Theoretical Study of the Benzene Dimer by the Density‐Functional‐Theory Formalism Based on Electron‐Density Partitioning

The density‐functional approach based on the partition into subsystems was applied to study the benzene dimer. For several structures, the calculated interaction energy and intermolecular distance were compared with the previous theoretical results. A good agreement with high level ab initio correlated methods was found. For instance, the interaction energies obtained in this work and the CCSD(T) method agree within 0.1 – 0.6 kcal/mol depending on the structure of the dimer. The structure with the largest interaction energy is T‐shaped, in agreement with CCSD(T) results. The T‐shaped structure of benzene dimer was suggested by several experimental measurements. The calculated interaction energy of 2.09 kcal/mol agrees also well with experimental estimates based on the dissociation energy which ranges from 1.6±0.2 to 2.4±0.4 kcal/mol and the estimated zero‐point vibration energy of 0.3 – 0.5 kcal/mol.     

Tautomerism of oxopyridines and oxopyrimidines: Theoretical study with complete optimization of geometry

The semiempirical MINDO /3 method is employed to calculate the energies of various tautomers of model tautomeric compounds— 2-oxo- and 4-oxopyridines and pyrimidines. The results are compared with experimental data in the gas phase, where the solute–solvent interactions not included in theoretical calculations are absent. Although the relative energies obtained by the MINDO /3 method appear to be superior to other semiempirical and ab initio calculations, the accuracy of the method was determined to be as low as 3–4 kcal/mol. It indicates that it is exceedingly difficult to account theoretically for intrinsic stabilities of the tautomers. The importance of various factors influencing calculated free-energy differences is discussed. Particular attention is paid to the problem of geometry optimization.     

A theoretical study of the rotational isomers of nitrosomethanol by semiempirical (AM1) and ab initio methods

The conformational potential energy surface as a function of the two internal torsion angles in C-nitrosomethanol has been obtained using the semiempirical AM1 method. Optimized geometries are reported for the local minima on this surface and also for the corresponding points on the HF/6-31G, 6-31G*, and 6-31G** surfaces. All methods predict cis and trans minima which occur in degenerate pairs, each pair being connected by a transition state of C_s symmetry. The AM1 structures are found to compare well with the corresponding ab initio structures. Ab initio HF/6-31G and HF/6-31G* harmonic vibrational frequencies are reported for the cis and trans forms of nitrosomethanol. When scaled appropriately the calculated frequencies are found to compare well with experimental frequencies. The ab initio calculations predict the energy barrier for cis → trans isomerization to be between 5.8 and 6.5 kcal/mol with the trans → cis isomerization barrier lying between 2.3 and 6.5 kcal/mol. The corresponding AM1 energy barriers are around 1 kcal/mol lower in energy. The ab initio calculations predict the barrier to conversion between the two cis rotamers to be very small with the AM1 value being around 1 kcal/mol. Both AM1 and ab initio calculations predict interconversion between trans rotamers to require between 1.2 and 1.4 kcal/mol.     

Structure of guest-host complexes of β-cyclodextrin with arenes: a quantum-chemical study

The structure of β-cyclodextrin (β-CD), as well as the structure and energetics of β-CD-naphthalene, β-CD-fluorene, β-CD-phenanthrene, β-CD-cyclohexane (1:1), and β-CD-naphthalene (2:2) inclusion complexes was studied by the semiempirical MNDO/PM3 method. Calculations of a β-CD-naphthalene-cyclohexane (1:1:1) complex were also performed. The minimum heat of formation was found for the symmetric β-CD conformation withC ₇ symmetry axis. The structure is stabilized by the ring of interunit H-bonds formed by the protons of the 2-OH groups and the O atoms of the 3′-OH groups of the glucose units. Preferableness of this orientation of interunit H-bonds was confirmed byab initio calculations of the molecule of α-(1–4)-glucobiose (maltose) in the MP2/6-31G(d,p)//6-31G(d,p) approximation. The formation of any inclusion compounds of β-CD with arenes is energetically favorable: the complexation energy varies in the range −9 to −12 kcal mol⁻¹. Among complexes with naphthalene, that of composition 2:2 is the most energetically favorable, which is in agreement with experimental data. In this complex, β-CD exists as a dimer of the “head-to-head” type, in which both partners are linked by a system of H-bonds. The structure of the “head-to-head” dimer of β-CD was simulated byab initio calculations of the H-bonded dimer of α-d-glucose in the RHF/6-31G(d,p) approximation. In the dimer, both components are linked by a pair of H-bonds formed by the protons of the 3-OH groups and the O atoms of the, 2-OH groups. The dimerization energies obtained fromab initio and semiempirical MNDO/PM3 and AM1 calculations differ by about 2.5 times (8.6vs 3.2 and 3.8 kcal mol⁻¹, respectively).     

