An analysis of SCF and geometry convergence for diatomic molecules

A geometry and SCF convergence study of Hartree-Fock calculations using the 6-31G* basis set is carried out on the set of all possible diatomic molecules formed from atoms with Z≤36. The utility of Hartree-Fock calculations using the smaller STO-3G basis set to improve the convergence behavior is demonstrated.      

Surface-enhanced Raman spectroscopic studies of coactivator-associated arginine methyltransferase 1

We report, for the first time, the surface-enhanced Raman spectra of an important enzyme, coactivator-associated arginine methyltransferase 1 (CARM1), involved in various biological activities such as tumor suppressor function and stem cell differentiation. We have employed surface-enhanced Raman scattering (SERS) to obtain insight into the structural details of CARM1 by adsorbing it to silver (Ag) nanoparticles. The enzyme retains its activity even after its adsorption onto Ag nanoparticles. We observe strong SERS modes arising from amide vibrations and aromatic ring amino acids. The SERS spectra revealed amide I bands at 1637 cm(-1) and 1666 cm(-1), which arise as a result of the alpha helix of the protein and the polypeptide backbone vibration of a random coil, respectively. In order to confirm the amide vibrations, we have performed SERS on deuterated CARM1, which exhibits a clear red shift in amide band positions. The SERS spectra may provide useful information, which could be harnessed to study the functional interactions of CARM1 with small molecule modulators.     

Analytical Hessian of electronic excited states in time-dependent density functional theory with Tamm-Dancoff approximation

We present the analytical expression and computer implementation for the second-order energy derivatives of the electronic excited state with respect to the nuclear coordinates in the time-dependent density functional theory (TDDFT) with Gaussian atomic orbital basis sets. Here, the Tamm-Dancoff approximation to the full TDDFT is adopted, and therefore the formulation process of TDDFT excited-state Hessian is similar to that of configuration interaction singles (CIS) Hessian. However, due to the replacement of the Hartree-Fock exchange integrals in CIS with the exchange-correlation kernels in TDDFT, many quantitative changes in the derived equations are arisen. The replacement also causes additional technical difficulties associated with the calculation of a large number of multiple-order functional derivatives with respect to the density variables and the nuclear coordinates. Numerical tests on a set of test molecules are performed. The simulated excited-state vibrational frequencies by the analytical Hessian approach are compared with those computed by CIS and the finite-difference method. It is found that the analytical Hessian method is superior to the finite-difference method in terms of the computational accuracy and efficiency. The numerical differentiation can be difficult due to root flipping for excited states that are close in energy. TDDFT yields more exact excited-state vibrational frequencies than CIS, which usually overestimates the values.     

Quantum-chemical study on conformations of molecular complexes formed by 2-methyl-1,3,2-dioxaborinane with methylamine

Conformations of 1: 1 molecular complexes of 2-methyl-1,3,2-dioxaborinane with methylamine were studied in terms of restricted Hartree-Fock approximation using STO-3G, 3-21G, and 6-31G(d) bass sets. The results showed possible formation of two types of complexes, one with dative N→B bond, and the other with intermolecular hydrogen bond NH … O. Their relative stability and conformations are determined by both mutual orientation of the components and basis set used.     

Solvent effect on the conformational behaviour of amino acid and oligopeptide derivatives

The solvent effect on acetyl amino acid methyl esters and C- and N-protected di- and tripeptide derivatives has been studied in deuterium oxide (D₂O), 1.1.1.3.3.3-hexafluoroisopropanol (HFiP), dimethyl sulfoxide (DMSO) and methylene chloride (CH₂Cl₂). The interpretation is based on the amide I region. For the amino acid derivatives the relative shift of the amide I signal clearly indicates the strength of the interaction with the solvent molecules. However, in HFiP and DMSO solutions the occurrence of two overlapping signals for the amide I and the ester carbonyl signal, respectively, indicates the existence of two major conformers. Knowing the solvent effects on the small amino acid esters allows the assignment of the signals in di- and tripeptide derivatives. Although the identification of turn structures in these flexible molecules is not possible, the band positions and intensity of the deconvoluted amide I region clearly shows that certain conformers can be stabilised. It can be concluded that the band profile in the amide I region is determined by the number of amino acid residues linked in the molecule, the bulkiness of the side chains and their sequence and to a major extend by the solvent properties.     

