due to O protonation.
Renuka Ganesan, F. Remacle

### Ewald-type formulas for Gaussian-basis studies of one-dimensionally periodic systems

Abstract
The history of computations at Namur and elsewhere on the electronic structures of stereoregular polymers is briefly reviewed to place the work reported here in the context of related efforts. Our earlier publications described methods for the formal inclusion of Ewald-type convergence acceleration in band-structure computations based on Gaussian-type orbitals, and that work is here extended to include a discussion of the calculation of total energies. It is noted that the continuous nature of the electronic density leads to different functional forms than are encountered for point-charge lattice sums. Examples are provided to document the correctness and convergence properties of the formulation.
Joseph G. Fripiat, Frank E. Harris

### Smoothed Gaussian molecular fields: an evaluation of molecular alignment problems

Abstract
Several smoothed Gaussian-based descriptors used in a molecular superposition algorithm are presented. One descriptor, as detailed in a previous work (Leherte in J Comput Chem 27:1800–1816, 2006), is the full electron density approximated through the promolecular atomic shell approximation (PASA) (Amat and Carbó-Dorca in J Chem Inf Comput Sci 40:1188–1198, 2000). Herein, we additionally present a new descriptor, that is, the charge density of a molecule calculated via the Poisson equation. The Coulomb potential as approximated by Good et al. (J Chem Inf Comput Sci 32:188–191, 1992) and atombased functions such as hydrogen bond donor or acceptor properties, lipophilicity as detailed in the work of Totrov (Chem Biol Drug Des 71:15–27, 2008) were also considered. A Monte Carlo/Simulated Annealing superposition method is applied to a set of six families of drug molecules, that is, elastase inhibitors, ligands of endothiapepsins, trypsins, thermolysins, p38 MAP kinases, and rhinovirus, all of them already reported in the literature, for discussing superposition problems. The results show that the descriptor selection can be guided by the nature of the interactions expected to occur between the drug molecules and their receptor. They also emphasize the particular efficiency of the PASA descriptor for molecules characterized by significant shape properties.
Laurence Leherte, Daniel P. Vercauteren

### Ab initio quantum chemical and ReaxFF-based study of the intramolecular iminium–enamine conversion in a proline-catalyzed reaction

Abstract
Among all strategies used by organic chemists to control the stereoselectivity of reactions, organocatalysis, which consists in using the chirality of a small organic molecule, is an increasingly popular method. The prolinecatalyzed aldol reaction was one of the first reported cases that demonstrated the power of organocatalysis in the field of asymmetric synthesis. Previous theoretical contributions focused on the reaction mechanism using quantum mechanics (QM) methods. We here present a theoretical study about one specific step of the proline-catalyzed aldol reaction, namely, the conversion of the iminium intermediate into the corresponding enamine. It consists of an intramolecular rearrangement that involves the transfer of a hydrogen atom. First, we investigate this transfer using modern QM models, that is, density functional theory calculations with the M06-2X functional. On the basis of these QM results, we then assess the performance of a reactive force field, ReaxFF, used in combination with molecular dynamics simulations in order to provide a complementary light on this reaction.
Pierre O. Hubin, Denis Jacquemin, Laurence Leherte, Jean-Marie André, Adri C. T. van Duin, Daniel P. Vercauteren

### Density functional theory for the description of charge-transfer processes at TTF/TCNQ interfaces

Abstract
In the field of organic electronics, a central issue is to assess how the frontier electronic levels of two adjacent organic layers align with respect to one another at the interface. This alignment can be driven by the presence of a partial charge transfer and the formation of an interface dipole; it plays a key role for instance in determining the rates of exciton dissociation or exciton formation in organic solar cells or light-emitting diodes, respectively. Reliably modeling the processes taking place at these interfaces remains a challenge for the computational chemistry community. Here, we review our recent theoretical work on the influence of the choice of density functional theory (DFT) methodology on the description of the charge-transfer character in the ground state of TTF/ TCNQ model complexes and interfaces. Starting with the electronic properties of the isolated TTF and TCNQ molecules and then considering the charge transfer and resulting interface dipole in TTF/TCNQ donor–acceptor stacks and bilayers, we examine the impact of the choice of DFT functional in describing the interfacial electronic structure. Finally, we employ computations based on periodic boundary conditions to highlight the impact of depolarization effects on the interfacial dipole moment.
Tanguy Van Regemorter, Maxime Guillaume, Gjergji Sini, John S. Sears, Victor Geskin, Jean-Luc Brédas, David Beljonne, Jérôme Cornil

