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The microwave spectrum of 2-methylthiophene was recorded in a frequency range from 2 to 26.5 GHz using a molecular-jet Fourier transform microwave spectrometer with a Fabry–Pérot type resonator chamber and coaxial arrangement of the resonator and the molecular beam. Measuring and assigning spectra of the 34S and 13C isotopologues allowed the determination of the semiexperimental equilibrium structure (reSE). Comparing the structure to that of thiophene revealed a decrease in the ∠(S−C2−C3) angle from 111.595(6)° to 111.37(1)° by addition of the methyl group to the C(2) position, as well as an increase in the S−C2 bond length from 1.7102(1) Å to 1.7219(2) Å. A–E splittings from internal rotation of the methyl group were observed, and the V3 potential in the vibrational ground state was determined to be 197.7324(18) cm−1. The V3 value and the rotational constants A, B, C were calculated with a large number of different methods and basis sets for benchmarking purposes by comparing them to the fitted parameters. The V3 value was also compared to those of other thiophene and furan derivatives to gain a better understanding of the steric and electrostatic effects in these classes of compounds.

International audience; For 2-acetylfuran, quantum chemistry predicted and proton magnetic resonance study reported two conformers, anti and syn, differing in the position of the carbonyl group with respect to the O1–C2 bond of the furan ring. The microwave spectrum of the title molecule was recorded in the frequency range from 2 to 26.5 GHz using a molecular jet Fourier transform microwave spectrometer, confirming the presence of both conformers. Spectroscopic parameters such as the rotational and centrifugal distortion constants could be determined with high precision. The spectra of all 13C- and 18O-isotopologues of the energetically more favorable anti-conformer could be assigned, allowing the experimental determination of bond lengths and bond angles from the heavy atom substitution rs and the semi-experimental equilibrium reSE structures. Splittings arising from the internal rotation of the acetyl methyl group could be resolved for both conformers as well as for all assigned isotopologues, from which the barrier to methyl internal rotation was determined. The torsional barrier is largely invariant at around 319 cm–1 in the parent species of anti-2-acetylfuran and its isotopologues, showing that though isotopic substitution greatly influences the rotational properties of the molecule and causes a different microwave spectrum, its effect on the methyl torsion is negligible. On the other hand, conformational effects play a decisive role, as the torsional barrier of 239.780(13) cm–1 found for syn-2-acetylfuran differs significantly from the value for anti-2-acetylfuran. The results are compared and discussed with other methyl-substituted furan derivatives and acetyl group containing ketones for a better understanding of different effects influencing molecular geometry parameters and methyl internal rotations.

Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures. Here, we outline a first principles approach to obtain these orders and contributions for arbitrary wave functions in a manner that is both, related to the quantum theory of atoms in molecules and consistent with valence bond theory insight: the Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|2. Doing so, we introduce a valence bond weight definition that does not collapse in the basis set limit.

International audience; The microwave spectra of thiophene and 2-acetylthiophene were recorded in the frequency range from 2 to 40 GHz using two molecular jet Fourier transform microwave spectrometers. For 2-acetylthiophene, two conformers with a syn and an anti orientation of the S1–C2 and C6=O bonds (with respect to the C2–C6 bond) were identified, and the syn-conformer was more stable. The spectra of the 34S- and 13C-isotopologues of syn-2-acetylthiophene were also assigned, and the semiexperimental equilibrium structure could be determined. Compared to thiophene, at the substitution position, the S1–C2 and C2=C3 bond lengths both increase by about 0.007 Å, and the bond angle S1–C2=C3 decreases by 0.06°, noticeably larger than the experimental uncertainties. A–E torsional splittings were observed due to internal rotation of the methyl group hindered by a barrier height of 330.187(35) and 295.957(17) cm−1 for the syn-conformer and the anti-conformer, respectively. Geometry and internal rotation parameters are compared with those of related thiophene derivatives, as well as those of furan and 2-acetylthiophene to gain a better understanding of structure determination in the presence of methyl internal rotation.