Characterization of low-frequency modes in aqueous peptides using far-infrared spectroscopy and molecular dynamics simulation

Far-infrared spectroscopy was used to study the dynamics of three aqueous peptides having varied helicity. Experimental data were compared to the molecular dynamics simulated far-infrared absorbance spectrum derived from the dipole time correlation function. Vibrational density of state (VDOS) simulation was then used to analyze the contribution of different structural elements to the bands. Frozen aqueous peptide samples were studied in the frequency range between 325 and 540 cm(-1) where the ice absorbance is low. Three resonances were identified; band I centered at approximately 333 cm(-1), band II centered at approximately 380 cm(-1), and band III comprising two constituent bands at approximately 519 and 528 cm(-1). The peak height and frequency of the maximum absorbance of bands I and II varied depending on the helicity of the peptide. VDOS of the far-infrared absorbance spectrum confirmed that bands I and II were associated with the peptide backbone and that band III had both potential backbone and side chain components.     

Single-conformation infrared spectra of model peptides in the amide I and amide II regions: Experiment-based determination of local mode frequencies and inter-mode coupling

Single-conformation infrared spectra in the amide I and amide II regions have been recorded for a total of 34 conformations of three α-peptides, three β-peptides, four α∕β-peptides, and one γ-peptide using resonant ion-dip infrared spectroscopy of the jet-cooled, isolated molecules. Assignments based on the amide NH stretch region were in hand, with the amide I∕II data providing additional evidence in favor of the assignments. A set of 21 conformations that represent the full range of H-bonded structures were chosen to characterize the conformational dependence of the vibrational frequencies and infrared intensities of the local amide I and amide II modes and their amide I∕I and amide II∕II coupling constants. Scaled, harmonic calculations at the DFT M05-2X∕6-31+G(d) level of theory accurately reproduce the experimental frequencies and infrared intensities in both the amide I and amide II regions. In the amide I region, Hessian reconstruction was used to extract local mode frequencies and amide I∕I coupling constants for each conformation. These local amide I frequencies are in excellent agreement with those predicted by DFT calculations on the corresponding (13)C = (18)O isotopologues. In the amide II region, potential energy distribution analysis was combined with the Hessian reconstruction scheme to extract local amide II frequencies and amide II∕II coupling constants. The agreement between these local amide II frequencies and those obtained from DFT calculations on the N-D isotopologues is slightly worse than for the corresponding comparison in the amide I region. The local mode frequencies in both regions are dictated by a combination of the direct H-bonding environment and indirect, "backside" H-bonds to the same amide group. More importantly, the sign and magnitude of the inter-amide coupling constants in both the amide I and amide II regions is shown to be characteristic of the size of the H-bonded ring linking the two amide groups. These amide I∕I and amide II∕II coupling constants remain similar in size for α-, β-, and γ-peptides despite the increasing number of C-C bonds separating the amide groups. These findings provide a simple, unifying picture for future attempts to base the calculation of both nearest-neighbor and next-nearest-neighbor coupling constants on a joint footing.     

Determination of ab initio polarizabilities of polymers: Application to polyethylene and polysilane

An ab initio method for calculating the longitudinal linear polarizability of polymeric chains is described. This method is equivalent to an uncoupled Hartree–Fock scheme. It is applied to polyethylene and polysilane in minimal STO-3G and extended 4-31G basis sets. The study describes important techniques for solving the difficulties met in actual calculations: band reordering of the band structures, calculation of analytical derivatives of the energy bands ?_n(k) and LCAO coefficients c_np(k), and errors caused by the improper lattice sum truncations of the Hartree–Fock matrix.     

