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International audience; We perform benchmark calculations of the Bethe Salpeter vertical excitation energies for the set of 28 molecules constituting the well-known Thiel's set, complemented by a series of small molecules representative of the dye chemistry field. We show that Bethe Salpeter calculations based on a molecular orbital energy spectrum obtained with non-self-consistent G(0)W(0) calculations starting from semilocal DFT functionals dramatically underestimate the transition energies. Starting from the popular PBEO hybrid functional significantly improves the results even though this leads to an average -0.59 eV redshift compared to reference calculations for Thiel's set. It is shown, however, that a simple self-consistent scheme at the GW level, with an update of the quasiparticle energies, not only leads to a much better agreement with reference values, but also significantly reduces the impact of the starting DFT functional. On average, the Bethe Salpeter scheme based on self-consistent GW calculations comes close to the best timedependent DFT calculations with the PBEO functional with a 0.98 correlation coefficient and a 0.18 (0.25) eV mean absolute deviation compared to TD-PBEO (theoretical best estimates) with a tendency to be red-shifted. We also observe that TD-DFT and the standard adiabatic Bethe Salpeter implementation may differ significantly for states implying a large multiple excitation character.

In der vorliegenden Arbeit wird die Entwicklung und Anwendung zweikomponentiger Coupled-Cluster-Methoden zur akkuraten Beschreibung von Spin-Bahn-Wechselwirkungen in elektronisch angeregten Zuständen beschrieben. Neben Nullfeldaufspaltungen und Phosphoreszenzlebensdauern von Molekülen in der Gasphase sind mit der im Rahmen dieser Arbeit entwickelten Methode 2c-PERI-CC2(CC) auch Lösungsmitteleinflüsse auf besagte Eigenschaften zugänglich.

Agregados de partículas cujas propriedades, em escala nanométrica, abrangem desde aquelas apresentadas pelos átomos ou moléculas individuais até aquelas apresentadas no limite do bulk são denominadas clusters. Esses compostos podem ser considerados como uma classe relativamente nova de materiais e são, atualmente, assunto frequente em pesquisas científicas. A hipersuperfície de energia potencial associada a clusters da liga sódio-potássio, gerada pela expressão empírica Gupta, é explorada via um algo ritmo genético modificado, aprimorado pela adição de dois novos operadores ao procedimento evolucionário padrão. A intenção desta abordagem clássica, para os clusters menores (até 10 átomos), é fornecer condições iniciais para métodos de estrutura eletrônica. Os mínimos gerados pelo potencial empírico são avaliados e corrigidos utilizando métodos ab initio de alto nível como CCSD(T), CR-CCSD(T)-L e MP2, e resultados de referência são obtidos para casos específicos. Tratam-se dos primeiros resultados apresentados para clusters nesta faixa de tamanho com a presente composição, podendo servir como referência para estudos ulteriores. A validade e escolha de funcionais e conjuntos de funções de base apropriados para cálculos DFT são exploradas usando os dados de referência obtidos, onde se observou que a abordagem DFT usual pode falhar na previsão de resultados qualitativos para sistemas específicos. De modo geral, o melhor acordo com os cálculos de referência foi obtido pela combinação def2-TZVPP/SVWN5, apesar de LANL2DZ/SVWN5 (com potencial nuclear efetivo) ter fornecido a melhor relação custo-benefício. A partir desta abordagem quãntica, pode-se inferir um limite inferior para aplicabilidade do potencial Gupta, e com isso a abordagem clássica se procedeu para clusters maiores, até a estrutura bem estabelecida de 55 átomos, calculando-se sempre os excessos de energia e a segunda diferença de energia. As ligas mais estáveis, comparadas às suas contrapartes homonucleares, apresentaram uma proporção de átomos de sódio na faixa de 30 a 40 %. A tendência experimental de segregação núcleo-superfície foi prevista com sucesso pela presente abordagem. Por fim, busca-se o acoplamento entre um eficiente algo ritmo genético, baseado em uma nova rotina para cruzamento, e a técnica de minimização BFGS implementada no GAMESS-US, de modo a prover uma metodologia eficiente capaz de gerar boas condições iniciais para uma avaliação subsequente mais rigorosa através de metodologias mais robustas. Particle aggregates which properties, at nanometric scale, embrace from those presented by its individual atoms or molecules to those presented at the bulk limit are referred to as clusters. These compounds may be considered as a relatively new type of material and are currently a frequent subject among scientific researches. The potential energy hypersurface associated with sodium-potassium alloy clusters, generated by the empirical Gupta expression, is explored via a modified genetic algorithm, enhanced by the addition of two different operators to the standard evolutionary procedure. Such classical approach is intended to provide, for the smaller clusters (up to 10 atoms), initial conditions for electronic structure methods. The minima of such empirical potential are assessed and corrected using high levei ab ínítío methods such as CCSD(T), CR-CCSD(T)-L and MP2, and benchmark results are obtained for specific cases. The results are the first calculations for such small alloy clusters and may serve as reference for further studies. The validity and choice of a proper functional and basis set for DFT calculations are then explored using the benchmark data, where it was found that the usual DFT approach may fail to provide the correct qualitative result for specific systems. The best general agreement to the benchmark calculations is achieved with def2-TZVPP basis set and SVWN5 functional, although the LANL2DZ basis set (with effective core potential) and SVWN5 functional provided the most cost-effective results. From this quantum approach, an insight is provided on the lower limits of applicability of the empirical Gupta potential, and thus the classical approach is proceeded to the larger clusters, up to the well-established 55 atoms structure, being their second-order energy difference and excess energies calculated. It is found that the most stable alloys (compared to the homonuclear counterparts) are achieved with the proportion of sodium atoms in the range of 30 to 40 %. The experimental propensity of core-shell segregation is successfully predicted by the current approach. Last but not least, the coupling between the efficient genetic algorithm, based on a new crossover routine, and the BFGS minimization technique implemented on GAMESS-US is pursued in order to provide an efficient methodology capable of generating good initial conditions for subsequent more rigorous evaluation through more robust techniques.

