Potential Energy Hypersurface Research Articles

Theoretical study of helical structure caused by chirality of cysteine dimer

In this work we report a theoretical study of the helix structure and chiral discrimination on the interactions between the chiral cysteine–cysteine. Two reasonable geometries on the potential energy hypersurface of the cysteine–cysteine system are considered with the global minimum. Accurate geometric structures, relative stabilities, harmonic vibrational frequencies, and infrared (IR) intensities were investigated. To take into account the water solvation effect, the Onsager model within the self-consistent reaction field (SCRF) method and the polarized continuum (PCM) method were used to evaluate the interaction energy, ΔGsolv at the same level employed in the gas phase. The results indicate that the polarity of the solvent plays an important role in the structures and relative stabilities of different isomers. Computational results indicate that the global minimum should be conformer I regardless of whether in the gas phase or in aqueous solution, which differs from previous theoretical reports. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Density Functional Theory Study of the Jahn−Teller Effect and Spin−Orbit Coupling for Copper and Gold Trimers

The Born-Oppenheimer potential energy hypersurfaces of copper and gold trimers were calculated using density functional theory with an analytic potential. The calculated Jahn-Teller distortion energies, pseudorotation barriers, dissociation, and isomerization energies for the two trimers are discussed. Global minima from the surfaces were optimized using the density functional theory method as well as the coupled cluster-singles-doubles-with-triples energies technique. The agreement of the optimized structures with the analytic potential was very good. The Mulliken population analysis compared favorably with the experimental electron spin resonance results. Spin-orbit coupling was subsequently included and the effect was significant for gold, but negligible for copper. The spin-orbit effect suppressed the Jahn-Teller distortion of the gold trimer, and the potential surface with the spin-orbit effect included was also obtained. The spin-orbit splitting for the D(3h) geometry of the gold trimer was in excellent agreement with the most recent infrared spectroscopic results.

Pople's Gaussian‐3 model chemistry applied to an investigation of (H2O)8 water clusters

AbstractThe Gaussian‐3 method developed by Pople and coworkers has been used to calculate the free energy of neutral octamer clusters of water, (H2O)8. The most energetically stable structures are in excellent agreement with those determined from experiment and those predicted from previous high‐level calculations. Cubic structures are favored over noncubic structures over all temperature ranges studied. The D2d cubic structure is the lowest free energy structure and dominates the potential energy and free energy hypersurfaces from 0 K to 298 K. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Neural Network Models of Potential Energy Surfaces: Prototypical Examples.

Neural networks can be used generate potential energy hypersurfaces by fitting to a data set of energies at discrete geometries, as might be obtained from ab initio calculations. Prior work has shown that this method can generate accurate fits in complex systems of several dimensions. The present paper explores fundamental properties of neural network potential representations in some simple prototypes of one, two, and three dimensions. Optimal fits to the data are achieved by adjusting the network parameters using an extended Kalman filtering algorithm, which is described in detail. The examples provide insight into the relationships between the form of the function being fit, the amount of data needed for an adequate fit, and the optimal network configuration and number of neurons needed. The quality of the network interpolation is substantially improved if gradients as well as the energy are available for fitting. The fitting algorithm is effective in providing an accurate interpolation of the underlying potential function even when random noise is added to the data used in the fit.

Povel isomers of hexasulfur: Prediction of a stable prism isomer and implications for the thermal reactivity of elemental sulfur.

High-level ab initio molecular orbital calculations were employed to explore the potential energy hypersurface of hexasulfur, S(6). Twelve isomeric structures of S(6) have been identified: two unbranched rings (chair and boat), one trigonal prism of D(3h) symmetry, two singly branched rings (S(5)double bondS), three triplet chains, one singlet chain, and three doubly branched rings (Sdouble bondS(4)double bondS). The prism structure is essentially a cluster of three S(2) molecules connected via a six-center pi(*)-pi(*)-pi(*) interaction. It is by 51 kJ mol(-1) less stable than the lowest-energy chair form. The reactions to generate the boat, the prism, and the singly branched isomers from the chair form are predicted to have lower barriers than the ring opening reaction of cyclo-S(6), which requires an activation energy of 149 kJ mol(-1). The prism and singly branched isomers are found to be more reactive species than the chair form and they are potential sources of S(2) in chemical reactions involving elemental sulfur.

Calculation of the transport properties of carbon dioxide. III. Volume viscosity, depolarized Rayleigh scattering, and nuclear spin relaxation.

