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In view of the observation that the concentration of hydrogen sulfide in brains with Alzheimer's disease (AD) is lower than that in normal brains and in line with our previous studies indicating that additional content in the aqueous environment (milieu) of a peptide can change its local energetic preference from a polyproline II (P) to a β conformation (and therefore its tendency to form the β-chain structures that lead to the amyloid plaques associated with the disease), we have studied the effect of H2 S concentration on such propensity in a simple model peptide, the alanine dipeptide (ADP). The two concentration states are represented by ADP(H2 O)18 (H2 S) and ADP(H2 O)18 (H2 S)2 . Ab initio calculations of these structures show that the lowest energy of the former is a β conformation while that of the latter is a P, mirroring the observed AD results and strengthening our proposal that amyloid diseases are better viewed in the context of a protein milieu-folding paradigm.

As we have previously shown, the predominance of the polyproline II conformation in the circular dichroism spectra of aqueous polypeptides is related to its lower energy than that of the beta conformation. To test whether this is still the case in the presence of additional components in the medium, we have calculated the energy difference between these two conformations in an alanine-dipeptide/12-water system without and with the addition of an HCl molecule. We find in the latter case that the beta conformer is of lower energy than the polyproline II. Energy profiles near the minima in both cases also permit conclusions about the relative entropies of these structures. These results emphasize the importance of considering the peptide-plus-medium state as the relevant entity in determining the structural properties of such systems. Such an inversion could be relevant to the formation of amyloid and could thus lead to new strategies for studying its role in the development of neurodegenerative diseases. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 305-311, 2016.

Extending our earlier analogous study of the alanine dipeptide (ADP), we have now analyzed the effect of the external environment on the polyproline II (P) and β relative energies, the P/β propensity, of the alanine tripeptide (ATP). Ab initio calculations of ATP(H2O)19 and ATP(H2O)19(HCl) exhibit the same propensity inversion as in ADP: in the pure-water case the PP conformation is favored while the addition of the HCl molecule results in the ββ conformation being of lower energy. A comparison, following an intermediate insertion and departure of an HCl molecule, shows that the energy of a hydrogen-bonded (H2O)19βATP::βATP(H2O)19 structure is lower than that of the sum of two separate PP systems, i.e., that the aggregated state of the peptide is favored. This arises from the basic physical response to their total environmental influences. Questions about quantitative results from molecular dynamics simulations, obviously needed to analyze longer chains and other side chains, are addressed via rigid-water calculations. The desirability of basing studies of amyloid formation on our proposed alternative milieufolding paradigm is discussed.

Although subsequent studies have provided extensive support for the 1968 Tiffany and Krimm proposal (Biopolymers 6, 1379) that the polyproline II (PPII) conformation is a significant component of the structure of unordered polypeptide chains, two issues are still not fully resolved: the PPII persistence length in a chain and the source of its relative stability with respect to the β-conformation. We examine the latter question by studying the B97-D/6-31++G** energy, in the absence and presence of a reaction field, of the alanine dipeptide hydrated by various amounts of explicit waters and resolving this into its three components: the energies of the individual solvated peptides and water structures plus the interaction energy involving them. We find that the relative stability of the PPII conformation is determined mainly by the difference in the interaction energies of the water structures in the near-peptide layers. © 2012 Wiley Periodicals, Inc. Biopolymers 97: 789–794, 2012.

As we have previously shown, the predominance of the polyproline II conformation in the circular dichroism spectra of aqueous polypeptides is related to its lower energy than that of the beta conformation. To test whether this is still the case in the presence of additional components in the medium, we have calculated the energy difference between these two conformations in an alanine-dipeptide/12-water system without and with the addition of an HCl molecule. We find in the latter case that the beta conformer is of lower energy than the polyproline II. Energy profiles near the minima in both cases also permit conclusions about the relative entropies of these structures. These results emphasize the importance of considering the peptide-plus-medium state as the relevant entity in determining the structural properties of such systems. Such an inversion could be relevant to the formation of amyloid and could thus lead to new strategies for studying its role in the development of neurodegenerative diseases. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 305-311, 2016.

