Pyrrolizidine alkaloids necine bases: II. Conformational analysis of free bases

Molecular mechanics calculations were applied to the conformational analysis of two diasteroisomers, the pyrrolizidine alkaloids (PAs) retronecine and heliotridine. The application of reoptimized parameters for H bonding corrected the tendency of MM3(92) calculations to give unrealistic H(DOTTED BOND)O distances for intramolecular OH interactions occurring in both diasterisomers. Inversions in the H-bond direction of exo-retronecine and in the relative stability of heliotridine endo–exo conformers were also observed with the application of the new parameters. A set of probable conformers was obtained for each diasterisomer, based on conformational and Boltzmann population analysis. Only exo-puckered conformers were found in the retronecine set, whereas both exo- and endo-puckered conformers were obtained for heliotridine. Transition state conformations supplied arguments supporting the design of models for H-bond interconversion in the case of exo-retronecine and for the exo–endo interconversion of heliotridine. Reactivity behaviors and ¹H-NMR data of both diasterisomers were elucidated in light of the theoretical results. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1853–1861, 1998     

Molecular mechanics study of conformational trends in simple alcohols and ethers. II. Intramolecular hydrogen bonding

In this article we present an extension of our modified MM2(80) force field MM2MOD in which a potential function for hydrogen bonding in alcohols and ethers is included. The results of applying MM2(85), MM2(87), and MM2MOD on ethylene glycol, 2-methoxyethanol and 1,3-propanediol are reported and compared with available experimental data and ab initio results. It is concluded that hydrogen bonding plays an important role in determining the molecular conformations of these systems. © 1992 by John Wiley & Sons, Inc.     

Optimizing efficiency of perturbative Monte Carlo method

We introduce error weighting functions into the perturbative Monte Carlo method for use with a hybrid ab initio quantum mechanics/molecular mechanics (QM/MM) potential. The perturbative Monte Carlo approach introduced earlier provides a means to reduce the number of full SCF calculations in simulations using a QM/MM potential by evoking perturbation theory to calculate energy changes due to displacements of an MM molecule. The use of weighting functions, introduced here, allows an optimal number of MM molecule displacements to occur between the performance of the full self-consistent field calculations. This will allow the ab initio QM/MM approach to be applied to systems that require more accurate treatment of the QM and/or MM regions. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1632–1638, 1998     

An analytic potential energy function for the amide–amide and amide–water intermolecular hydrogen bonds in peptides

An analytic potential energy function is proposed and applied to evaluate the amide–amide and amide–water hydrogen‐bonding interaction energies in peptides. The parameters in the analytic function are derived from fitting to the potential energy curves of 10 hydrogen‐bonded training dimers. The analytic potential energy function is then employed to calculate the N? H…O?C, C? H…O?C, N? H…OH₂, and C?O…HOH hydrogen‐bonding interaction energies in amide–amide and amide–water dimers containing N‐methylacetamide, acetamide, glycine dipeptide, alanine dipeptide, N‐methylformamide, N‐methylpropanamide, N‐ethylacetamide and/or water molecules. The potential energy curves of these systems are therefore obtained, including the equilibrium hydrogen bond distances R(O…H) and the hydrogen‐bonding energies. The function is also applied to calculate the binding energies in models of β‐sheets. The calculation results show that the potential energy curves obtained from the analytic function are in good agreement with those obtained from MP2/6‐31+G** calculations by including the BSSE correction, which demonstrate that the analytic function proposed in this work can be used to predict the hydrogen‐bonding interaction energies in peptides quickly and accurately. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Importance of selecting proper basis set in quantum mechanical studies of potential energy surfaces of carbohydrates

An extensive quantum mechanical study of a water dimer suggests that the introduction of a diffuse function into the basis set, which significantly reduces the basis set superposition error (BSSE) in the hydrogen bonding energy calculation, is the key to better calculations of the potential energy surfaces of carbohydrates. This article examines the potential energy surfaces of selected d -aldo- and d -ketohexoses (a total of 82 conformers) by quantum mechanics (QM) and molecular mechanics (MM) methods. In contrast to the results with a smaller basis set (B3LYP/6-31G** 5d), we found at the higher level calculation (B3LYP/6-311++G(2d,2p)//B3LYP/6-31G** 5d) that, in most cases, the furanose forms are less stable than the pyranose forms. These discrepancies are mainly due to the fact that intramolecular hydrogen bonding energies are overestimated in the lower level calculations. The higher level QM calculations of the potential energy surfaces of d -aldo- and d -ketohexoses now are more comparable to the MM3 results. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1593–1603, 1999     