The point charge nuclear quadruple moment PCNQM model for the picture-change-error free determination of electric . field gradients EFG is extended to systems with low symmetry in order to determine the full EFG tensor. The carbon EFG tensor in 1-fluoro-1-chloroethane was chosen to test the accuracy of our model. It is shown that the EFG tensor components calculated by applying the PCNQM model at the Hartree-Fock and second-order Moller-Plesset level of theory are in excellent agreement with analytically derived expectation values. q 2000 Elsevier Science B.V. All rights reserved.

In this paper we present time-dependent density functional calculations on frequency-dependent first (β) and second (γ) hyperpolarizabilities for the set of small molecules, N2, CO2, CS2, C2H4, NH3, CO, HF, H2O, and CH4, and compare them to Hartree–Fock and correlated ab initio calculations, as well as to experimental results. Both the static hyperpolarizabilities and the frequency dispersion are studied. Three approximations to the exchange-correlation (xc) potential are used: the widely used Local Density Approximation (LDA), the Becke–Lee–Yang–Parr (BLYP) Generalized Gradient Approximation (GGA), as well as the asymptotically correct Van Leeuwen–Baerends (LB94) potential. For the functional derivatives of the xc potential the Adiabatic Local Density Approximation (ALDA) is used. We have attempted to estimate the intrinsic quality of these methods by using large basis sets, augmented with several diffuse functions, yielding good agreement with recent numerical static LDA results. Contrary to claims which have appeared in the literature on the basis of smaller studies involving basis sets of lesser quality, we find that the static LDA results for β and γ are severely overestimated, and do not improve upon the (underestimated) Hartree–Fock results. No improvement is provided by the BLYP potential which suffers from the same incorrect asymptotic behavior as the LDA potential. The results are however clearly improved upon by the LB94 potential, which leads to underestimated results, slightly improving the Hartree–Fock results. The LDA and BLYP potentials overestimate the frequency dependence as well, which is once again improved by the LB94 potential. Future improvements are expected to come from improved models for asymptotically correct exchange-correlation potentials. Apart from the LB94 potential used in this work, several other asymptotically correct potentials have recently been suggested in the literature and can also be expected to improve considerably upon the relatively poor LDA and GGA results, for both the static properties and their frequency dependence.