A polarization model for molecular mechanics energy functions is developed that is based on a local group paradigm, namely the polarizability of a rigid substructure of covalently connected atoms. Axes at a "diffuse" site within the group define an anisotropic local group polarizability as well as hyperpolarizability. The theoretical basis for this model is presented, and its performance is described through applications to water, alkanes, and N-methylacetamide. The excellent agreement with quantum mechanical electric potentials and molecular polarizabilities indicates that this model must be considered an important candidate for the inclusion of polarization into such force fields. The ab initio-based spectroscopically determined force field (SDFF) protocol for the calculation of parameters assures that, in addition to structures and energies, forces will be accurately modeled.

Conformational energy calculations indicate that the peptide backbones of the low-energy conformations of the cyclized dipeptide derivatives cyclo (L-alanyl-L-alanyl-epsilon-aminocaproyl) and cyclo (L-alanyl-D-alanyl-epsilon-aminocaproyl) are constrained to form beta-bends of types I + III and II, respectively. Thus, the two compounds can serve as models for the spectroscopic properties of beta-bends of these types. The coupling constants obtained from 1H n.m.r. spectra in DMSO-d6 are consistent with the dihedral angeles of the computed lowest-energy conformations. Differences in 13C chemical shifts between the two compounds can be correlated with differences in shielding by C=O groups in bends of various types. 1H and 13C chemical shifts suggest association of cyclo (L-Ala-L-Ala-Aca) but not of cyclo (L-Ala-D-Ala-Aca) in dimethylsulfoxide. The different tendencies to associate can be explained in terms of the difference in conformation. The circular dichroism spectra of the two compounds are quite different. In methanol, trifluoroethanol and water, the L-Ala-L-Ala derivative has a positive extremum near 190 nm and two negative extrema near 206 and 220 nm, whereas the L-Ala-D-Ala derivative has a positive extremum at about 203 nm and negative extrema at about 187 and 229 nm. The spectra can be used to estimate the contribution of various bend types in a related series of compounds. A normal mode analysis of the vibrations of the computed low-energy conformations was compared with solid state infrared and Raman spectra, in order to determine the predominant conformations. The bend types determined by this comparison fully agree with the predictions of the theoretical computations for both derivatives.

Normal mode calculations have been carried out on three low-energy structures of gramicidin S obtained from conformational energy calculations. When the results on the amide modes are compared with observed bands in the infrared and Raman spectra of crystalline gramicidin S and its N-deuterated derivative, one of the structures is clearly disfavored. Of the other two, one is slightly favored, and it corresponds to the lowestenergy structure obtained from the energy calculations. Spectra from solutions in DMSO and CH3 OH suggest that the molecular conformation is essentially retained in these solvents.

Normal mode calculations have been carried out on three low-energy structures of gramicidin S obtained from conformational energy calculations. When the results on the amide modes are compared with observed bands in the infrared and Raman spectra of crystalline gramicidin S and its N-deuterated derivative, one of the structures is clearly disfavored. Of the other two, one is slightly favored, and it corresponds to the lowest-energy structure obtained from the energy calculations. Spectra from solutions in DMSO and CH3 OH suggest that the molecular conformation is essentially retained in these solvents.

The normal modes have been calculated for three kinds of low energy gamma-turn structures resulting from recent conformational energy calculations by Némethy. Frequencies have been computed for a gamma-turn, a mirror-related gamma-turn, and an inverse gamma-turn of CH3-CO-(L-Ala)n-NH-CH3, with n = 3 and n = 5, and for certain 14C and 15N derivatives of the n = 3 molecule. Correlations are evident between amide frequencies and gamma-turn structures, and it is found that only amide I modes of peptide groups in the turn are relatively insensitive to the lengths of attached chains.

Ab initio normal mode calculations have been performed on isolated alanine di- through octa-(i.e., blocked) peptides in uniform alphaR, beta, and polyproline II conformations to determine how the CalphaDalpha stretch mode, which has been proposed as a possible determinant of the varphi,psi conformation at the Calpha atom (Mirkin, N. G.; Krimm, S. J. Phys. Chem. A 2004, 108, 10923), depends on conformation and sequence length. This set of frequencies, including results on some kinked structures, demonstrates that such a discrimination is likely to be possible through experimental observations of peptides synthesized with successive deuteration at the Halpha sites, on the basis of at least three properties: the values of the frequency at the first residue, the pattern of successive frequency differences, and the frequency differences between the first and last residues.