Suitability of the PM3-derived molecular electrostatic potentials

A systematic study of the suitability of PM3-derived molecular electrostatic potentials (MEPs) is presented. Forty-six MEP minima, 81 electrostatic charges, and 17 electrostatic dipoles were determined at the PM3 level and compared with those obtained from the ab initio 6-31G* wave function, as well as from the semiempirical MNDO and AM1 wave functions. The statistical results of the comparison analysis between semiempirical and ab initio 6-31G* MEPs show that PM3 is in general reliable for the study of the MEP minima but a mediocre method as a source of electrostatic charges. © 1993 John Wiley & Sons, Inc.     

Hydration of small anions: Calculations by the AM1 semiempirical method

The AM1 semiempirical molecular orbital method has been used to calculate successive heats of hydration of small anions, including hydride, hydroxide, and the halogen ions, for cluster sizes up to 11 water molecules surrounding the central anion. Heats of hydration agree with available experimental data to within a few kcal/mol. Structures, however, do not always agree well with available ab initio calculations on clusters with one or two water molecules. The results indicate that the AM1 semiempirical technique applied to finite-sized clusters must be used with caution in understanding how hydration affects the chemical reactions of anions.     

Electron donor-acceptor complexes: Evaluation of MNDO as a computational tool to probe intermolecular interactions

Donor-acceptor pairs form EDA complexes that exist as conformational isomers exhibiting different ground-state and photochemical properties. We have sought a rapid, general, and accurate quantum mechanical computational method to generate potential energy surfaces that are representative of the donor-acceptor intermolecular interactions at the self-consistent field (SCF) level. The semiempirical molecular orbital (MO) method MNDO has been compared to ab initio methods to assess its behavior with respect to energy, dipole moment and ionization potential shifts. MNDO correctly distinguishes between repulsive and bound EDA complex states at the SCF level and produces potential curves that are smooth and free of spurious minima or cusps. MNDO curves are systematically more repulsive than those for ab initio STO-3G calculations; calculated interaction energies exhibit a mean absolute deviation of 2.90 kcal/mol. MNDO appears to provide a reliable qualitative estimate of the nondispersion portion of the interaction energy. Limitations and errors arising from minimal basis sets, single determinants, and neglect of dispersion are discussed.     

Extension of the PDDG/PM3 and PDDG/MNDO semiempirical molecular orbital methods to the halogens

The new semiempirical methods, PDDG/PM3 and PDDG/MNDO, have been parameterized for halogens. For comparison, the original MNDO and PM3 were also reoptimized for the halogens using the same training set; these modified methods are referred to as MNDO' and PM3'. For 442 halogen-containing molecules, the smallest mean absolute error (MAE) in heats of formation is obtained with PDDG/PM3 (5.6 kcal/mol), followed by PM3' (6.1 kcal/mol), PDDG/MNDO (6.6 kcal/mol), PM3 (8.1 kcal/mol), MNDO' (8.5 kcal/mol), AM1 (11.1 kcal/mol), and MNDO (14.0 kcal/mol). For normal-valent halogen-containing molecules, the PDDG methods also provide improved heats of formation over MNDO/d. Hypervalent compounds were not included in the training set and improvements over the standard NDDO methods with sp basis sets were not obtained. For small haloalkanes, the PDDG methods yield more accurate heats of formation than are obtained from density functional theory (DFT) with the B3LYP and B3PW91 functionals using large basis sets. PDDG/PM3 and PM3' also give improved binding energies over the standard NDDO methods for complexes involving halide anions, and they are competitive with B3LYP/6-311++G(d,p) results including thermal corrections. Among the semiempirical methods studied, PDDG/PM3 also generates the best agreement with high-level ab initio G2 and CCSD(T) intrinsic activation energies for S(N)2 reactions involving methyl halides and halide anions. Finally, the MAEs in ionization potentials, dipole moments, and molecular geometries show that the parameter sets for the PDDG and reoptimized NDDO methods reduce the MAEs in heats of formation without compromising the other important QM observables.     