Chemists explaining a molecule’s stability and reactivity often refer to the concepts of delocalization, resonance, and aromaticity. Resonance is commonly discussed within valence bond theory as the stabilizing effect of mixing different Lewis structures. Yet, most computational chemists work with delocalized molecular orbitals, which are also usually employed to explain the concept of aromaticity, a ring delocalization in cyclic planar systems which abide certain number rules. However, all three concepts lack a real space definition, that is not reliant on orbitals or specific wave function expansions. Here, we outline a redefinition from first principles: delocalization means that likely electron arrangements are connected via paths of high probability density in the many-electron real space. In this picture, resonance is the consideration of additional electron arrangements, which offer alternative paths. Most notably, the famous 4n + 2 Hückel rule is generalized and derived from nothing but the antisymmetry of fermionic wave functions., The concept of delocalization, resonance and aromaticity are commonly discussed within electronic structure frameworks relying on specific wave function expansions. Here the authors propose a redefinition of these concepts from first-principles by investigating saddle points of the all-electron probability density.

When chemists want to explain a molecule’s stability and reactivity, they often refer to the concepts of delocalization, resonance, and aromaticity. Resonance is commonly discussed within the electronic structure framework of valence bond theory as the stabilizing effect of mixing different Lewis structures. Yet, most computational chemists work with delocalized molecular orbitals, which are also usually employed to explain the concept of aromaticity, a special kind of ring delocalization that shows up in cyclic planar systems which abide certain number rules. As an intuitive picture for aromaticity, an electronic ring current has been hypothesized. However, all three concepts lack a real space definition, that is not reliant on orbitals or specific wave function expansions. Here, we outline a redefinition from first principles: the concepts are of kinetic nature and related to saddle points of the all-electron probability density |Ψ|². Delocalization means that likely electron arrangements are connected via paths of high probability density in the many-electron real space. In this picture, resonance is the consideration of additional electron arrangements, which offer alternative paths of higher probability. Most notably, the concept of aromatic ring currents in absence of a magnetic field is rejected and the famous 4n+2 Hückel rule is derived from nothing but the antisymmetry of fermionic wave functions. The analysis developed in this work allows for a quantitative discussion of important chemical concepts that were previously only accessible qualitatively or restricted to specific electronic structure frameworks.

Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures. Here, we outline a first principles approach to obtain these orders and contributions for arbitrary wave functions in a manner that is both, related to the quantum theory of atoms in molecules and consistent with valence bond theory insight: the Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|². Doing so, we introduce a valence bond weight definition that does not collapse in the basis set limit.

International journal of molecular sciences 22(15), 8033 (2021). doi:10.3390/ijms22158033 special issue: "Physical Chemistry and Chemical Physics", Published by Molecular Diversity Preservation International, Basel

Molecules : a journal of synthetic chemistry and natural product chemistry 26(4), 911 (2021). doi:10.3390/molecules26040911 special issue: "Special Issue "Advances in the Theory of Chemical Bonding" / Special Issue Editor: Prof. Dr. Ángel Martín Pendás, Guest Editor", Published by MDPI, Basel

Diffusion quantum Monte Carlo calculations with partial and full optimization of the guide function are carried out for the dissociation of the FeS molecule. For the first time, quantum Monte Carlo orbital optimization for transition metal compounds is performed. It is demonstrated that energy optimization of the orbitals of a complete active space wave function in the presence of a Jastrow correlation function is required to obtain agreement with the experimental dissociation energy. Furthermore, it is shown that orbital optimization leads to a $^5\Delta$ ground state, in agreement with experiments, but in disagreement with other high-level ab initio wave function calculations which all predict a $^5\Sigma^+$ ground state. The role of the Jastrow factor in DMC calculations with pseudo potentials is investigated. The results suggest that a large Jastrow factor may improve the DMC accuracy substantially at small additional cost.