The stability of a general molecular dynamics (MD) integration scheme is examined for simulations in generalized (internal plus external) coordinates (GCs). An analytic expression is derived for the local error in energy during each integration time step. This shows that the explicit dependence of the mass-matrix on GCs, which makes the system's Lagrange equations of motion nonlinear, causes MD simulations in GCs to be less stable than those in Cartesian coordinates (CCs). In terms of CCs, the corresponding mass-matrix depends only on atomic masses and thus atomistic motion is subject to the linear Newton equations, which makes the system more stable. Also investigated are two MD methods in GCs that utilize nonzero elements of the vibrational spectroscopic B-matrices. One updates positions and velocities in GCs that are iteratively adjusted so as to conform to the velocity Verlet equivalent in GCs. The other updates positions in GCs and velocities in CCs that are adjusted to satisfy the internal constraints of the new constrained WIGGLE MD scheme. The proposed methods are applied to an isolated n-octane molecule and their performances are compared with those of several CCMD schemes. The simulation results are found to be consistent with the analytic stability analysis. Finally, a method is presented for computing nonzero elements of B-matrices for external rotations without imposing the Casimir-Eckart conditions.

Physical accuracy in MM calculations requires maximally correct forces in addition to structures and energies. This requires inclusion of charge and polarizability fluxes in the energy function. Using our spectroscopically determined force field, which is designed to include these, we present three examples of the improved physical predictions that result from the incorporation of charge fluxes: the reproduction of the water angle opening on going from the isolated molecule to the liquid, the reproduction of the ψ peptide torsion potential with only a single threefold (almost zero barrier) Fourier term, and reproduction of the quantum-mechanical MD ϕ, ψ map of a dipeptide analog.

In a previous paper [J. Phys. Chem. A 109 (2005) 5608], we developed a charge density treatment of the electrical interaction between a molecule and point charges, which was applied to the electrical component of the hydrogen-bond interaction in donor-molecule/acceptor-charge model systems. This approach has two important advantages: it is very accurate by avoiding the deficiencies of multipole treatments, and it provides a complete electrostatic, polarization, and hyperpolarization description of interaction forces as well as energies. In this paper, we present a more general treatment of the theory and an extended demonstration of the physical accuracy of this approach, and we explore the geometric dependence of the parameters of this treatment (charge density, linearly and non-linearly induced charge density, and their derivatives) for a series of fluoromethane molecules interacting with a two-site FH. We find that, for variation in linear separation along the C–H⋯F–H line, these parameters are very well represented by a αr−β dependence, α and β being constants. For a large number of configurations, the relative rms between the predicted energies and atomic forces and the ab initio calculated values is ∼3–5%. This study opens the way to a more complete description of the three-dimensional characterization of these parameters.

Computational tools and the underlying theoretical framework for direct simulation of complex molecular behavior have become extremely sophisticated. Nevertheless, further improvements in speed, accuracy, and usability can be expected. The future application of these tools to chemical, biochemical, and materials problems needs to be critically considered in any new developmental work, for it is important to understand the role of detailed information all the way down to the quantum mechanical level. To what extent information from the most fundamental treatments, particularly molecular electronic structure theory, needs to be incorporated should be assessed. This report offers several perspectives on the connections and developments that exist now and that may be ahead.

The theory of conventional constrained molecular dynamics (MD) simulations is reexamined based on a projection operator approach. A new algorithm, named WIGGLE, is presented for MD simulations with internal constraints. At each time step, the algorithm utilizes the constrained accelerations derived from velocity adjustments to satisfy the hidden constraints, and provides both initial and final constrained values that are almost an order of magnitude closer to the desired values than does RATTLE. Its performance is compared with those of RATTLE and SHAKE for an octane molecule. Also presented are a formalism to additionally constrain the angular momentum about the center of mass and an expression for the local energy drift during each integration time step.

The theory of dipole polarization as used in molecular mechanics energy functions is analyzed, and the difference in induction energy between an iterative (self-consistent) and non-iterative (one-step) scheme is derived. It is concluded that this difference is bound to be small in most cases, so that a non-iterative polarization model can be expected to give a satisfactory representation of the induction energy. This is demonstrated with examples of configurations of water molecules. The advantages of a one-step procedure are discussed.