Transport properties of pure carbon dioxide have been calculated from the intermolecular potential using the classical trajectory method. Results are reported in the dilute-gas limit for volume viscosity, depolarized Rayleigh scattering, and nuclear spin relaxation for temperatures ranging from 200 to 1000 K. Three recent carbon dioxide potential energy hypersurfaces have been investigated. Calculated values for the rotational collision number for all three intermolecular surfaces are consistent with the measurements and indicate that the temperature dependence of the Brau-Jonkman correlation is not applicable for carbon dioxide. The results for the depolarized Rayleigh scattering cross section and the nuclear spin relaxation cross section show that calculated values for the generally more successful potentials differ from the observations by 9% at about 290 K, although agreement is obtained for nuclear spin relaxation at about 400 K.

Doppler-limited FTIR spectrum of the v 3(a′)/v 8 (a″) Coriolis resonance dyad of CHC1F2: analysis and comparison with ab initio calculations

The Doppler-limited FTIR spectrum of the band system in the region 1070–1170 cm−1 (Doppler width ≈ 0.0015 cm−1, FWHM) was measured with our new Bruker IFS 120 HR Zürich prototype (ZP2001) spectrometer. This instrument allows for an unapodized resolution of 0.0007 cm−1 (FWHM). This is the highest resolution realized so far by a commercial FTIR spectrometer system. It allows high-resolution analysis of the room temperature spectra of the strongly coupled modes v 3(a′) and v 8 (a″), corresponding to the symmetric and antisymmetric CF-stretching vibrations, including also further couplings not analysed previously. The present analysis is based on effective rotational Hamiltonians for the v 3=1 and v 8=1 states, including all terms up to sextic, and involves the full first-order Coriolis interaction operator Consideration of both the and first-order Coriolis terms proved essential in order to obtain good line-by-line agreement between observed and calculated rovibrational structures over the full band system. In addition, the analysis of two local resonances allowed us to determine the vibrational wavenumbers of the 3v 9 and v 6+2v 9) levels with good accuracy. We describe possible approaches to the analysis. The final analysis involves both chlorine isotopomers and includes all hybrid components which are allowed by symmetry. It results in the band centres cm−1, cm−1, cm−1 and (v 6+2v 9)0=1144.32 cm−1, where the last digit is rounded, relating to the first digits differing in two types of analyses and data sets from our work. The main Coriolis interaction parameters are cm−1 and cm−1. In addition, smaller interactions could also be determined quantitatively. Our results are in essential agreement with the original analysis of Luckhaus and Quack (1989, Molec. Phys., 68, 745), which was, however, much less complete and precise. We discuss the comparison of different types of analyses and further recent results on this band system. We report ab initio calculations for this molecule on the MP2 level of theory with an aug-cc-pVDZ or an aug-cc-pVTZ basis set. Various subspaces of the potential energy and electric dipole moment hypersurface have been calculated in reduced normal coordinates including up to three dimensions. With these hypersurfaces we determined the corresponding vibrational absorption spectra, comprising transition wave- numbers and intensities. An analysis of the vibrational levels with an effective Hamiltonian was used to derive anharmonic constants. We also derived Coriolis coupling constants and integrated absorption intensities ab initio, which are compared with the present and previous experimental and theoretical results. The complete set of data as analysed is tabulated in Appendix A of this publication [61].

Density Functional Theory Study of the Hydrogen-Bonding Interaction of 1:1 Complexes of Alanine with Water

The hydrogen bonding of 1:1 complexes formed between alanine and water molecules has been completely investigated in the present study using density functional theory, method B3LYP at varied basis set levels from 6-31G to 6-311++G(d,p) and the second-order Møller−Plesset perturbation method at the 6-31++G(d,p) level. Eight reasonable geometries on the potential energy hypersurface of the alanine and water system are considered with the global minimum. The optimized geometric parameters and interaction energies for various isomers at different levels are estimated. The infrared spectrum frequencies, IR intensities, and vibrational frequency shifts are reported. Finally, the solvent effects on the geometries of the alanine−water complexes have also been investigated using self-consistent reaction-field calculations at the B3LYP/6-311++G(d,p) level. The results indicate that the polarity of the solvent plays an important role in determining the structures and relative stabilities of different isomers.