Amide–π interactions between formamide and benzene

High‐level ab initio calculations have been carried out using a formamide–benzene model system to evaluate amide–π interactions. The interaction energies were estimated as a sum of the CCSD(T) correlation contribution and the HF energy at the complete basis set limit, for the geometries of the model structures at the energy minimum obtained by potential energy surface (PES) scans. NH/π geometry in a face‐on configuration was found to be the most attractive among the various geometries considered, with interaction energy of ?3.75 kcal/mol. An interaction energy of ?2.08 kcal/mol was calculated for the stacked N/Center type geometry, where the nitrogen atom of formamide points directly toward the center of the aromatic ring. The weakest C?O/π geometry, where a carbonyl oxygen atom points toward the plane of the aromatic ring, was found to have energy minimum at an intermolecular distance of 3.67 Å from the PES, with a repulsive interaction energy less than 1 kcal/mol. However, if there are simultaneous attractive interactions with other parts of the molecule besides the amide group, the weak repulsion could be easily overcome, to give a C?O/π geometry interaction. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Theoretical calculations of proton affinities of azines. Prediction of the relative basicities and preferred protonation sites

Theoretical calculations at the 3-21G and 3-21 + G ab initio levels and at the MNDO and AM1 semiempirical levels of several six-membered nitrogenated heterocycles and their protonated species have been carried out. The 3–21G calculated proton affinities are systematically too high, in relation to the available experimental data, and it is estimated that inclusion of electron correlation and zero-point corrections is not sufficient to reach the desired agreement; however, additional inclusion of diffuse functions (3-21 + G/3-21G calculations) lowers the calculated proton affinities by 5.4–6.8 kcal/mol, a good agreement being thus obtained, at least for 1–7 . On the other hand, semiempirical methods underestimate the repulsion between each pair of vicinal nitrogens; however, if a correction of ?9 kcal/mol is added to the AM1 results for each pair of neighboring nitrogens containing lone pairs of electrons, the corresponding proton affinities match fairly well the available exoerimental data and corrected 3-21 + G results. As expected, all methods predict that the introduction of additional nitrogens decreases the overall absolute basicity. Futhermore, comparison of the relative basicity of the isomers and of the preferred protonation site for each isomer indicates that nitrogen atoms with (only) one α-nitrogen and without a γ-nitrogen are more basic than any others. In benzazines, MNDO and AM1 suggest that the 2,3-diaza arrangement has a higher intrinsic basicity than the 1,2-diaza arrangement.     

Study of hydrogen bonding interactions relevant to biomolecular structure and function

Ab initio molecular orbital calculations were used to study hydrogen bonding interactions and interatomic distances of a number of hydrogen bonded complexes that are germane to biomolecular structure and function. The calculations were carried out at the STO-3G, 3-21G, 6-31G*, and MP2/6-31G* levels (geometries were fully optimized at each level). For anionic species, 6-31 + G* and MP2/6-31 + G* were also used. In some cases, more sophisticated calculations were also carried out. Whenever possible, the corresponding enthalpy, entropy, and free energy of complexation were calculated. The agreement with the limited quantity of experimental data is good. For comparison, we also carried out semiempirical molecular orbital calculations. In general, AM1 and PM3 give lower interaction enthalpies than the best ab initio results. With regard to structural results, AM1 tends to favor bifurcated structures for O? H-O and N? HO types of hydrogen bonds, but not for hydrogen bonds involving O-H? S and S-H? O, where the usual hydrogen bond patterns are observed. Overall, AM1 geometries are in general in poor agreement with ab initio structural results. On the other hand, PM3 gives geometries similar to the ab initio ones. Hence, from the structural point of view PM3 does show some improvement over AM1. Finally, insights into the formation of cyclic or open formate–water hydrogen bonded complexes are presented. © 1992 by John Wiley & Sons, Inc.     

Conformational analysis,part 43. A theoretical and LIS/NMR investigation of the conformations of substituted benzamides