The NH stretch (s) frequency, v(NH), in peptides and proteins, as in many amide group hydrogen bond (HB) systems, is used as an indicator of the presence and strength of the bond. This is based on the concept that v(NH) is associated with an essentially localized mode whose frequency is influenced only by the HB interaction. We examine this assumption through ab initio studies of N-methylacetamide (NMA) and of 78 conformers of the alanine dipeptide (ADP). Based on our recent studies of nitrogen pyramidalization in NMA (J. Phys. Chem. A 2003, 107, 1825), we find that such nonplanarity, whether deriving from a nonplanar peptide group or only from a steric constraint, results in an increase in the NH bond length, r(NH), and thus in a decrease in v(NH). This is accompanied by changes in other internal coordinates that make small contributions to this mode, emphasizing that although NH s is a highly localized mode it is not completely so. It is not surprising, therefore, to find that changes in the environment of the NH group, such as exist in the ADP conformers, lead to variations in v(NH) even in the absence of traditional HB configurations. The ADP results permit an analysis of these effects and also illustrate the important role, as we recently emphasized (J. Phys. Chem. A 2002, 106, 11663), of electrical interactions in affecting r(NH) and thus v(NH). We show how the increased strength of this interaction in ADP conformers with "standard" HBs leads, through the much larger induced dipole derivative, to the large increase in infrared intensity of NH s bands in such structures.

We review our methodology for producing physically accurate potential energy func- tions, particularly relevant in the context of Lifson's goal of including frequency agreement as one of the criteria of a self-consistent force field. Our spectroscopically determined force field (SDFF) procedure guarantees such agreement by imposing it as an initial constraint on parameter optimization, and accomplishes this by an analytical transformation of ab initio "data" into the energy function format. After describing the elements of the SDFF protocol, we indicate its implementation to date and then discuss recent advances in our representation of the force field, in particular those required to produce an SDFF for the peptide group. © 2003 Wiley Periodicals, Inc. Biopolymers 68: 383-394, 2003

Pyramidalization at the peptide group nitrogen atom is analyzed using N-methylacetamide (NMA) as a model molecule. Mutually orthogonal peptide CN torsion and NH out-of-plane bend coordinates are necessary for a correct description of the energetics of nonplanar deformations of the peptide group. Using such coordinates, ab initio calculations at the MP2/6-31++G(d,p) level of theory show that the energy minimum of the NH out-of-plane bend angle shifts significantly away from zero for nonzero CN torsion angles. Not being due to nonbonded interactions alone, this energy behavior needs to be taken explicitly into account in molecular mechanics force fields. By use of different schemes for calculating potential-derived atomic charges, the charge distribution of NMA was also investigated in connection with the pyramidalization. Large variations in the charges were found as a function of the NH out-of-plane angle. These could not be reproduced only by polarization through the (molecular mechanics) electric field....

A new treatment is presented for calculating the molecular mechanics intramolecular atom–atom Coulomb potential energy. It is shown that the standard method of only including charge pairs in the 1,4 and higher positions is unphysical, and leads to erratic electrostatic relative energies especially when the atomic charges are allowed to vary during a simulation. The problem is removed with the new scheme that partially also includes 1,2 and 1,3 interactions as needed to balance the charges in the 1,4 positions. A few simple molecules that involve conformation-dependent charges are used to illustrate the advantages of the new procedure.

Our previous analysis of the effect of a constant (Onsager reaction) electric field on a formic acid molecule showed that it produced an elongating force on the O−H bond resulting from the parallelism of field and dipole derivative, leading to a red-shifting of the frequency and an increase in infrared band intensity with the field, and a contracting force on the C−H bond resulting from the antiparallelism in the above quantities, leading to a blue-shifting of frequency and an initial decrease, followed by an increase, in band intensity with the field. In this paper we extend this analysis to the characterization of the O−H···O and C−H···O hydrogen bonds in the nonconstant fields present in the formic acid dimer. We use a QM/MM treatment that incorporates exchange-repulsive forces and we also include forces generated by intramolecular cross-term interactions. The excellent agreement with the ab initio bond length changes as a function mainly of the balance of the electrical and repulsive forces demonstrat...