Density Functional Theory Study of the Hydrogen Bonding Interaction of 1:1 Complexes of Formamide with Glycine

The hydrogen bonding of 1:1 complexes formed between formamide and glycine molecule has been completely investigated in the present study using density functional theory (DFT) method at varied basis set levels from 6-31G to 6-31 1++G(2d,2p). Twelve reasonable geometries on the potential energy hypersurface of formamide and glycine system are considered with the global minimum, 10 of which have a cyclic double-hydrogen-bonded structure and the other two have a one-hydrogen-bonded structure. The optimized geometric parameters and interaction energies for various isomers at different levels are estimated. The infrared spectrum frequencies, IR intensities and the vibrational frequency shifts are reported.

Pharmacophore Fragment-Based Prediction and Gas-Phase ab Initio Optimization of Carvedilol Conformations

This current communication gives the results of a novel computational molecular method of selecting, from a vast number of possible conformations, the dominant low-energy states of a large molecule by dividing it into separately analyzable structure-activity fragments. Carvedilol is a cardiovascular drug of proven efficacy with multiple molecular targets: it acts as a nonselective β-adrenoceptor (β 1 and β 2 ) and selective α 1 -adrenoceptor antagonist, an antioxidant able to reduce reactive oxygen species (ROS)-mediated oxidative stress, a beneficial modulator of cardiac electrophysiological properties (K + and Ca 2 + ion channels), a multifaceted cardioprotector, and novel antifibrillar agent able to inhibit amyloid-beta (Aβ) fibril formation. Given carvedilol's varied pharmacodynamic profiles, and the fact that a thorough analysis of its potential energy hypersurface (PEHS) has not yet been performed, an original molecular fragmentation method was developed to reveal carvedilol's low-energy states, to divulge their relevance to its biological activity. Multidimensional conformational analysis (MDCA) leads to a total of 177 147 (3 1 1 ) conformational possibilities, whereas fragmentation studies predict 240 gas-phase conformations. Structural predictions were tested on protonated R-carvedilol with gas-phase molecular orbital (MO) computations of PEHS minima at the restricted Hartree-Fock (RHF) (RHF/3-21G) level of theory, using the Gaussian 98 software program. Computation of the 240 predicted (input) carvedilol conformations revealed 121 converged (i.e., fully optimized) structures, of which nine possessed a conformer relative energy of <4 kcal/mol. Seven of these nine conformers possess a unique tetra-centric (four-centered) spiro-type structure that is composed of two rings (six- and eight-membered) enclosed by two O...H-N hydrogen bonds (H-bonds) that are connected via the protonated N atom in the side chain of carvedilol; this conformation is largely determined by the carbazole-containing pharmacophore (Fragment A) of carvedilol. In regard to the utility of the rational molecular fragmentation method used to predict and optimize the carvedilol structures, it is determined that 8 of the 11 torsional angles were accurately predicted (72.7%), according to torsional angle conformation distribution. The strength of this fragmentation method relies on full MDCA optimization of the individual fragments, which are then used to predict the carvedilol conformations. As such, the predicted inputs possess an inherent degree of energy minimization and, thus, are able to provide a better hypothesis of relevant sections of the carvedilol surface versus a random sampling of the PEHS. The elucidation of carvedilol's conformational identity greatly aids the full molecular understanding of carvedilol's adrenoceptor binding structure and carvedilol's involvement, at the molecular level, in ameliorating pathological states such as oxidative stress and Alzheimer's disease.

Ab initio calculation of parity‐violating potential energy hypersurfaces of chiral molecules

AbstractWe introduce the explicit concept of parity‐violating potential energy hypersurfaces which govern the rotation–vibration tunneling dynamics as well as the time‐dependent parity violation in chiral molecules. Calculations are reported for sections of the hypersurfaces of H2O2 and H2S2 at various levels of electroweak quantum chemistry, including CIS‐RHF, CIS‐LR, and CASSCF‐LR. Important findings concern the observed increase of the parity‐violating potentials (Epv) with increasing bond lengths rOO and rSS, which is to some extent physical and partly a consequence of the only approximate electronic wavefunction and perturbational treatment, the confirmation of lines and surfaces of “accidentally” zero Epv at chiral geometries, and the absence of a precise, simple scaling law for observables such as the measurable parity‐violating energy difference between enantiomers ΔEpv. The latter is due to the complicated geometry dependent Epv, although a rough scaling on the order of Z(5±1) with nuclear charges of the two heavy centers can be confirmed. The results are discussed in relation to possible experiments on molecular parity violation. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

An ab initio study on the mechanism of the F + O 3 → FO + O 2 reaction: comparative reactivity study along the isoelectronic NH 2, OH and F radicals series

The title reaction has been theoretically studied by using MP2, QCISD, QCISD(T), CCSD(T), CASSCF, and CASPT2 methods with various basis sets. At single-reference MP2 and QCISD levels of theory, the potential energy hypersurface (HPES) shows a two-step reaction mechanism through two transition states (TS1 and TS2) and an intermediate (Int). However, the multiconfigurational CASSCF HPES shows a one-step reaction mechanism, as was previously found for the NH 2 + O 3 and OH + O 3 reactions. The results show that the reactivity of the isoelectronic series of NH 2, OH, and F radicals increases from the amino radical to the fluorine atom.