The efficient evaluation of tensor expressions involving sums over multiple indices is of significant importance to many fields of research, including quantum many-body physics, loop quantum gravity, and quantum chemistry. The computational cost of evaluating an expression may depend strongly upon the order in which the index sums are evaluated, and determination of the operation-minimising contraction sequence for a single tensor network (single term, in quantum chemistry) is known to be NP-hard. The current preferred solution is an exhaustive search, using either an iterative depth-first approach with pruning or dynamic programming and memoisation, but these approaches are impractical for many of the larger tensor network Ansaetze encountered in quantum many-body physics. We present a modified search algorithm with enhanced pruning which exhibits a performance increase of several orders of magnitude while still guaranteeing identification of an optimal operation-minimising contraction sequence for a single tensor network. A reference implementation for MATLAB, compatible with the ncon() and multienv() network contractors of arXiv:1402.0939 and arXiv:1310.8023 respectively, is supplied., Comment: 25 pages, 12 figs, 2 tables, includes reference implementation of algorithm, v2.01. Update corrects the display of contraction sequences involving single-tensor traces (i.e. where an index in the input appears twice on the same tensor)

We present a simple and non-empirical method to determine optimal scaling coefficients, within the (spin-component)-scaled MP2 approach, for calculating intermolecular potential energies of noncovalently-interacting systems. The method is based on an observed proportionality between (spin-component) MP2 and CCSD(T) energies for a wide range of intermolecular distances and allows to compute with high accuracy a large portion of the dissociation curve at the cost of a single CCSD(T) calculation. The accuracy of the present procedure is assessed for a series of noncovalently-interacting test systems: the obtained results reproduce CCSD(T) quality in all cases and definitely outperform conventional MP2, CCSD and SCS-MP2 results. The difficult case of the Beryllium dimer is also considered., 9 pages, 7 figures

By analysing the properties of the electron density in the structurally simple perhalogenated ethanes, X3C-CY3 (X, Y = F, Cl), a previously overlooked non-covalent attraction between halogens attached to opposite carbon atoms is found. Quantum chemical calculations extrapolated towards the full solution of the Schrödinger equation reveal the complex nature of the interaction. When at least one of the halogens is a chlorine, the strength of the interaction is comparable to that of hydrogen bonds. Further analysis shows that the bond character is quite different from standard non-covalent halogen bonds and hydrogen bonds; no bond critical points are found between the halogens, and the σ-holes of the halogens are not utilised for bonding. Thus, the nature of the intramolecular halogen⋯halogen bonding studied here appears to be of an unusually strong van der Waals type We are grateful to Dr Eduard Matito, Dr Pedro Salvador, and Dr Raphael Berger for enlightening discussions. CSC - the Finnish IT Centre for Science hosted part of the calculations. This work has been supported by the Ministerio de Ciencia e Innovacion (MICINN projects JCI-2009-05953, CTQ2011-25086/BQU), the Academy of Finland (project 136079), MICINN and the European Fund for Regional Development (FEDER grant UNGI08-4E-003), and the DIUE of the Generalitat de Catalunya (project 2009SGR528)