The spectroscopic behavior of the C−H···O hydrogen bond is generally opposite to that of typical (e.g., O−H···O and N−H···O) hydrogen bonds: the C−H stretching frequency is blue-shifted and the infrared band intensity decreases on hydrogen bonding. We show that this can be understood on the basis of the dynamic properties of the donor group, in particular the force on the bond resulting from the interaction of the external electric field created by the acceptor atom with the permanent and induced dipole derivatives of the X−H bond: when the field and dipole derivative are parallel, as in the case of O−H···O, the bond lengthens, and red shift and intensity increases result; when the field and dipole derivative are antiparallel, as in the case of C−H···O, the bond shortens and blue shift results with the possibility of intensity decrease. We demonstrate these properties in an ab initio and perturbation study of cis formic acid in an Onsager reaction field. This analysis provides the basis for a more gener...

A vibrationally accurate potential energy function, our spectroscopically determined force field (SDFF), is used to calculate the relative zero-point-corrected energies of various forms I−IV syndiotactic polypropylene (sPP) crystal structures, both in their unconstrained and room-temperature unit cells. The results confirm the instability of the pure Ibca structure and support suggestions that form I sPP may be a statistical mixture of structures. Form IV is shown to have an energy close to form I structures, making its participation in kink bands possible. The relatively high energy of the form III unit cell makes it understandable that this structure is found only under external tension.

A vibrational frequency map of the amide III mode of the alanine dipeptide has been obtained at the B3LYP/6-31+G* level. It shows that, contrary to an earlier speculation by Lord, the frequency of this mode is a function of φ and ψ rather than ψ alone. We note that an analysis of the Hα bend mode, which independently depends on φ and ψ, together with amide III may permit determination of these two torsion angles. Preliminary results on the alanine tripeptide indicate that such studies will be needed to establish the exact relationships in polypeptide chains.

Thus far, the Casimir–Eckart condition (CEC) has been considered to be the general requirement in a rigorous transformation of differential tensor quantities like dipole moment derivatives or polarizability derivatives from Cartesian coordinates to internal coordinates. It is well known that this conventional transformation matrix ( A -matrix) based on the Wilson method, which always guarantees the CEC, depends on the atomic masses and provides atomic mass-dependent differential quantities. Since this conventional method may give abnormal isotope effects in dipole derivatives or polarizability derivatives even in mass-free internal coordinates, we have re-examined the validity of the CEC and propose a new transformation method that does not impose this condition. We show that the A -matrix obtained by the method used in internal coordinate molecular dynamics (ICMD) formalisms is mass-free for mass-free generalized (internal and external) coordinates and does not cause such an abnormal isotope effect. Since the CEC itself depends on the choice of a moving coordinate frame, the transformed internal coordinate dipole derivatives by the Wilson method also depend on the choice of the moving coordinate frame, while those by the ICMD method are independent of the choice of the moving coordinate frame. As Eckart comments, the Casimir condition is not valid in general but its validity depends on the type of internal coordinates used. All the additional degrees of freedom in defining a moving coordinate frame can be satisfactorily removed by relations from the orthogonality of internal coordinates to external translations and rotations. Moreover, an analogy with normal coordinates for internal modes provides the very equivalent to Eckart's original derivation.

Internal coordinate molecular dynamics (ICMD) has been used in the past in simulations for large molecules as an alternative way of increasing step size with a reduced operational dimension that is not achievable by MD in Cartesian coordinates. A new ICMD formalism for flexible molecular systems is presented, which is based on the spectroscopic B -matrix rather than the A -matrix of previous methods. The proposed formalism does not require an inversion of a large matrix as in the recursive formulations based on robot dynamics, and takes advantage of the sparsity of the B -matrix, ensuring computational efficiency for flexible molecules. Each molecule’s external rotations about an arbitrary atom center, which may differ from its center of mass, are parameterized by the SU (2) Euler representation, giving singularity free parameterization. Although the formalism is based on the use of nonredundant generalized (internal and external) coordinates, an MD simulation in linearly dependent coordinates can be done by finding a transformation to a new set of independent coordinates. Based on the clear separability in the generalized coordinates between fast varying degrees of freedom and slowly varying ones, a multiple time step algorithm is introduced that avoids the previous nontrivial interaction distance classification. Also presented is a recursive method for computing nonzero A -matrix elements that is much easier to apply to a general molecular structure than the previous method.