A refined Lanthanide‐Induced‐Shift Analysis (LISA) is used with molecular mechanics and ab initio calculations to investigate the conformations of benzamide ( 1 ), N‐methylbenzamide ( 2 ), N,N‐dimethylbenzamide ( 3 ) and the conformational equilibria of 2‐fluoro ( 4 ), 2‐chloro ( 5 ) and N‐methyl‐2‐methoxy benzamide ( 6 ). The amino group in 1 is planar in the crystal but is calculated to be pyramidal with the CO/phenyl torsional angle (ω) of 20–25°. The LISA analysis gave acceptable agreement factors (Rcryst ≤ 1%) for the ab initio geometries when ω was decreased to 0°, the other geometries were not as good. In 2 , the N‐methyl is coplanar with the carbonyl group in all the geometries. Good agreement was obtained for the RHF geometries, with ω 25°, the other geometries were only acceptable with increased values of ω. In 3 , good agreement for the RHF and PCModel geometries was found when ω was changed from the calculated values of 40° (RHF) and 90° (PCModel) to ca. 60°, the X‐ray and B3LYP geometries were not as good. The two substituted compounds 4 , 5 and 6 are interconverting between the cis (O,X) and trans (O,X) conformers. The more stable trans conformer is planar in 4 and 6 but the cis form non‐planar. Both the cis and trans conformers of 5 are non‐planar. There is an additional degree of freedom in 6 due to the 2‐methoxy group, which can be either planar or orthogonal to the phenyl ring in both conformers. The conformer ratios were obtained from the LISA analysis to give Ecis‐Etrans in 4 > 2.3 kcal/mol (CDCl₃) and 1.7 kcal/mol (CD₃CN), in 5 0.0 kcal/mol (CD₃CN) and in 6 > 2.5 kcal/mol (CDCl₃) and 2.0 kcal/mol (CD₃CN). These values were used with the observed versus calculated ¹H shifts to determine the conformer ratios and energies in DMSO solvent to give Ecis‐Etrans 1.1, ?0.1 and 1.8 kcal/mol for ( 4 ), ( 5 ) and ( 6 ). Comparison of the observed versus calculated conformer energies show that both the MM and ab initio calculations overestimate the NH..F hydrogen bond in ( 4 ) by ca. 2 kcal/mol. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparative semiempirical and ab initio study of the harmonic vibrational frequencies of aniline—I. The ground state

The harmonic vibrational frequencies of the ground state S₀ of aniline obtained from various ab initio methods [6-31G, 6-31G(*) and 6-31G* basis sets] and semiempirical methods (MINDO/3, MNDO, AM1 and PM3) have been compared to the experimental vibrational spectra. Detailed theoretical analyses of the atomic Cartesian displacements of all normal modes are presented. The semiempirical PM3 method reproduces the experimental frequencies of aniline with comparable accuracy to the ab initio methods. Ale PM3 method will be useful in predicting the vibrational spectra of larger aromatic amines.     

Molecular dynamics simulations of fluid methane properties using ab initio intermolecular interaction potentials

Intermolecular interaction energy data for the methane dimer have been calculated at a spectroscopic accuracy and employed to construct an ab initio potential energy surface (PES) for molecular dynamics (MD) simulations of fluid methane properties. The full potential curves of the methane dimer at 12 symmetric conformations were calculated by the supermolecule counterpoise‐corrected second‐order Møller‐Plesset (MP2) perturbation theory. Single‐point coupled cluster with single and double and perturbative triple excitations [CCSD(T)] calculations were also carried out to calibrate the MP2 potentials. We employed Pople's medium size basis sets [up to 6‐311++G(3df, 3pd)] and Dunning's correlation consistent basis sets (cc‐pVXZ and aug‐cc‐pVXZ, X = D, T, Q). For each conformer, the intermolecular carbon–carbon separation was sampled in a step 0.1 Å for a range of 3–9 Å, resulting in a total of 732 configuration points calculated. The MP2 binding curves display significant anisotropy with respect to the relative orientations of the dimer. The potential curves at the complete basis set (CBS) limit were estimated using well‐established analytical extrapolation schemes. A 4‐site potential model with sites located at the hydrogen atoms was used to fit the ab initio potential data. This model stems from a hydrogen–hydrogen repulsion mechanism to explain the stability of the dimer structure. MD simulations using the ab initio PES show quantitative agreements on both the atom‐wise radial distribution functions and the self‐diffusion coefficients over a wide range of experimental conditions. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

Comparison of NDDO and quasi-ab initio approaches to compute semiempirical molecular electrostatic potentials

The suitability of the two most widely used strategies to compute semiempirical MEPs is examined. For this purpose, MEP minima, electrostatic charges, and dipoles for a large number of molecules were computed at the AM1, MNDO, and PM3 levels using both the NDDO strategy developed by Ferenczy, Reynolds, and Richards and our own quasi-ab initio method. Results demonstrate that the quasi-ab initio is preferred over the NDDO method for the computation of MEP minima. It is also found that the best set of semiempirical charges and dipoles are obtained using either the AM1 NDDO or the MNDO quasi-ab initio methods. In these two cases, the quality of the results is fully comparable with 6-31G* values. © 1994 by John Wiley & Sons, Inc.     