Density Functional Theory Study on the Initial Step of the Permanganate Oxidation of Substituted Alkynes

The initial step of the oxidation of alkynes by permanganate has been studied by DFT (B3LYP/6-311+G(d,p)) calculations. The influence of electron-withdrawing as well as electron-donating substituents was explored. The singlet and triplet potential energy hypersurfaces (PES) for a concerted [3 + 2] and a stepwise [2 + 2] mechanism were investigated. The crossing point between the singlet and triplet PES has been identified. The reaction proceeds via a [3 + 2] mechanism on the singlet PES with free energy activation barriers (ΔG298) between 18.4 and 28.9 kcal/mol, while the lowest lying identified state is a reactive triplet intermediate. Available experimental and computed data are in good agreement. For the [2 + 2] case a reaction on the triplet surface would be preferred over the singlet, but both pathways lay well above the [3 + 2] pathway.

Calculation of the transport properties of carbon dioxide. II. Thermal conductivity and thermomagnetic effects.

The transport properties of pure carbon dioxide have been calculated from the intermolecular potential using the classical trajectory method. Results are reported in the dilute-gas limit for thermal conductivity and thermomagnetic coefficients for temperatures ranging from 200 K to 1000 K. Three recent carbon dioxide potential energy hypersurfaces have been investigated. Since thermal conductivity is influenced by vibrational degrees of freedom, not included in the rigid-rotor classical trajectory calculation, a correction for vibration has also been employed. The calculations indicate that the second-order thermal conductivity corrections due to the angular momentum polarization (< 2%) and velocity polarization (< 1%) are both small. Thermal conductivity values calculated using the potential energy hypersurface by Bukowski et al. (1999) are in good agreement with the available experimental data. They underestimate the best experimental data at room temperature by 1% and in the range up to 470 K by 1%-3%, depending on the data source. Outside this range the calculated values, we believe, may be more reliable than the currently available experimental data. Our results are consistent with measurements of the thermomagnetic effect at 300 K only when the vibrational degrees of freedom are considered fully. This excellent agreement for these properties indicates that particularly the potential surface of Bukowski et al. provides a realistic description of the anisotropy of the surface.

Theoretical study on the hydrogen bond interaction between diacetamide and methanol

The hydrogen bonding of 1:1 complexes formed between diacetamide and methanol molecule have been completely investigated in the present study using density functional theory and second order Moller–Plesset perturbation (MP2) method. Various basis sets from 6-31G to 6-311++G** have been employed to determine the equilibrium structure of the interacting complexes. Three reasonable geometries on the potential energy hypersurface of diacetamide with methanol system are considered with the global minimum being a cyclic double-hydrogen bonded structure. The optimized geometric parameters and interaction energies for various isomers at different levels are estimated showing that the two carbonyl groups have about the same proton acceptor ability. Special attention was paid to the basis set superposition error and zero-point energy corrections that were not given appropriate attention in previous studies. Finally, the solution phase studies are also carried out using the Onsager reaction field model at B3LYP/6-311++G** level for the hydrogen-bonded complex of diacetamide with methanol. The results indicate the polarity of the solvent has played an important role on the structures and relative stabilities of different isomers or the proton acceptor ability of two carbonyl groups.

Potential energy curves, surfaces and hypersurfaces. A model to follow and understand the conformational transformations in amino acids

Applicability of two different concepts has been investigated for the exploration of conformational properties of flexible molecules, such as α- and β-amino acids. The first concept is based on multidimensional conformation analysis (MDCA), while the second one is calculation of potential energy curves, surfaces and hypersurfaces (PEC, PES, PEHS). In this study, we investigated four different molecules by ab initio molecular computations. The obtained PECs for histidine and methionine, and PEHS for β-alanine were evaluated and compared to PECs of smaller molecules (ethylimidazole and methyl–ethyl–thioether), with similar functional groups. Prediction of the minima, (i.e. MDCA) worked well for all molecules, however, it generally overestimates the number of minima in molecular systems different from alkanes. Histidine and methionine had several unpredicted minima due to spatial proximity of structurally distant atoms. In addition, MDCA was not able to predict the orientation of the minima of β-Ala. However, our results indicate that MDCA is a reliable tool in exploring molecular conformational properties.