Our previously developed polarizable electrostatic model is applied to isolated N-methylacetamide (NMA) and to three hydrogen-bonded configurations of the NMA dimer. Two versions of the model are studied. In the first one (POL1), polarizability along the valence bonds is described by induced bond charge increments, and polarizability perpendicular to the bonds is described by cylindrically isotropic induced atomic dipoles. In the other version (POL2), the induced bond charge increments are replaced by induced atomic dipoles along the bonds. The parameterization is done by fitting to ab initio MP2/6-31++G(d,p) electric potentials. The polarizability parameters are determined by subjecting the NMA molecule to various external electric fields. POL1 turns out to be easier to optimize than POL2. Both models reproduce well the ab initio electric potentials, molecular dipole moments, and molecular polarizability tensors of the monomer and the dimers. Nonpolarizable models are also investigated. The results show that polarization is very important for reproducing the electric potentials of the studied dimers, indicating that this is also the case in hydrogen bonding between peptide groups in proteins. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1933–1943, 2001

A new electrostatic model, designed for use in molecular mechanics force fields, is presented. In addition to atomic charges the model consists of atomic dipoles and is further enhanced by the possibility of explicitly accounting for polarizability in the form of induced charges and anisotropically induced atomic dipoles. The parameters of the model are determined in a consistent way from isolated molecules by fitting to ab initio electric potentials. The polarizability in different directions is probed by subjecting the molecules to various external electric fields. As an illustration of the model, parameters have been obtained for isolated water and formaldehyde molecules, and applied to a few hydrogen-bonded water dimers and water–formaldehyde complexes. The parameters transferred from the isolated molecules successfully reproduce the ab initio (MP2/6-31++G(d,p)) electric potentials, molecular dipole moments, and molecular polarizabilities of all the studied dimers and complexes. The performance of nonpolarizable models for these systems is also evaluated, and, for fixed hydrogen-bond distances, is found to be acceptable in most cases.

A scaled ab initio HF/6-31G force field has been optimized that provides an accurate description of normal mode frequencies and eigenvectors of branched alkanes. This force field reproduces 159 observed non-CH stretch bands of 10 conformers of 2-methylpropane, 2,2-dimethylpropane, 2-methylbutane, 2,2-dimethylbutane, and 3-methylpentane with an rms deviation of 6.1 cm −1 . A number of modes have been reassigned based on this vibrational analysis. The force field serves as the basis for the development of a spectroscopically accurate molecular mechanics energy function for saturated hydrocarbon chains.

An MP2/6-31+G ∗ calculation of the N -methylacetamide dimer shows that it has two minimum energy structures, both hydrogen bonded with peptide planes roughly perpendicular to each other. A complete molecular mechanics optimization of the dimer has been done, using a model for the intermolecular interactions consisting of charges, atomic dipoles, and van der Waals interactions and the methodology of our spectroscopically determined force field for the intramolecular interactions. The two structures are satisfactorily reproduced, as are their interaction energies, their dipole moments, and, from the point of view of our goal of a spectroscopically accurate force field, their six intermolecular normal mode frequencies.

With currently used definitions of out-of-plane angle and bond angle internal coordinates, Cartesian derivatives have singularities, at "pr 2i n the former case and p in the latter. If either of these occur during molecular mechanics or dynamics simulations, the forces are not well defined. To avoid such difficulties, we provide new out-of-plane and bond angle coordinates and associated potential energy functions that inherently avoid these singularities. The application of these coordinates is illustrated by ab initio calculations on ammonia, water, and carbon dioxide. Q 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1067)1084, 1999

Polarized ir spectra of oriented films ofa-helical poly(L-alanine) (a-PLA) have been obtained as a function of residual solvent dichloroacetic acid (DCA). The amide A, B, II, and V regions exhibit multiple bands whose structure depends on the residual DCA content, and those associated with the aI-PLA structure have been identified. A calculation of the relevant cubic anharmonic force constants indicates that, contrary to previous assignments, the overtone of amide II(A) is in Fermi resonance with the NH stretch fundamental, whose unperturbed frequency we now find to be at 3314 cm 21 , significantly higher than the previously suggested 3279 cm 21 . The presence of a structure in addition to the standardaI-PLA is indicated by our analysis. © 1999 John Wiley & Sons, Inc. Biopoly 49: 195-207, 1999