### Implementation in the Pyvib2 program of the localized mode method and application to a helicene

Abstract
In this paper, after reviewing key elements for simulating and interpreting IR, Raman, VCD, and ROA spectra, as well as after describing the localized mode procedure, we present a graphical user interface to carry out the normal mode localizations and we illustrate its application on the ROA spectra of the [19]helicene molecule. The overall procedure consists of four steps, and therefore, a specific interface has been designed for each of them. The first and most important part of the procedure is the selection of the mode ensemble under which the localization procedure is performed. Then, during our stepby- step guided tour of the localized mode procedure in Pyvib2, we highlight the importance of the ordering of the localized modes and the importance to set correctly the phase factor between the localized modes. Finally, the vibrational coupling matrix ($$\boldsymbol{\tilde{\Omega}}$$ ), the intensity coupling matrix (Ĩ), and the unitary transformation matrix (U) can be analyzed from their representation in the different panels. The ROA spectrum of the [19]helicene molecule is dominated by the positive peaks associated with two normal modes. From the localized mode procedure, we have identified the atomic displacements of these modes as a few-node combination of localized modes characterized by atomic displacements that look like the motion of a “claw”.
Vincent Liégeois, Benoît Champagne

### Time-dependent density functional theory study of charge transfer in collisions

Abstract
We study the charge transfer between colliding ions, atoms, or molecules, within time-dependent density functional theory. Two particular cases are presented, the collision between a proton and a Helium atom, and between a gold atom and a butane molecule. In the first case, proton kinetic energies between 16 keV and 1.2 MeV are considered, with impact parameters between 0.31 and 1.9 Å. The partial transfer of charge is monitored with time. The total cross-section is obtained as a function of the proton kinetic energy. In the second case, we analyze one trajectory and discuss spin-dependent charge transfer between the different fragments.
Guillermo Avendaño-Franco, Bernard Piraux, Myrta Grüning, Xavier Gonze

### A simple DFT-based diagnostic for nondynamical correlation

Abstract
We propose a simple DFT-based diagnostic for nondynamical correlation effects, namely Aλ = (1 - TAE[XλC]/TAE[XC])/λ where TAE stands for the molecular total atomization energy, XC is a pure-DFT exchange-correlation functional, and XλC represents the corresponding hybrid with 100λ % Hartree–Fock-type exchange. The diagnostic is a good predictor for sensitivity of energetics to the level of theory, unlike most wavefunction- based diagnostics. For GGA functionals, Aλ values approaching unity indicate severe nondynamical correlation, while values between 0 and about 0.1 indicate systems where correlation is predominantly dynamical in character (or entirely absent). The diagnostic is only weakly sensitive to the basis set (beyond polarized valence double zeta) and can easily be applied to problems beyond the practical reach of wavefunction ab initio methods required for other diagnostics. We also propose a simple measure for the importance of dynamic correlation..
Uma R. Fogueri, Sebastian Kozuch, Amir Karton, Jan M. L. Martin

### Electronic structure analysis of small gold clusters Au m (m ≤ 16) by density functional theory

Abstract
Small gold clusters Au m (m ≤ 16) were analyzed step by step using the density functional theory at B3LYP level with a Lanl2DZ pseudopotential to understand the rules governing the structures obtained for the most stable clusters. After a characterization by means of the NBO population analysis and spin densities, the particular electronic structure of such species was confronted to their structural parameters and stability. It appears that the most stable structures can be described in an original way through resonance structures resulting from an analysis of Aum clusters into dimeric Au2 subunits. These are arranged so as to promote: 1. A good overlap between bonding σ and anti-bonding σ* areas belonging to different Au2 units. 2. A cyclic flow of electrons over the whole cluster. This model uses relatively simple chemical concepts in order to justify most of the structures already found in the literature as well as to establish a new approach explaining the structural transition from two- to threedimensional configurations.
Giuseppe Zanti, Daniel Peeters

### Combining molecular dynamics with Monte Carlo simulations: implementations and applications

Abstract
In this contribution, we present an overview of the various techniques for combining atomistic molecular dynamics with Monte Carlo simulations, mainly in the context of condensed matter systems, as well as a brief summary of the main accelerated dynamics techniques. Special attention is given to the force bias Monte Carlo technique and its combination with molecular dynamics, in view of promising recent developments, including a definable timescale. Various examples of the application of combined molecular dynamics / Monte Carlo simulations are given, in order to demonstrate the enhanced simulation efficiency with respect to either pure molecular dynamics or Monte Carlo.
Erik C. Neyts, Annemie Bogaerts
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