AB initio calculations of oscillator and rotatory strengths in the random-phase approximation: planar and twisted butadiene

Minimal basis set (STO-4G) ab initio calculations in the random-phase approximation (RPA) are presented for the ordinary and rotatory intensities of the low-lying electronic transitions of twisted cis-butadiene, and planar trans-butadiene. The formally equivalent intensities agree much better in the RPA than in either monoexcited CI or Hartree-Fock virtual orbital calculations. Comparisons with other work are given, and an explanation is suggested for the sensitivity of the rotatory strengths to substituents.     

Numerical study of the exchange effects in the valence and core energy bands of the metallic lithium chain

Minimal basis-set STO-3G calculations on the infinite metallic chain of lithium atoms, (SINGLE BOND Li SINGLE BOND)_x, performed within the Fourier space-restricted Hartree-Fock approach (FS-RHF), are reported to illustrate that the Fourier representation method, in which all lattice summations are accurately carried out to infinity, is able to reproduce the genuine features of the RHF approach for the metallic cases, i.e., the vanishing of the density of states at the Fermi energy. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 709–718, 1997     

Molecular electronic virial theorem

The partitioning of the molecular electronic energy into true one-electron quantities defined by a molecular electronic virial theorem (MEVT) is studied for a number of molecules. Since the theorem is derived for exact wavefunctions, its applicability to various ab initio wavefunctions at difierent levels of accuracy is examined. The average percentage deviations of the theorem for near Hartree-Fock, double zeta, STO-6G and STO-3G type wave functions are 0.4, 1.7, 2.3 and 3.3, respectively.     

Energy barriers to rotation in axially chiral analogues of 4-(dimethylamino)pyridine.

The barriers to enantiomerization of a series of axially chiral biaryl analogues of 4-(dimethylamino)pyridine (DMAP) 1-10 were determined experimentally by means of dynamic HPLC measurements and racemization studies. The barriers to rotation in derivatives 1-6 (based on the bicyclic 5-azaindoline core) were lower than those in the corresponding derivatives 7-10 (based on the monocyclic DMAP core). Semiempirical (PM3), ab initio Hartree-Fock (HF/STO-3G), and density functional theory (DFT/B3LYP/6-31G*) calculations reveal that these differences in barriers to rotation are the result of differing degrees of hybridization of the non-pyridyl nitrogen in the enantiomerization transition states (TSs). The importance of heteroatom hybridization as a factor in determining nonsteric contributions to barriers to rotation in azabiaryls of this type is discussed.     

Accuracy of finite‐difference harmonic frequencies in density functional theory

Analytic Hessians are often viewed as essential for the calculation of accurate harmonic frequencies, but the implementation of analytic second derivatives is nontrivial and solution of the requisite coupled‐perturbed equations engenders a sizable memory footprint for large systems, given that these equations are not required for energy and gradient calculations in density functional theory. Here, we benchmark the alternative approach to harmonic frequencies based on finite differences of analytic first derivatives, a procedure that is amenable to large‐scale parallelization. Not only for absolute frequencies but also for isotopic and conformer‐dependent frequency shifts in flexible molecules, we find that the finite‐difference approach exhibits mean errors < 0.1 cm⁻¹ as compared to results based on an analytic Hessian. For very small frequencies corresponding to nonbonded vibrations in noncovalent complexes (for which the harmonic approximation is questionable anyway), the finite‐difference error can be larger, but even in these cases the errors can be reduced below 0.1 cm⁻¹ by judicious choice of the displacement step size and a higher‐order finite‐difference approach. The surprising accuracy and robustness of the finite‐difference results suggests that availability of the analytic Hessian is not so important in today's era of commodity processors that are readily available in large numbers. © 2017 Wiley Periodicals, Inc.     