Most methods of quantum chemistry calculate total energies rather than directly the energy differences that are of interest to chemists. In the case of statistical methods like quantum Monte Carlo the statistical errors in the absolute values need to be considerably smaller than their difference. The calculation of small energy differences is therefore particularly time consuming. Correlated sampling techniques provide the possibility to compute directly energy differences by simulating the underlying systems with the same stochastic process. The smaller the energy difference the smaller its statistical error. Correlated sampling is well established in variational quantum Monte Carlo, but it is much more difficult to implement in diffusion quantum Monte Carlo because of the fixed node approximation. A correlated sampling formalism and a corresponding algorithm based on a transformed Schrödinger equation having the form of a Kolmogorov’s backward equation is derived. The numerical verification of the presented algorithm is given for the harmonic oscillator. The extension of the algorithm to electron structure calculations is discussed.

A new partitioning scheme for the electron density of a many-electron wavefunction into single electron densities is proposed. These densities are based on the most probable arrangement of the electrons in an atom or molecule. Therefore, they contain information about the electron-electron interaction and, most notably, the Fermi hole due to the antisymmetry of the many-electron wavefunction. The single electron densities overlap and can be combined to electron pair distributions close to the qualitative electron pairs that represent, for instance, the basis of the valence shell electron pair repulsion model. Single electron analyses are presented for the water, ethane, and ethene molecules. The effect of electron correlation on the single electron and pair densities is investigated for the water molecule.

Simulations of complex systems have seen rapid progress over the last decade not only due to the continuous acceleration of computer resources but also due to improvements of methods and algorithms. Simulations complement experiments and model calculations in the effort to get insight into complex systems such as materials, complex liquids, or complicated molecules. As such, computer simulations are a strongly interdisciplinary field where chemistry meets physics, biology, and material science. Most simulations are based on classical physics because the interaction between atoms or even larger entities can be modeled accurately with classical mechanics for most problems as long as no chemical reactions are involved. If the interaction between atoms in a molecule or between molecules is to be calculated, for instance, to obtain parameters for modeling the interactions in classical simulations, classical physics has to be abandoned because these interactions involve the electron distributions which require a quantum mechanical description. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 388–402 DOI: 10.1002/wcms.40

Accurate quantum Monte Carlo, MP2, coupled cluster, and DFT calculations of rotational barriers of several small molecules are presented. With the diffusion quantum Monte Carlo method (DMC) excellent agreement with experimental barriers is obtained except for the gauche–gauche barriers of n -butane and ethylmethylether. It is argued that these two experimental values might be erroneous. Additionally, barriers calculated with the more efficient variational quantum Monte Carlo method (VMC) are presented. The VMC barriers are less accurate than the DMC results, but it is demonstrated that accurate barriers can be obtained with sophisticated Jastrow correlation functions.

The diffusion quantum Monte Carlo method (DMC) is capable of calculating accurately the electronic energy for molecules and molecular aggregates. An overview is given on recent developments for the optimization of the guide function that determines the accuracy of the method. Furthermore, the versatility of DMC is shown with applications to Rydberg states, transition metal compounds, and weakly interacting systems.

The adsorption of methanol in zeolites of the faujasite type with sodium and calcium counter ions is studied with quantum chemical methods. The zeolite is represented with a cluster model allowing calculations at the Moller-Plesset as well as the DFT level of theory. An adsorption energy of −62.4 kJ/mol is calculated at the MP2/TZVP//BP86/TZVP level of theory for one methanol molecule at one site II sodium cation. Insight into the adsorption process is obtained with a three-body decomposition which reveals a strong destabilisation of the adsorption strength by large, positive three-body terms, which is important for force field development.