Variation of atomic charges during proton transfer in hydrogen bonds

The point atomic charges in a number of ionic H-bonded systems are studied by ab initio calculations as functions of the proton transfer coordinate. In the proton-bound complexes of water–water, ammonia–ammonia, formamide–water, formamide–ammonia, and dimethylether–ammonia, the net atomic charges were obtained using Mulliken population analysis and from the diagonal elements of the atomic polar tensors calculated at the HF/4–31G and MP2/6–31 + G** levels. The dependence of the atomic charges upon the coordinate of the transferring proton was found to be close (within an error of 0.02 e) to a linear function for intermolecular distances in the 2.5–2.8 Å range. The obtained charge and charge flux dependencies highlight the electron redistribution during the proton transfer process and provide insights into the source of the high infrared (IR) intensities of stretching modes of N? H and O? H bonds undergoing hydrogen bonding. © 1994 by John Wiley & Sons, Inc.     

Rapid Prediction of the Hydrogen Bond Cooperativity in N‐methylacetamide Chains

A method is proposed to rapidly predict the hydrogen bond cooperativity in N‐methylacetamide chains. The parameters needed are obtained from the fittings to the hydrogen bonding energies in the formamide chains containing 2 to 8 monomeric units. The scheme is then used to calculate the individual hydrogen bonding energies in N‐methylacetamide chains containing 2 to 7 monomeric units. The cooperativity predicted is in good agreement with those obtained from MP2/6‐31+G** calculations by including the BSSE correction. Our scheme is further employed to predict the individual hydrogen bonding energies in larger N‐methylacetamide chains containing up to 200 monomeric N‐methylacetamide units, to which the MP2 method cannot be applied. Based on our scheme, a cooperative effect of over 170 % of the dimer hydrogen bonding energy in long N‐methylacetamide chains is predicted. The method is also applied to heterogeneous chains containing formamide, acetamide, N‐methylformamide, and N‐methylacetamide. The individual hydrogen bonding energies in these heterogeneous chains are also in good agreement with those obtained from MP2 calculations with the BSSE correction, further demonstrating that our method is reasonable.     

A scheme for rapid prediction of cooperativity in hydrogen bond chains of formamides,acetamides, and N‐methylformamides

A scheme is proposed in this article to predict the cooperativity in hydrogen bond chains of formamides, acetamides, and N‐methylformamides. The parameters needed in the scheme are derived from fitting to the hydrogen bonding energies of MP2/6‐31+G** with basis set superposition error (BSSE) correction of the hydrogen bond chains of formamides containing from two to eight monomeric units. The scheme is then used to calculate the individual hydrogen bonding energies in the chains of formamides containing 9 and 12 monomeric units, in the chains of acetamides containing from two to seven monomeric units, in the chains of N‐methylformamides containing from two to seven monomeric units. The calculation results show that the cooperativity predicted by the scheme proposed in this paper is in good agreement with those obtained from MP2/6‐31+G** calculations by including the BSSE correction, demonstrating that the scheme proposed in this article is reasonable. Based on our scheme, a cooperativity effect of almost 240% of the dimer hydrogen bonding energy in long hydrogen bond formamide chains, a cooperativity effect of almost 190% of the dimer hydrogen bonding energy in long hydrogen bond acetamide chains, and a cooperativity effect of almost 210% of the dimer hydrogen bonding energy in long hydrogen bond N‐methylformamide chains are predicted. The scheme is further applied to some heterogeneous chains containing formamide, acetamide, and N‐methylformamide. The individual hydrogen bonding energies in these heterogeneous chains predicted by our scheme are also in good agreement with those obtained from Møller‐Plesset calculations including BSSE correction. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Effect of hydrogen bonding and cooperativity on stretching force constants of formamide

Stretching force constants for formamide and its seven associated species involving two to four molecules hydrogen-bonded through linear and cyclic configurations and 10 structures containing formamide hydrogen-bonded with one to five water molecules are reported. Since ab initio calculations are rather inconvenient to perform on such big clusters and are time-consuming, CNINDO MO calculations were carried out using the gradient method. The results demonstrate, on the one hand, the feasibility of semiempirical calculations for the evaluation of trends in force constants for big clusters where generally ab initio calculations become much involved and, on the other hand, explain the effect of hydrogen bonding and cooperativity on force constants and vibrational spectra of biologically important systems composed of formamide in the condensed phase and its aqueous solutions. The C?O and N? H stretching force constants are found to reduce significantly on hydrogen bonding. The reduction in force constant is further enhanced when two cyclic dimers become associated through a linear hydrogen bond. The results indicate justification for the stabilization of the formamide structure with two cyclic dimers hydrogen-bonded together. The reduction in the force constants on hydrogen bonding also reflect the cooperativity contribution. The C?O and C? N stretching force constants for the structures corresponding to formamide in liquid and aqueous solution phases are in agreement with the experimental vibrational frequencies reported.     