Joint quantum chemical and polarizable molecular mechanics investigation of formate complexes with penta- and hexahydrated Zn2+: Comparison between energetics of model bidentate,monodentate, and through-water Zn2+ binding modes and evaluation of nonadditivity effects

In order to gain an understanding of the energetics of polycoordinated Zn²⁺ binding to the formate anion (the end side chain of the Asp and Glu residues of proteins), we compare three competing binding modes in the presence of five and six water molecules: a, bidentate binding of Zn²⁺ to both formate oxygens; b, monodentate binding of Zn²⁺ to one formate oxygen; and c, through-water binding of Zn²⁺ to formate, in which the cation remains bound to its first-hydration shell waters and interacts with both formate oxygens through three water molecules. We also investigate a complex d, which is similar to c, in which formate is protonated into formic acid and one water molecule is deprotonated. The computations are carried out using the ab initio self-consistent field/MP2 with three basis sets of increasing size density functional theory, semiempirical AM1 and PM3, and the sum of interactions between fragments ab initio computed (SIBFA) molecular mechanics procedures. The summed energies of the isolated molecules making up the complexes disfavor tautomer d compared to a–c. On the other hand, the ab initio computations give the ordering of intermolecular interaction energies as d formic acid tautomer >b monodentate >a bidentate >c through-water. Whereas the first-order energy E₁ favors both inner-shell Zn²⁺ complexes with formate over the outer-shell complex, the polarization and the charge-transfer components of the second-order energy E₂ both favor the outer-shell complex over the inner-shell one, despite the increased separation between the cation and the highly polarizable formate ion. Energy balances including continuum solvation enthalpies produce an equilibration of complexes a–d. The preference favoring the monodentate complex over the bidentate one is consistent with other ab initio results for formate binding by a fully coordinated Zn²⁺ cation and with structural results from X-ray crystallography. The SIBFA results are consistent with the ab initio results, and the computed interaction energy values match the ab initio ones to within 3%. The effects of nonadditivity are analyzed in the ab initio, SIBFA, and semiempirical computations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1379–1390, 1999     

Intermolecular and intramolecular interactions calculated with ab initio perturbative configuration interaction method using strongly localized orbitals

We have applied the ab initio formulation of the perturbative configuration interaction using localized orbitals (PCILO ) method up to third order to calculate intermolecular and intramolecular interaction energies going beyond the ab initio Hartree–Fock calculation. For the rotational barrier in ethane our results agree well with the experimental value and the cis- and even the trans-barriers in HOOH are at least qualitatively reproduced with the aid of the STO -3G basis set. In the case of the water dimer we obtain an equilibrium intermolecular distance and interaction energy which are confirmed by other calculations. We can further conclude from our studies that one has to include higher orders in the perturbation expansion as the system becomes more complicated. It is especially the last aspect which hinders the application of the ab initio PCILO to estimate the major part of the electron correlation energy for large molecules.     

Application of a semi-empirical dispersion correction for modeling water clusters

The Grimme-D3 semi-empirical dispersion energy correction has been implemented for the original effective fragment potential for water (EFP1), and for systems that contain water molecules described by both correlated ab initio quantum mechanical (QM) molecules and EFP1. Binding energies obtained with these EFP1-D and QM/EFP1-D methods were tested using 27 benchmark species, including neutral, protonated, deprotonated, and auto-ionized water clusters and nine solute–water binary complexes. The EFP1-D and QM/EFP1-D binding energies are compared with those obtained using fully QM methods: second-order perturbation theory, and coupled cluster theory, CCSD(T), at the complete basis set (CBS) limit. The results show that the EFP1-D and QM/EFP1-D binding energies are in good agreement with CCSD(T)/CBS binding energies with a mean absolute error of 5.9 kcal/mol for water clusters and 0.8 kcal/mol for solute–water binary complexes. © 2018 Wiley Periodicals, Inc.     

Theoretical Calculations of β-Lactam Antibiotics. Part VII. Influence of the solvent on the basic hydrolysis of the β-lactam ring

We used semi-empirical and ab initio calculations to investigate the nucleophilic attack of the OH^? ion on the β-lactam carbonyl group. Both allowed us to detect reaction intermediates pertaining to proton-transfer reactions rather than the studied reaction. We also used the PM3 semi-empirical method to investigate the influence of the solvent on the process. The AMSOL method predicts the occurrence of a potential barrier of 20.7 kcal/mol due to the desolvation of the OH^? ion in approaching the β-lactam carbonyl group. Using the supermolecular approach and a H₂O solvation sphere of 20 molecules around the solute, the potential barrier is lowered to 17.5 kcal/mol, which is very close to the experimental value (16.7 kcal/mol).