Peptide models XLII. Ab initio study on conformational changes of N-formyl- l-histidinamide caused by protonation or deprotonation of its side chain

The imidazole ring in the side chain of N-formyl- l-histidinamide may have four forms of protonation, two tautomeric neutral forms and two charged forms. The four molecules, though they only differ in the protonation state of the imidazole nitrogen atoms, have potential energy hypersurfaces of significantly different topology; i.e. the hypersurfaces have minima at different ϕ and ψ values of the peptide backbone. A complete conformational library of the above mentioned single amino acid dipeptide model [J. Mol. Struct. (Theochem) 583 (2002) 117; J. Mol. Struct. (Theochem) 583 (2002) 199] is evaluated to map the possible conformational changes caused by protonation or deprotonation. It was determined, that a protonation or deprotonation itself can induce significant conformational changes involving the side chain, the backbone or both. Such conformational changes can lower the relative energy by up to 10 kcal mol −1. On acquiring a net positive charge α-helical ( α L) and polyproline II ( ε L) structures are willing to adopt extended ( β L) and inverse γ-turn ( γ L) conformation, respectively, while acquiring a net negative charge by an extended ( β L) conformer results in the formation of α-helical ( α L) or inverse γ-turn ( γ L) structures. The formation of a charged entity, is frequently accompanied by conformational changes, in contrast to the process of neutralization, that is seldom followed by significant modification of torsional angles.

Density functional theory study of the hydrogen bonding interaction complexes of hydrogen peroxide with glycine

The hydrogen bonding of 1:1 complexes formed between hydrogen peroxide and glycine molecule have been completely investigated in the present study using density functional theory method at varied basis set levels from 6-31g to 6-311++g(2d,2p). For comparison, we have also used the second-order Moller–Plesset Perturbation method at the 6-31+g(d,p) level. Five reasonable geometries on the potential energy hypersurface of hydrogen peroxide and glycine system are considered with the global minimum being a cyclic double-hydrogen bonded structure. The optimized geometric parameters and interaction energies for various isomers at different levels are estimated. The infrared spectrum frequencies, IR intensities and the vibrational frequency shifts are reported.

The case of a very weakly π-hydrogen bonded fluorobenzene–methanol complex. A gradient-corrected density functional and MP2 study of the ground electronic state potential energy surface

The π-hydrogen bonded minimum on the standard and the counterpoise-corrected B3LYP, PBE1PBE/6-31++G(d,p) and MP2/6-31++G(d,p) potential energy hypersurfaces of the methanol–fluorobenzene dimer is studied. Anharmonic OH stretching frequency shift calculated at MP2 level is in excellent agreement with the experiment (20.5 vs. 20 cm −1), while all DFT values are too large, the B3LYP results being superior to the PBE1PBE ones, especially for the counterpoise-corrected PES. The OH stretching vibrational potentials are analyzed with the charge field perturbation methodology. Interaction and dissociation energy calculations, along with the NBO and AIM analyses of the MP2 and Kohn–Sham densities are carried out as well.

Study of the diacetamide–water dimer with ab initio and density functional theory methods

Abstract The hydrogen bonding of 1:1 complexes formed between diacetamide and water molecule have been completely investigated in the present study using density functional theory and second order Moller–Plesset perturbation (MP2) method. The large basis sets 6-311++g(d,p) and 6-311++g(2d,2p) have been employed to determine the equilibrium structure of the interacting complexes. All the results reveal a planar configuration of the amide groups and a tendency of the CH 3 group to eclipse the CO bond for the geometry of the isolated diacetamide molecule. Calculations at different theoretical levels indicate that cis – trans configuration is the most stable isomer in both gas phase and solution phase. Three reasonable geometries on the potential energy hypersurface of diacetamide with water system are considered with the global minimum being a cyclic double-hydrogen bonded structure. The optimized geometric parameters and interaction energies for various isomers at different levels are estimated and a result that two carbonyl groups have about the same proton acceptor ability has been obtained. Finally, the solution phase studies are also carried out using the onsager reaction field model at B3LYP/6-311++g** level for the isolated diacetamide molecule and the hydrogen-bonded complex of diacetamide with water. The results indicate the polarity of the solvent has played an important role on the structures and relative stabilities of different isomers.