Study of the formamide–methanol dimer with ab initio and density functional theory methods

For the first time, the structures and energies for the hydrogen bonding of a 1:1 complex formed between formamide and methanol molecules have been computed with various pure and hybrid density functional theory (DFT) and ab initio methods at varied basis set levels from 6‐31g to 6‐31+g(d,p). Five reasonable geometries on the potential energy surface of methanol and formamide system are considered and their relative stability is discussed. The infrared (IR) spectrum frequencies, IR intensities, and vibrational frequency shifts are reported. From the systematic studies, it is found that all the DFT methods selected here correctly compute the dimerization energies and geometries, with the B3P86 method predicting the hydrogen bond lengths relatively shorter and BPW91 yielding the interaction energies relatively lower. Finally, the solvent effects on the geometries of the formamide–methanol complexes have also been investigated using self‐consistent reaction field (SCRF) calculations with five different DFT methods at the 6‐31+g(d,p) basis set level. The results indicate that the polarity of the solvent has played an important role on the structures and relative stabilities of different isomers. Moreover, the basis set superposition error correction is critical to the interaction energies in the polar solvents. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Meshed tert-butyl gears on a quasirigid backbone

MM3-based calculations showed that bicycles and polycycles with four- to six-membered rings-components of the bi- and polycyclic backbone are sufficiently rigid to keep a syn-periplanar orientation of vicinal tert-butyl substituents. As a result of the spatial proximity of these groups, their rotation occurs in a concerted manner as demonstrated by conformational schemes that are built using MM3-derived methodology. Only correlated disrotation in saturated systems with four- to five-membered rings-components and in the adamantane system leads to isochronism for Me groups of the tert-Bu substituents (i.e., to dynamic gearing in Mislow's terms). Moreover, correlated rotation of these substituents is coupled with a change of the backbone geometry (pseudorotation) except in the most rigid bicyclo[2.1.1]hexa-2-ene system. Thus, a new type of dynamic gearing, correlated rotation–rotation–pseudorotation, is predicted for quasirigid bi- and polycycles with syn-periplanar oriented tert-Bu substituents. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1786–1794, 1998     

Density functional theory study on hydrogen‐bonded complexes of adenine with polyformamide molecules

The structures of hydrogen‐bonded complexes A–F_n (n = 2–7) of adenine with polyformamide molecules have been fully optimized at B3LYP/6‐31G(d) basis set level. All the formamide molecules prefer to be N? H proton donor rather than C? H proton donor and are favorably bound to the five‐numbered moiety of adenine. A displacement of formamide molecules to one side of adenine mean plane has happened with an increasing number of formamide molecules. An obvious effect of hydrogen‐bonding cooperativity can be seen during the complex process. The most interesting geometrical change of adenine upon the complex is the shortening of the bond C4? N6 resulting from the strengthening of the conjugation between the π system of the adenine ring and the lone pair of the nitrogen atom. An existence of weak N? H···π bonding interaction between the π system of adenine and N? H bond of F7 is found and further conformed by an natural bond orbital analysis specially carried out on A–F₇. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Young’s modulus calculations for cellulose I<Subscript>β</Subscript> by MM3 and quantum mechanics