The coordination behaviour of the chiral tren-type tripodal ligand 3-H6 with gallium(III) and titanium(IV) ions was investigated and it was found that only mononuclear complexes are formed. In the presence of Na+, one of the cations acts as a template and is bound inside the “cap” of [Na(3)M]n– (M = Ga, n = 2; M = Ti, n = 1). If no such cation is present, three protons are bound to the iminocatechol units in order to prevent repulsion between lone pairs at nitrogen and oxygen. To minimize the charge repulsion between the protonated imines of [H3(3)M]n+ (M = Ga, n = 0; M = Ti, n = 1), an enaminone/chinomethine mesomeric structure becomes important. The adoption of this unusual mesomeric form by the iminocatecholates was supported by computational methods. In further investigations, we found, that the addition of protons (H2SO4) to the dinuclear (catecholimine)titanium helicate K4[(4)3Ti2] leads to protonation of the imine part of the iminocatechol. An excess of acid results in the hydrolysis of the complexes as well as of the imine units. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)

Previously unknown quantities of a general trial wavefunction are derived, namely the measure of the splittings between the nodal hypersurfaces obtained from the Hamiltonian operation , the kinetic energy operation , and that of itself, which occur because is not the true wavefunction. Insight into the structure of the true nodes is also revealed. In particular, we establish a bound for the location of a node of the exact wavefunction with respect to the node of the trial wavefunction. The nodal structure is of particular interest for quantum Monte Carlo calculations (QMC) and also for assessing and optimizing a trial wavefunction.

Jastrow correlation factors play an important role in quantum Monte Carlo calculations. Together with an orbital based antisymmetric function, they allow the construction of highly accurate correlation wave functions. In this paper, a generic expansion of the Jastrow correlation function in terms of polynomials that satisfy both the electron exchange symmetry constraint and the cusp conditions is presented. In particular, an expansion of the three-body electron-electron-nucleus contribution in terms of cuspless homogeneous symmetric polynomials is proposed. The polynomials can be expressed in fairly arbitrary scaling function allowing a generic implementation of the Jastrow factor. It is demonstrated with a few examples that the new Jastrow factor achieves 85%–90% of the total correlation energy in a variational quantum Monte Carlo calculation and more than 90% of the diffusion Monte Carlo correlation energy.

The microwave spectrum of (CH3)3SiI and its isotopic species (CH3)329SiI, (CH3)330SiI, and (13CH3)(CH3)2SiI has been studied using a pulsed molecular beam Fourier transform microwave spectrometer in the frequency range of 3–26.5 GHz. The barrier to internal rotation, the iodine quadrupole coupling and the molecular structure were determined. Ab initio calculations were compared with the experimental results.

The scaling of the diffusion quantum Monte Carlo method can be greatly improved when localized orbitals and short-range correlation functions are employed as recently suggested by the authors. The local diffusion quantum Monte Carlo method is described in detail with a careful analysis of errors. The new method achieves near linear scaling in the calculation of the local energy. Results demonstrating the improved performance are presented.

The accuracy of the fixed-node diffusion quantum Monte Carlo (FN-DQMC) method is compared to the coupled cluster method CCSD(T). For a test set of 20 small molecules and 17 reactions the electronic contribution to the reaction enthalpy is calculated with the FN-DQMC method using the nodes of a Slater determinant calculated at the HF/cc-pVTZ level. By comparison with reference reaction enthalpies the FN-DQMC method is shown to be more accurate than the CCSD(T)/cc-pVDZ method and almost as accurate as CCSD(T)/cc-pVTZ. The deviation from the reference data is comparable to the CCSD(T)/cc-pVTZ deviation, but, with only two exceptions, of opposite sign.

Using a variety of methods phenol water clusters phenol(H2O)n, n⩽7, are investigated with a focus on phenol(H2O)5,6. A comprehensive search for low-energy isomers is conducted on a polarizable intermolecular potential energy surface. Zero-point energy contributions are calculated rigorously with the rigid-body quantum Monte Carlo method. The OH stretch vibrational spectra of the isomers are calculated using a local-mode model and compared with experimental isomer-selective IR–UV spectral hole burning (SHB) spectra. The topology of the clusters phenol(H2O)5,6 is shown in deviate from the corresponding pure water clusters.