Raman spectroscopic characterization of secondary structure in natively unfolded proteins: alpha-synuclein

The application of Raman spectroscopy to characterize natively unfolded proteins has been underdeveloped, even though it has significant technical advantages. We propose that a simple three-component band fitting of the amide I region can assist in the conformational characterization of the ensemble of structures present in natively unfolded proteins. The Raman spectra of alpha-synuclein, a prototypical natively unfolded protein, were obtained in the presence and absence of methanol, sodium dodecyl sulfate (SDS), and hexafluoro-2-propanol (HFIP). Consistent with previous CD studies, the secondary structure becomes largely alpha-helical in HFIP and SDS and predominantly beta-sheet in 25% methanol in water. In SDS, an increase in alpha-helical conformation is indicated by the predominant Raman amide I marker band at 1654 cm(-1) and the typical double minimum in the CD spectrum. In 25% HFIP the amide I Raman marker band appears at 1653 cm(-1) with a peak width at half-height of approximately 33 cm(-1), and in 25% methanol the amide I Raman band shifts to 1667 cm(-1) with a peak width at half-height of approximately 26 cm(-1). These well-characterized structural states provide the unequivocal assignment of amide I marker bands in the Raman spectrum of alpha-synuclein and by extrapolation to other natively unfolded proteins. The Raman spectrum of monomeric alpha-synuclein in aqueous solution suggests that the peptide bonds are distributed in both the alpha-helical and extended beta-regions of Ramachandran space. A higher frequency feature of the alpha-synuclein Raman amide I band resembles the Raman amide I band of ionized polyglutamate and polylysine, peptides which adopt a polyproline II helical conformation. Thus, a three-component band fitting is used to characterize the Raman amide I band of alpha-synuclein, phosvitin, alpha-casein, beta-casein, and the non-A beta component (NAC) of Alzheimer's plaque. These analyses demonstrate the ability of Raman spectroscopy to characterize the ensemble of secondary structures present in natively unfolded proteins.     

Comparison of the use of the MNDO and MINDO/3 methods with ab initio methods to study tautomerism in histamine, 2- and 4-methylhistamine

The semiempirical MNDO and MINDO/3 methods are used to study the various tautomeric forms of histamine, 2-methylhistamine, and 4-methylhistamine. Comparisons of the optimized structures and tautomerization energies are made with values obtained from ab initio Hartree-Fock calculations using the 3-21G and STO-3G basis sets. Based on these results and previous comparisons of STO-3G results with x-ray structures, the present results indicate that while there are some differences in the values of the structural parameters, the changes in structure upon tautomerization and/or protonation are very similar. Further analysis of the MNDO and MINDO/3 structures by means of their utilization in 3-21G and STO-3G calculations indicates that either of these semiempirical methods provides reliable values for the structural parameters. Both methods give good qualitative agreement with the ab initio calculations for the relative energies of the various tautomers in the three compounds. In these studies the MNDO method appears to give better quantitative agreement with the 3-21G and STO-3G results than the MINDO/3 method.     

A new perspective on beta-sheet structures using vibrational Raman optical activity: from poly(L-lysine) to the prion protein

The vibrational Raman optical activity (ROA) spectrum of a polypeptide in a model beta-sheet conformation, that of poly(l-lysine), was measured for the first time, and the alpha-helix --> beta-sheet transition monitored as a function of temperature in H(2)O and D(2)O. Although no significant population of a disordered backbone state was detected at intermediate temperatures, some side chain bands not present in either the alpha-helix or beta-sheet state were observed. The observation of ROA bands in the extended amide III region assigned to beta-turns suggests that, under our experimental conditions, beta-sheet poly(L-lysine) contains up-and-down antiparallel beta-sheets based on the hairpin motif. The ROA spectrum of beta-sheet poly(L-lysine) was compared with ROA data on a number of native proteins containing different types of beta-sheet. Amide I and amide II ROA band patterns observed in beta-sheet poly(L-lysine) are different from those observed in typical beta-sheet proteins and may be characteristic of an extended flat multistranded beta-sheet, which is unlike the more irregular and twisted beta-sheet found in most proteins. However, a reduced isoform of the truncated ovine prion protein PrP(94-233) that is rich in beta-sheet shows amide I and amide II ROA bands similar to those of beta-sheet poly(L-lysine), which suggests that the C-terminal domain of the prion protein is able to support unusually flat beta-sheets. A principal component analysis (PCA) that identifies protein structural types from ROA band patterns provides a useful representation of the structural relationships among the polypeptide and protein states considered in the study.     