Quantum mechanics (QM) and molecular mechanics (MM) calculations were performed to elucidate Young’s moduli for a series of cellulose I_β models. Computations using the second generation empirical force field MM3 with a disaccharide cellulose model, 1,4′-O-dimethyl-β-cellobioside (DMCB), and an analogue, 2,3,6,2′,3′,6′-hexadeoxy-1,4′-O-dimethyl-β-cellobioside (DODMCB), that cannot make hydrogen bonds reveal a considerable contribution of intramolecular hydrogen bonding to the molecular stiffness of cellulose I_β; the moduli for DMCB and DODMCB being 85.2 and 37.6 GPa, respectively. QM calculations confirm this contribution with modulus values of 99.7 GPa for DMCB and 33.0 GPa for DODMCB. However, modulus values for DMCB were considerably lower than values previously reported for cellulose I_β. MM calculations with extended cellulose chains (10–40 glucose units) resulted in modulus values, 126.0–147.5 GPa, more akin to the values reported for cellulose I_β. Comparison of the cellodecaose model, 1,4′-O-dimethyl-β-cellodecaoside (DMCD), modulus with that of its hydrogen bonding-deficient analogue, 2,3,6,2′,3′,6′-hexadeoxy-1,4′-O-dimethyl-β-cellodecaoside (DODMCD), corroborates the observed stiffness conferred by intramolecular hydrogen bonds; the moduli for DMCD and DODMCD being 126.0 and 63.3 GPa, respectively. Additional MM3 determinations revealed that modulus values were not strongly affected by intermolecular hydrogen bonding, with multiple strand models providing values similar to the single strand models; 87.5 GPa for a 7-strand DMCB model and 129.5 GPa for a 7 strand DMCD model.     

Non empirical quantum mechanical calculations of the1H,13C,15N and17O magnetic shielding constants and of the spin-spin coupling constants in formamide,hydrated formamide and N-methylformamide

The magnetic shielding constants of the different atoms of formamide, hydrated formamide and N-methylformamide are calculated by anab initio method. For the protons of formamide the measured differences between their chemical shifts are correctly reproduced by theory, provided that the molecular geometry used as input is carefully chosen. The differences between the values of the magnetic shielding constants calculated for formamide and hydrated formamide show that intermolecular hydrogen bonding produces variations of chemical shifts for all the atoms of the molecule except the formyl proton. The calculated chemical shift variations between formamide and N-methylformamide are compared to the experimental values and discussed in relation with different hydrogen bonding possibilities of the two molecules. The calculation of the contact term of the spin-spin coupling constants of formamide and hydrated formamide shows that in most cases the measured trends are satisfactorily reproduced and that the variations of these terms upon hydration are less than 3%.     

On the relative strengths of amide…amide and amide…water hydrogen bonds

We have performed Hayes—Stone intermolecular perturbation theory (IMPT) calculations on amide…water and amide…amide complexes in order to estimate the change ΔW in intermolecular interaction energy associated with the hydrogen bond exchange process amide(NH)…water+water…(OC)amideamide(NH)…(OC)amide+water…water. ΔW is found to be small and varies by almost 5 kJ/mol and in sign for the amides formamide, acetamide, N-methyl formamide and N-methyl acetamide. The main variations in the amide hydrogen bond energies occur in the electrostatic and exchange-repulsion contributions. This reflects the variation in the charge distributions of the hydrogen bonding groups between the different amides. Thus, we cannot quantify an isolated hydrogen bond strength with any great accuracy, and care must be used in extrapolating model potentials based on small model systems to peptides and proteins.     

Alcohols,ethers, carbohydrates,and related compounds. III. The 1,2-dimethoxyethane system

Ethylene glycol, its dimethyl ether, and some related compounds have been studied using the MM4 molecular mechanics force field. The MM4 calculated structural and energetic results have been brought into satisfactory agreement with a considerable number of experimental data and MP2/6-311++G(2d,2p) ab initio calculations. The heats of formation of these compounds are also well calculated. The MM4 ethylene glycol conformations in particular are in good agreement, both geometrically and in terms of energy, with those from the ab initio calculations. The corresponding dimethyl ether is of special interest, because it has been suggested that the trans-gauche conformation is unusually stable due to the hydrogen bonding of a hydrogen on a methyl group with the more distant oxygen. It is shown in the present work that while this conformation is more stable than might have been expected, the energy is adequately calculated by MM4 without using any hydrogen bonding between the Cbond;H bond and the oxygen. If such hydrogen bonding occurs, it amounts to no more than about 0.5 kcal/mol in energy, and is too small to detect with certainty. Additionally, energetic relationships in trans-1,2-dimethoxycyclohexane, 1,3,5,7-tetraoxadecalin, and 3-methoxytetrahydropyran have been studied, and the calculated results are compared with experimental information, which is adequately reproduced.     