CNPq e FACEPE Este documento apresenta a Tese de doutorado do estudante Marcus Vinicius Pereira dos Santos ao Programa de P´os-Gradua¸c˜ao em Ciˆencia de Materiais da Universidade Federal de Pernambuco. Neste trabalho procurou-se avaliar propriedades eletrˆonicas, espectrosc ´opicas e catal´ıticas de trˆes tipos de materiais moleculares: fenestranos, alcaplanos e o 1,4-benzenodimetanol. Os fenestranos possuem uma subunidade espiroalcano e apresentam como caracter´ısticas energ´eticas principais: energias de ioniza¸c˜ao da mesma ordem de metais alcalinos terrosos tais como c´alcio (6,11 eV), magn´esio (7,64 eV) e ber´ılio (9,32 eV), cujos valores est˜ao intimamente relacionados com o menor valor do ˆangulo torsional envolvendo o carbono central e seus carbonos vizinhos ( ). Por sua vez, o valor deste ˆangulo torsional est´a associado aos tipos de an´eis, `a presen¸ca ou n˜ao das liga¸c˜oes duplas e a quantidade de liga¸c˜oes duplas por anel. Isto permite um controle muito sens´ıvel n˜ao s´o da energia de ioniza¸c˜ao, mas tamb´em da energia de tens˜ao do anel, o que ´e essencial para se propor, simultaneamente, compostos com car´ater doador de el´etrons e sinteticamente vi´aveis para aplica¸c˜ao em sistemas aceitador-ponte-doador (A-B-D) utilizados em ´optica n˜ao-linear (NLO). Contudo, os alcaplanos s˜ao os materiais moleculares mais indicados como doadores de el´etrons em sistemas A-B-D, uma vez que possuem energias de ioniza¸c˜ao menores que 5 eV, mesmo em compostos que n˜ao possuem o ´atomo de carbono central tetracoordenado completamente plano (ptC), e assim como os fenestranos, possuem um controle sens´ıvel das propriedades energ´eticas com rela¸c˜ao ao valor de . A presen¸ca de liga¸c˜oes duplas nos an´eis e de grupos laterais do tipo -CH2- permite um controle diferenciado dessas propriedades, inclusive a supress˜ao da dependˆencia da energia de ioniza¸c˜ao com a planaridade (valor de ), o que permite o relaxamento da estrutura sem perder o baixo valor da energia de ioniza¸c˜ao do material. Por´em, os alcaplanos normalmente possuem tens˜oes de anel e entalpias de forma¸c˜ao maiores que os fenestranos, o que explica a dificuldade de s´ıntese desses compostos. A aproxima¸c˜ao PICVib, procedimento in´edito para an´alise da frequˆencia de modos normais espec´ıficos, mostra-se como uma alternativa simples, geral, robusta e com excelente desempenho na previs˜ao de frequˆencias vibracionais, mesmo com baixas energias (100 cm−1). Com seu aux´ılio, ´e poss´ıvel transpor facilmente a barreira de utiliza¸c˜ao de m´etodos p´os-Hartree-Fock mais sofisticados, com fun¸c˜oes de base triplo zeta que incluem fun¸c˜oes difusas e de polariza¸c˜ao, em sistemas moleculares com cerca de 50 ´atomos. J´a sua vers˜ao de baixo custo, a PICVib-v, requer bastante cautela para uso, uma vez que depende fortemente do qu˜ao diferente ´e a geometria obtida como m´etodo low comparada vi RESUMO vii `aquela fornecida pelo m´etodo high. Existe algum alcaplano ptC est´avel? Ao contr´ario do que foi comentado e proposto na literatura, acreditamos que uma resposta definitiva n˜ao pode ser dada por metodologias baseadas no funcional da densidade ou at´e mesmo com a teoria de perturba¸c˜ao de segunda ordem, pois em v´arios casos estudados nesta tese esses m´etodos forneceram resultados discordantes e contradit´orios. Com teorias mais sofisticadas, como ´e o caso de “coupled-cluster”(CC) aliado ao PICVib (ou PICVib-v), constata-se que dentre os quatro compostos analisados contendo ptC, o dimetilespiroalcaplano proposto por Radom apresenta uma frequˆencia imagin´aria no valor de 371i cm−1 calculada com o m´etodo CCSD, contradizendo um dos principais resultados obtidos na literatura, al´em dos pr´oprios resultados obtidos neste trabalho com o m´etodo MP2 (com diferentes fun¸c˜oes de base). Os resultados CCSD mostram ainda que dois compostos com ptC apresentam frequˆencias reais, mas ambos apresentam instabilidade da fun¸c˜ao de onda. Assim, acreditamos que o tratamento empregado ´e inadequado. A nossa proposta de alcaplano com ptC ´e inst´avel, pois apresenta constante de for¸ca negativa. Assim, n˜ao resta nenhum composto proposto com ptC que seja est´avel. Acreditamos que por causa da estrutura eletrˆonica ex´otica e pouco usual destes compostos, o uso de m´etodos quˆanticos tradicionais podem levar `a conclus˜oes equivocadas acerca da estabilidade de alcaplanos com ptC. Entretanto, a problem´atica da estabilidade n˜ao afeta a proposta desta tese, pois excelentes grupos doadores de el´etrons podem ser obtidos com alcaplanos contendo carbono central tetracoordenado quase-plano (quase-ptC). Desse modo, utilizando esses grupos doadores em sistemas A-B-D, obtivemos valores de polarizabilidades (), primeira () e segunda () hiperpolarizabilidades compar´aveis aos maiores valores j´a relatados na literatura. Infelizmente, problemas na instabilidade da fun¸c˜ao de onda n˜ao permitem que esses c´alculos sejam realizados com fun¸c˜oes de base mais sofisticadas. Com rela¸c˜ao ao processo de cat´alise com o 1,4-benzenodimetanol (BDM), os mecanismos de rea¸c˜oes SN2 e E2 envolvendo o ´ıon acetato e o cloroetano s˜ao espontˆaneos, mas somente s˜ao catalisados pela intera¸c˜ao com o BDM no solvente dimetilsulf´oxido (DMSO), mostrando que os efeitos do solvente s˜ao essenciais para se observar a cat´alise dessa rea ¸c˜ao. Mesmo com a proposi¸c˜ao de novos caminhos reacionais SN2 e E2, essa tendˆencia se mant´em. A modifica¸c˜ao do BDM com a inclus˜ao de mais um grupo -CH2-OH n˜ao favorece a cat´alise desses mecanismos. Contudo, do ponto de vista termodinˆamico, os mecanismos de rea¸c˜oes SN2 s˜ao espontˆaneos n˜ao apenas em DMSO, mas tamb´em em fase g´as. O mesmo n˜ao ocorre para os diferentes mecanismos E2, em que a espontaneidade ocorre apenas em DMSO.