Polarized ir and Raman spectra have been obtained on oriented films of α-helical poly(L-alanine) (α-PLA) and its N-deuterated derivative. These improved spectra permit a more complete assignment of observed bands to A-, E1-, and E2-species modes. A new empirical force field has been refined, based on ab initio force fields of N-methylacetamide and L-alanyl-L-alanine, which reproduces observed frequencies above 200 cm−1 to less than 5 cm−1. A new transition dipole coupling treatment avoids the weak coupling and perturbation approximations, and can now account for the newly observed and reassigned amide I (E2) mode. As a result of this improved force field, several other observed bands have also been reassigned. © 1998 John Wiley & Sons, Inc. Biopoly 46: 283–317, 1998

Our methodology for producing a spectroscopically determined force field (SDFF) (i.e., a molecular mechanics energy function) that, in addition to structures and relative energies, reproduces vibrational frequencies to spectroscopic standards, has been extended from its previous implementation on the linear to include branched saturated hydrocarbon chains. To the ab initio force fields of the 14 stable conformers of n-pentane and n-hexane, we have now added those of the 7 stable conformers of isopentane, 3-methylpentane, and neopentane, plus specific force constants from a secondary set of branched molecules, to optimize the parameters of the SDFF. This SDFF reproduces 791 ab initio non-CH stretch frequencies with a root-mean-square deviation of 6.2 cm-1. When applied to other molecules not in the optimization set, viz., cyclobutane, cyclohexane, isobutane, tri-tert-butylmethane, and tetra-tert-butylmethane, not only are ab initio as well as experimental geometries and frequencies well reproduced, but the...

We have developed a general formalism for the vibrational dynamics of a helical macromolecule that avoids the assumption of weak coupling between groups along the helix as well as the use of perturbation theory to calculate the frequencies. We have applied the concepts of this theory to the calculation of the amide I and amide II frequencies of α-helical poly (l-alanine). Although intergroup dipole derivatives required by the theory are not presently available, we have been able to show that they are important in accounting for the observations, particularly the E2-species amide I frequency. An optimized set of intergroup force constants, which implies a non-weak-coupling-non-perturbation treatment, gives excellent reproduction of the observed frequencies.

Polarized Raman spectra were obtained on well oriented films of α-helical poly(L-alanine) (α-PLA) and its N-deuterated analogue in order to obtain definitive assignments of the E2-species modes. Such assignments were aided by an analysis of factors that can lead to ‘cross-talk’ between A, E1 and E2 spectra, viz. reflection of the incident beam and non-perfect lateral and axial chain orientation in the sample. The convincing assignment of at least eleven significant E2 modes in α-PLA has led to the refinement of a new empirical force field and a more detailed normal mode analysis. © 1998 John Wiley & Sons, Ltd.

The isotropic and anisotropic Raman spectra of neat N-methylacetamide (NMA) at different temperatures between −10 and 60 °C and NMA in acetonitrile were measured in order to spectroscopically compare and characterize the crystallized (T < 28 °C) and liquid states. These plus infrared data were subjected to a self-consistent component band analysis. We found that the amide I band is composed of two subbands in the solid phase and three in the liquid phase. For the former, the subbands at 1633 and 1656 cm-1 arise from transition dipole coupling interactions associated with the Ag and B2g species of the crystal unit cell. Depolarization ratio measurements suggest a departure from strict D2h symmetry. The three subbands in the liquid phase reflect different aggregate structures. The lowest frequency band at 1634 cm-1 results from an NMA oligomer exhibiting a structure similar to that observed in the ordered crystal phase. The most intense subband shows a significant negative noncoincidence effect, its isotrop...

We have developed a new form of the intermolecular potential that is consistent with ab initio structures, interaction energies, interaction forces, intermolecular force constants, and dipole derivatives of four different hydrogen-bonded structures of the formic acid dimer. The ab initio “data” are based on a scaled HF/6-311++G** force field in nonredundant coordinates and reflect a reassignment of some bands in the spectrum. The model incorporates charges, charge fluxes, atomic dipoles, and van der Waals interactions, and its successful reproduction of the intermolecular force constants indicates that it may provide a more general description of detailed features of the hydrogen bond.