The effect of intermolecular hydrogen bonding on the planarity of amides

Ab initio and density functional theory (DFT) calculations on some model systems are presented to assess the extent to which intermolecular hydrogen bonding can affect the planarity of amide groups. Formamide and urea are examined as archetypes of planar and non-planar amides, respectively. DFT optimisations suggest that appropriately disposed hydrogen-bond donor or acceptor molecules can induce non-planarity in formamide, with OCNH dihedral angles deviating by up to ca. 20° from planarity. Ab initio energy calculations demonstrate that the energy required to deform an amide molecule from the preferred geometry of the isolated molecule is more than compensated by the stabilisation due to hydrogen bonding. Similarly, the NH(2) group in urea can be made effectively planar by the presence of appropriately positioned hydrogen-bond acceptors, whereas hydrogen-bond donors increase the non-planarity of the NH(2) group. Small clusters (a dimer, two trimers and a pentamer) extracted from the crystal structure of urea indicate that the crystal field acts to force planarity of the urea molecule; however, the interaction with nearest neighbours alone is insufficient to induce the molecule to become completely planar, and longer-range effects are required. Finally, the potential for intermolecular hydrogen bonding to induce non-planarity in a model of a peptide is explored. Inter alia, the insights obtained in the present work on the extent to which the geometry of amide groups may be deformed under the influence of intermolecular hydrogen bonding provide structural guidelines that can assist the interpretation of the geometries of such groups in structure determination from powder X-ray diffraction data.     

Efficient treatment of out-of-plane bend and improper torsion interactions in MM2, MM3, and MM4 molecular mechanics calculations

Simple and very efficient formulas are presented for four-body out-of-plane bend (used in MM2 and MM3 force fields) and improper torsion (used in the MM4 force field) internal coordinates and their first and second derivatives. The use of a small set of bend and stretch intermediates allows for order of magnitude decreases in calculation time for potential energies and their first and second derivatives, which are required in molecular mechanics calculations. The formulas are eminently suitable for use in molecular simulations of systems with complicated bond networks. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1804–1811, 1997     

Nature of the Fe-O2 bonding in oxy-myoglobin: effect of the protein

The nature of the Fe-O2 bonding in oxy-myoglobin was probed by theoretical calculations: (a) QM/MM (hybrid quantum mechanical/molecular mechanical) calculations using DFT/MM and CASSCF/MM methods and (b) gas-phase calculations using DFT (density functional theory) and CASSCF (complete active space self-consistent field) methods. Within the protein, the O2 is hydrogen bonded by His64 and the complex feels the bulk polarity of the protein. Removal of the protein causes major changes in the complex. Thus, while CASSCF/MM and DFT/MM are similar in terms of state constitution, degree of O2 charge, and nature of the lowest triplet state, the gas-phase CASSCF(g) species is very different. Valence bond (VB) analysis of the CASSCF/MM wave function unequivocally supports the Weiss bonding mechanism. This bonding arises by electron transfer from heme-Fe(II) to O2 and the so formed species coupled then to a singlet state Fe(III)-O2(-) that possesses a dative sigma(Fe-O) bond and a weakly coupled pi(Fe-O2) bond pair. The bonding mechanism in the gas phase is similar, but now the sigma(Fe-O) bond involves higher back-donation from O2(-) to Fe(III), while the constituents of pi(Fe-O2) bond pair have greater delocalization tails. The protein thus strengthens the Fe(III)-O2(-) character of the complex and thereby affects its bonding features and the oxygen binding affinity of Mb. The VB model is generalized, showing how the protein or the axial ligand of the oxyheme complex can determine the nature of its bonding in terms of the blend of the three bonding models: Weiss, Pauling, and McClure-Goddard.     

Theoretical Study of the Interplay between Lithium Bond and Hydrogen Bond in Complexes Involved with HLi and HCN

The lithium‐ and hydrogen‐bonded complex of HLi? NCH? NCH is studied with ab initio calculations. The optimized structure, vibrational frequencies, and binding energy are calculated at the MP2 level with 6‐311++G(2d,2p) basis set. The interplay between lithium bonding and hydrogen bonding in the complex is investigated with these properties. The effect of lithium bonding on the properties of hydrogen bonding is larger than that of hydrogen bonding on the properties of lithium bonding. In the trimer, the binding energies are increased by about 19 % and 61 % for the lithium and hydrogen bonds, respectively. A big cooperative energy (?5.50 kcal mol^?1) is observed in the complex. Both the charge transfer and induction effect due to the electrostatic interaction are responsible for the cooperativity in the trimer. The effect of HCN chain length on the lithium bonding has been considered. The natural bond orbital and atoms in molecules analyses indicate that the electrostatic force plays a main role in the lithium bonding. A many‐body interaction analysis has also been performed for HLi? (NCH)_N (N=2–5) systems.