While the diffusion quantum Monte Carlo method (DQMC) is capable, in principle, of calculating exact ground state energies, in practice the fixed-node (FN) approximation leads to node location errors which make FN-DQMC energies upper bounds. It is shown that the node location error can be reduced systematically and without prohibitive increase of computer time requirements by using nodes derived from pair natural orbital CI wave functions (PNO-CI). The reduction is demonstrated for the N atom and the molecules N2 and H2O. With the DQMC/PNOCI method, we obtain a variational energy of −109.520(3) H for the N2 molecule and −76.429(1) H for the ground state of the water molecule which is only 22 and 9 mH above the estimated nonrelativistic ground state energy, respectively.

Quantum Monte Carlo methods have recently made it possible to calculate the electronic structure of relatively large molecular systems with very high accuracy. These large systems range from positron complexes [NH2,Ps] with ∼10 electrons to C20 isomers with 120 electrons, to silicon crystal structures of 250 atoms and 1000 valence electrons. The techniques for such calculations and a sampling of applications are reviewed.

The energetics of the ring, bowl, and cage isomers of C 20 were determined in all-electron fixed-node quantum Monte Carlo calculations. In good agreement with results from valence-only quantum Monte Carlo calculations and from Moller–Plesset calculations with large basis sets, the calculations predict the lowest-energy isomer to be the bowl isomer. The energies of the ring and cage, relative to the bowl, are 1.1±0.5 and 2.1±0.5 eV, respectively.

The discovery of metallo-carbohedrenes (Met-Cars) such as the titanium carbon cluster Ti8C12 by Guo et al. [Science 255 (192) 1411] gave rise to many questions about its structure and bonding. In a first step toward the full cluster, the Ti atom and the TiC dimer are investigated using the diffusion quantum Monte Carlo (DQMC) method. The dissociation energy and the energy splittings of low-lying states are calculated.

The energetics of carbon clusters C8 and C10 in several configurations have been determined in all-electron fixed-node quantum Monte Carlo calculations. The total electronic energies obtained are 0.4–1.2 hartrees lower than those of the lowest-energy analytic variational and coupled-cluster calculations, and they are only 0.2 to 0.4 hartrees above the experimentally based total energies. The recovery of correlation energy is 89%–94%. For C8, relative values are found to be in agreement with earlier calculations: the cyclic C4h 1Ag structure, the linear 3Σg− (cumulenic), and the linear 1Σg+ (cumulenic) structures are found lowest in energy and within 10 kcal/mol of each other. For C10, relative values are found to be in agreement with earlier calculations: the cyclic D5h 1A1′ (distorted cumulenic) and D10h 1A1g (cumulenic) structures are found to be lowest in energy, within 5 kcal/mol of each other, 60 kcal/mol below the linear 3Σg− (cumulenic) structure. An analysis of the scaling of computational effort ...

Hylleraas–configuration interaction (CI) calculations have been carried out with double-linked basis sets for the Be atom. Our best upper bound for the 1S ground state is E0 = −14.6673547Eh. Furthermore, upper bounds for the two lowest excited 1S states have been calculated. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66: 241–247, 1998

An improved transition matrix for variational Monte Carlo calculations is proposed. This matrix allows the use of larger time steps than the usual Langevin-based transition matrix and provides efficient sampling of electron positions in both the core and valence regions. Its efficiency and accuracy in predictions of energies for hydrogen-like systems and for the neon atom are demonstrated.