The linear optical absorption spectra in neutral boron cluster B$_{6}$ and cationic B$_{6}^{+}$ are calculated using a first principles correlated electron approach. The geometries of several low-lying isomers of these clusters were optimized at the coupled-cluster singles doubles (CCSD) level of theory. With these optimized ground-state geometries, excited states of different isomers were computed using the singles configuration-interaction (SCI) approach. The many body wavefunctions of various excited states have been analysed and the nature of optical excitation involved are found to be of collective, plasmonic type., Comment: 22 pages, 38 figures. An invited article submitted to European Physical Journal D. This work was presented in the International Symposium on Small Particles and Inorganic Clusters - XVI, held in Leuven, Belgium

Van der Waals heterodimers of p-difluorobenzene (DFB) with other molecules, prepared in a supersonic jet beam expansion, were studied by resonant two-photon ionization (R2PI) through their S(1)

We report a theoretical study on the optical properties of bithiophene and terthiophene N-succinimidyl esters, which have been functionalized with a methylsulfanyl group in the alpha or the beta positions. Time-dependent density functional theory (TD-DFT) and approximate coupled-cluster singles and doubles with the resolution of identity technique (RI-CC2) calculations have been performed in the ground and excited states. The RI-CC2 results for absorption and fluorescence energies are in better qualitative agreement with experiments, whereas TD-DFT does not correctly describe the higher energy part of the absorption spectra of beta-substituted bithiophenes, due to the presence of charge-transfer states. Systems functionalized at the alpha position show a large red-shift of the main absorption and fluorescence band and a larger Stokes-shift compared to the unsubstituted species. These effects are in most cases less pronounced for the beta-substituted structures. In particular, we found that the Stokes-shift of the alpha-substituted structures is larger than the one of the beta-substituted species due to a more planar orientation of the methylsulfanyl group with respect to the neighbouring thiophene in the excited state.

Quantum chemical calculations have been performed to investigate radical cation rearrangement, radical carbonylation, and homolytic substitution reactions of organic molecules. The rearrangement of the bicyclopropylidiene radical cation to the tetramethyleneethane radical cation is predicted to proceed with stepwise disrotatory opening of the two rings. Each ring opening is found to be combined with a striking pyramidalization of a carbon atom in the central bond. The isomerization of the norbornadiene radical cation to the cycloheptatriene radical cation (CHT.+), initialized by opening of a bridgehead–methylene bond, is investigated. The most favorable path involves concerted rearrangement to the norcaradiene radical cation followed by ring opening to CHT.+. The barrier of this channel is found to be significantly reduced upon substitution of the methylene group with C(CH3)2. Stepwise mechanisms are predicted to be favored over concerted isomerization for the McLafferty rearrangement of the radical cations of butanal and 3-fluorobutanal. The barrier for the concerted rearrangement is found to be lowered by 17.2 kcal/mol upon substitution, a result which is rationalized by the calculated dipole moments and atomic charges. Recent experiments showed that photoinitiated carbonylation of alkyl iodides with [11C]carbon monoxide may be significantly enhanced by using small amounts of ketones that have nπ* character of their excited triplet state. DFT calculations show the feasibility of an atom transfer type mechanism, proposed to explain these observations. Moreover, the computational results rationalize the observed differences in yield when using various alcohol solvents. Finally, following photolysis of methyliodide, recent electron spin resonance spectroscopy experiments demonstrated that the SH2 reaction •CD3 + SiD3CH3 → CD3SiD3 + •CH3 proceeds with high selectivity over the energetically more favorable D abstraction. The role of geometrical effects, especially the formation of prereactive complexes between methylsilane and methyliodide is studied, and a plausible explanation for the experimentally observed paradox is presented.