Amide I infrared spectral features characteristic of some untypical conformations appearing in the structures suggested for amyloids

Amide I infrared (IR) spectral features are studied, by using the density functional theoretical method, for two untypical (but possibly rather prevalent) structures inspired from those recently suggested for amyloids: a structure consisting of loop regions in the (alpha L, alpha R) conformation stacked to form an alpha-sheet, and a structure involving some main-chain peptide groups (of any residues) and some side-chain amide groups of glutamine and asparagine residues closely located with each other. The amide I vibrational (off-diagonal) coupling constants are examined by extracting them from the calculated Cartesian-based force constants with the average partial vector method and by comparing them with those estimated on the basis of the transition dipole coupling mechanism. It is suggested that the amide I IR band characteristic of the alpha-sheet conformation in dry environment (without hydrogen bonding to solvent water molecules) is located in a high-frequency region (approximately >1670 cm(-1), somewhat higher than that of alpha-helix), because of the dependence of the diagonal (uncoupled) frequency and the off-diagonal coupling constant on the Phi and Psi dihedral angles. It is also shown that the amide I vibrations of the closely located peptide and amide groups are strongly coupled through-space with each other, and in the presence of this type of strong vibrational coupling, a noticeable change in the IR intensity upon (13)C=O substitution may occur even for a mode that arises mainly from an unsubstituted group and is not much shifted in frequency. The meaning of these results in the interpretation of observed amide I spectral profiles, especially the possible usefulness of IR spectroscopic measurements for detecting those untypical structures in the process of amyloid formation, is also discussed.     

Amide I two-dimensional infrared spectroscopy of beta-hairpin peptides

In this report, spectral simulations and isotope labeling are used to describe the two-dimensional IR spectroscopy of beta-hairpin peptides in the amide I spectral region. 2D IR spectra of Gramicidin S, PG12, Trpzip2 (TZ2), and TZ2-T3(*)T10(*), a dual (13)C(') isotope label, are qualitatively described by a model based on the widely used local mode amide I Hamiltonian. The authors' model includes methods for calculating site energies for individual amide oscillators on the basis of hydrogen bonding, nearest neighbor and long-range coupling between sites, and disorder in the site energy. The dependence of the spectral features on the peptide backbone structure is described using disorder-averaged eigenstates, which are visualized by mapping back onto the local amide I sites. beta-hairpin IR spectra are dominated by delocalized vibrations that vary by the phase of adjacent oscillators parallel and perpendicular to the strands. The dominant nu(perpendicular) band is sensitive to the length of the hairpin and the amount of twisting in the backbone structure, while the nu(parallel) band is composed of several low symmetry modes that delocalize along the strands. The spectra of TZ2-T3(*)T10(*) are used to compare coupling models, from which we conclude that transition charge coupling is superior to transition dipole coupling for amide groups directly hydrogen bound across the beta strands. The 2D IR spectra of TZ2-T3(*)T10(*) are used to resolve the redshifted amide I band and extract the site energy of the labeled groups. This allows the authors to compare several methods for calculating the site energies used in excitonic treatments of the amide I band. Gramicidin S is studied in dimethyl sulfoxide to test the role of solvent on the spectral simulations.