Accurate ground state energies comparable to or better than the best previous ab initio results can be obtained using the fixed‐node quantum Monte Carlo (FN‐DQMC) method. The residual energy, the nodal error due to the error in the nodal structure of a trial wave function, is examined in this study using nodal surfaces given by near HF‐limit wave functions. The study is aimed at better understanding of the nodal error and the cancellation of nodal errors in calculating energy differences. Calculations have been carried out for the first‐row hydrides LiH to FH and the corresponding atoms. The FN‐DQMC ground state energies are among the lowest to date. The dissociation energies De have been calculated with accuracies of 0.5 kcal mol−1 or better. For all hydrides, the dissociation energies are consistent with experimental values. The fixed‐node quantum Monte Carlo method can therefore offer a very straight‐forward way to calculate highly accurate dissociation energies.

fixed-node dissociation energy D e 5141.3~4! kcal mol 21 is in excellent agreement with experimental data. The cancellation of the nodal error was achieved with trial wave functions having nodal surfaces determined by Slater determinants of the near Hartree-Fock limit quality. With the released-node Green's function quantum Monte Carlo method the lowest upper bounds to the ground state energies to date for both F @E 0 5299.731~4! Hartree# and FH @E 0 52100.458~5! Hartree# have been obtained. © 1996 American Institute of Physics.@S0021-9606~96!00935-X# I. INTRODUCTION The quantum Monte Carlo method has been successful in calculating accurately the ground state energy and other properties of many atoms and molecules. 1-3 For few-electron systems such as H2 ,H 3, and LiH, quantum Monte Carlo methods provide exact solutions of the Schrodinger equation. 1 For larger systems, quantum Monte Carlo meth- ods do not at present provide exact solutions, but they do provide highly accurate solutions. 2 In this paper we report accurate QMC calculations for the F atom and the FH molecule. Two methods have been used: the fixed-node diffusion quantum Monte Carlo ~FN- DQMC! and the released-node Green's function quantum Monte Carlo ~RN-GFQMC!, to obtain accurate total energies for each species and an accurate dissociation energy for FH. The results indicate the magnitude of the nodal errors and their effects on the accuracy of the calculated dissociation energy. More than 90% of the correlation energy can be obtained for a ten-electron system like FH using the fixed-node approximation 4 in which the nodes of a trial wave function are imposed on the solution of the Schrodinger equation. Since the remaining part of the correlation energy, the nodal error, is of the order of 10 kcal mol 21 for hydrogen fluoride, the calculation of the dissociation energy and other energy differences with a chemical accuracy better than 1 kcal mol 21 remains a challenge for QMC methods. The ac- curate determination of energy differences like the dissocia- tion energy depends on an efficient cancellation of the nodal error, making it important to control the nodal error. The effects of the nodal error have been investigated in only a few studies. 5,6 The nodal error may be avoided with the use of the RN-GFQMC method. 7,8 In principle, this method allows the exact determination of the ground state energy, but in prac- tice it is currently difficult to obtain error bars of the order of the chemical accuracy for systems with more than about six electrons. We have applied the RN-GFQMC method to both F and FH.

An accurate upper bound calculation for the two lowest 4 S states of the Li I isoelectronic series from Be II-Ne VIII is given using an extensive Hylleraas-CI calculation.

Atomic Hylleraas-CI calculations with liked correlation terms of the form r{sub ij}{sup p}r{sub kl}{sup 1} are discussed. Formulas for the integration of the radial part and the arising auxiliary integrals are deduced and convergence proofs are given. 7 refs., 4 figs.

The first nonrelativistic lower bound to the ground state of the lithium atom is give with E0 > −7.47816 au using the method of variance minimization and an extension of Temple's formula. With large Hylleraas–CI basis sets, high-precision upper bounds and isotope shifts are calculated for the three lowest 2S states of the lithium atom, which are best to date. © 1994 John Wiley & Sons, Inc.

In this paper, a general method is presented that allows the derivation of the expansion coefficients of the product of two orthogonal functions provided the generating function is known. For the three classical orthogonal polynomials, the Laguerre, the Hermite, and the Legendre polynomials, the coefficients blmn with ϕmϕn = ∑lblmnϕl are derived. © 1993 John Wiley & Sons, Inc.