Theory Group, Department of PhysicalChemistry, Indian Association for the Cultivation of Science, Jadavpur, Calcutta-700 032 Department of Chemistry, Krishnanagar Government College, Krishnanagar An Orthogonally Spin-adapted Coupled-cluster Based Linear Response Theory for Electron Detachment and Attachment Processes

A comprehensive theoretical study on the electronic absorption spectra of a representative group of organic dyes (L0, D4, D5, C217, and JK2) employed in dye-sensitized solar cell devices is reported. A benchmark evaluation on different time-dependent density functional theory (TDDFT) approaches with respect to high-level correlated coupled cluster (CC) and multireference perturbation theory (MRPT) benchmark calculations is performed in the gas phase. The benchmark results indicate that TDDFT calculations using the hybrid MPW1K and the long-range correct CAM-B3LYP functionals represent a valuable tool of comparable accuracy to that of the much more computationally demanding ab initio methods. Thus, the problem of the comparison between the calculated excitation energies and the measured absorption maximum wavelengths has been addressed employing the MPW1K functional and including the solvation effects by a polarizable continuum model. The present results show that taking into account the chemical and physical phenomena occurring in solution (i.e., protonation/deprotonation of the carboxylic function and the explicit solute solvent interactions) is of crucial importance for a meaningful comparison between the calculated and the experimental absorption spectra. Our investigation paves the way to the reliable computational design and predictive screening of organic dye sensitizers, even before their synthesis, in analogy to what has been achieved for transition-metal complexes.

Metal cations often play an important role in shaping the three-dimensional structure of peptides. As an example, the model system AcPheAla5LysH+ is investigated in order to fully understand the forces that stabilize its helical structure. In particular, the question of whether the local fixation of the positive charge at the peptide's C-terminus is a prerequisite for forming helices is addressed by replacing the protonated lysine residue by alanine and a sodium cation. The combination of gas-phase cold-ion vibrational spectroscopy with molecular simulations based on density-functional theory (DFT) revealed that the charge localization at the C-terminus is imperative for helix formation in the gas phase as this stabilizes the structure through a cation-helix dipole interaction. For sodiated AcPheAla6, globular rather than helical structures were found caused by the strong cation-backbone and cation-pi interactions. Interestingly, the global minimum-energy structure from simulation is not present in the experiment where the system remains kinetically trapped in a solution-state structure. Thereby calculated energies and IR spectra that are sufficiently accurate relied on DFT with computationally costly hybrid functionals, while for the structure search low-computational-cost force field (FF) models are crucial. This inspired a study where the goodness of commonly applied levels of theory, i.e. FFs, semi-empirical methods, density-functional approximations, composite methods, and wavefunction-based methods are being evaluated with respect to benchmark-grade coupled-cluster calculations. Acetylhistidine - either bare or in presence of a zinc cation - thereby serves as a molecular benchmark system. Neither FFs nor semi-empirical methods are reliable enough for a description of these systems within "chemical accuracy" of 1 kcal/mol. Accurate energetic description within chemical accuracy is achieved for all systems using the meta-GGA SCAN or computationally more demanding hybrid functionals. The double-hybrid functional B3LYP+XYG3 is best resembling the benchmark method DLPNO-CCSD(T). Despite poor energetic performances of conventional FFs for peptides in the gas phase, their low computational costs still render them appealing tools for large-scale structure searches. Consequently, a machine learning approach is presented where the torsional parameters and (if desired) van der Waals parameters in the potential-energy function of a particular FF are adjusted by fitting it against DFT energies using regularized regression models like LASSO or Ridge regression. For the peptide AcAla2NMe, this resulted in a significant improvement when comparing to standard OPLS-AA parameters. For more challenging peptide-cation systems, e.g. AcAla2NMe + Na+, this approach does not give satisfying results, which is caused by the formulation of the potential energy of the FF itself: While derived empirical partial charges using Hirshfeld partitioning or the electrostatic potential (ESP) decrease the accuracy, part of the energetic discrepancy can be "compensated" due to the flexibility of the torsional contributions in terms of the energetic description.