The construction of molecular mechanics potential energy functions is discussed from the viewpoint of vibrational spectroscopy. The rapid growth in computer capacity has made it possible to use increasingly higher level quantum chemical methods to derive information about molecular potential energy surfaces and electrostatic properties. If such information is fully utilized it could lead to a breakthrough in the ability of molecular mechanics and dynamics simulations to predict vibrational spectra. Two methods that make extensive use of quantum chemically calculated data are compared. It is concluded that the Spectroscopically Determined Force Field technique, in which scaled ab initio force constants and structures are mathematically transformed into molecular mechanics energy parameters, has several advantages compared to least squares fitting procedures. Torsion potentials are discussed separately, with special attention given to C(sp2)-C(sp2) bonds. Finally, a few existing force fields are compared in their ability to reproduce vibrational frequencies.

Raman longitudinal acoustic mode (LAM ) spectra have been obtained during isothermal crystallization from the melt at various temperatures of a poly( ethylene oxide) ( PEO ) fraction of molecular weight about 3000 and an α,ω-methoxylated fraction (MPEO) derived from it. For both fractions, we find that noninteger fold ( NIF ) chains are formed in the initial stages of crystallization. With time, and more rapidly at higher crystallization temperatures, the NIF chains transform into integer-fold (IF) structures. The final morphologies of the two fractions are similar, consisting of IF mixed-crystal lamellae composed mainly of extended ( E ) chains with embedded once-folded (F2) chains. This solid-state transformation from the NIF state may proceed through the F2 state. The effect of hydrogen bonds in the case of PEO is not to change the transformation process but to slow it when compared to MPEO. Comparison with small-angle x-ray scattering (SAXS) data indicates that in both cases the NIF chains are tilted to the lamellar surface and that the tilt from perpendicular eventually disappears as IF chains form at the later stages of crystallization.

Normal modes have been calculated for a CH 3 CONHCH 3 (H 2 O) 2 [NMA(H 2 O) 2 ] system and its CCD 3 , NCD 3 , 13 C 15 N, and ND derivatives. Fully optimized structures were obtained with the 6–31+ G ∗ basis set. The scale factors for the NMA force constants were obtained by optimizing the scale factors for the isolated molecule to experimental frequencies of aqueous NMA. HOH bend scale factors were found that are consistent with observed resonance Raman enhancements and infrared intensities of the components of the amide I doublet. Its frequency splitting can be reproduced quantitatively by a reaction field calculation. The calculated frequency difference between the two allowed NMA conformers confirms the assignment of the two observed amide II bands to the presence of these conformers in aqueous solution. An evaluation is made of the assignments of other bands.

Our SDFF for linear saturated hydrocarbon chains has been used to calculate the chain modulus of isolated and crystalline chains of n-alkanes of varying lengths. This has been done for static deformations and for the dynamic deformation in the longitudinal acoustic mode (LAM). Extrapolation to infinite chain length gives a common value of the room-temperature crystal modulus of 303 GPa (also obtained in an infinite chain calculation). Experimental Raman LAM measurements, corrected for chain-end interactions, give a modulus of 305 GPa, in excellent agreement. Problems with the experimental values obtained by inelastic neutron scattering and x-ray diffraction are discussed.

Raman longitudinal acoustic mode (LAM) spectra have been obtained during isothermal crystallization from the melt at various temperatures of a poly(ethylene oxide) (PEO) fraction of molecular weight about 3000. At all temperatures, we find an initial single well-defined LAM band corresponding to a helical chain length that represents a non-integral-fold (NIF) structure. With time, and more rapidly at higher crystallization temperatures, the NIF chains transform into integer-fold (IF) structures. The final morphology consists of IF mixed crystals composed mainly of extended (E) chains but with once-folded (F2) chains embedded in them. This solid-state transformation from the NIF state may proceed through the F2 state.

The structure of trans-N-methylacetamide has been fully optimized, i.e., all frequencies real, at the Hartree-Fock (HF) level with twelve basis sets from 6G–31G∗ through 6–311 + + G∗∗ and with electron correlation at the second-order Moller-Plesset perturbation level (MP2) with the 6G–31G∗, 6G–311G∗∗, 6–31 + G∗, 6–311 + G∗, and 6–311 + + G∗∗ basis sets. Minimum energy structures are non-planar at HF and MP2 levels without diffuse functions. With diffuse functions included, the minimum energy structure is planar for all basis sets at the HF level and tends toward planarity at more complete levels of MP2 electron correlation. These results, as well as MP3, MP4 (SDQ), and CISD optimizations without frequency calculations, lead us to conclude that, within the expected torsion angle variations in such calculations, the equilibrium structure of the isolated molecule has planar symmetry.