Brina Brauer

Frequency and Zero-Point Vibrational Energy Scale Factors for Double-Hybrid Density Functionals (and Other Selected Methods): Can Anharmonic Force Fields Be Avoided?

We have obtained uniform frequency scaling factors λ(harm) (for harmonic frequencies), λ(fund) (for fundamentals), and λ(ZPVE) (for zero-point vibrational energies (ZPVEs)) for the Weigend-Ahlrichs and other selected basis sets for MP2, SCS-MP2, and a variety of DFT functionals including double hybrids. For selected levels of theory, we have also obtained scaling factors for true anharmonic fundamentals and ZPVEs obtained from quartic force fields. For harmonic frequencies, the double hybrids B2PLYP, B2GP-PLYP, and DSD-PBEP86 clearly yield the best performance at RMSD = 10-12 cm(-1) for def2-TZVP and larger basis sets, compared to 5 cm(-1) at the CCSD(T) basis set limit. For ZPVEs, again, the double hybrids are the best performers, reaching root-mean-square deviations (RMSDs) as low as 0.05 kcal/mol, but even mainstream functionals like B3LYP can get down to 0.10 kcal/mol. Explicitly anharmonic ZPVEs only are marginally more accurate. For fundamentals, however, simple uniform scaling is clearly inadequate.

Spectroscopically-tested, improved, semi-empirical potentials for biological molecules: Calculations for glycine, alanine and proline

A modification of the semi-empirical PM3 electronic structure method is proposed. It employs a coordinate scaling procedure, such that the harmonic frequencies from the modified PM3 potentials for lower-energy conformers of glycine (conformer I), alanine (conformers I and II) and proline (conformer II), fit more closely with ab initio (MP2/DZP) harmonic frequencies. The anharmonic frequencies are then calculated using the modified PM3 surfaces with the Vibrational Self-Consistent Field (VSCF) and Correlation-Corrected VSCF (CC-VSCF) methods. The computed anharmonic frequencies are in very good accord with spectroscopic experiments for the three amino acids. The results are much superior to those obtained from standard (unscaled) PM3 potentials, indicating that the modified PM3 potentials may be used as high quality potentials for biological molecules, at least in the configuration ranges pertinent to vibrational spectroscopy. The scaling parameters computed for the lowest energy conformers listed above were tested for transferability: they were used in computing the anharmonic spectra of two other conformers (glycine II and proline I). The good agreement of the resulting frequencies with observed frequencies, indicates the transferability of the scaling parameters. It is concluded from this study that the improved PM3 potentials offer accurate and computationally efficient force fields for vibrational spectroscopy calculations of biological molecules. Possible additional applications of the new potentials are discussed.

Mid-IR spectra of different conformers of phenylalanine in the gas phase

The experimental mid- and far-IR spectra of six conformers of phenylalanine in the gas phase are presented. The experimental spectra are compared to spectra calculated at the B3LYP and at the MP2 level. The differences between B3LYP and MP2 IR spectra are found to be small. The agreement between experiment and theory is generally found to be very good, however strong discrepancies exist when -NH2 out-of-plane vibrations are involved. The relative energies of the minima as well as of some transition states connecting the minima are explored at the CCSD(T) level. Most transition states are found to be less than 2000 cm(-1) above the lowest energy structure. A simple model to describe the observed conformer abundances based on quasi-equilibria near the barriers is presented and it appears to describe the experimental observation reasonably well. In addition, the vibrations of one of the conformers are investigated using the correlation-corrected vibrational self-consistent field method.

Vibrational spectra of α-glucose, β-glucose, and sucrose: anharmonic calculations and experiment.

The anharmonic vibrational spectra of α-D-glucose, β-D-glucose, and sucrose are computed by the vibrational self-consistent field (VSCF) method, using potential energy surfaces from electronic structure theory, for the lowest energy conformers that correspond to the gas phase and to the crystalline phase, respectively. The results are compared with ultraviolet-infrared (UV-IR) spectra of phenyl β-D-glucopyranoside in a molecular beam, with literature results for sugars in matrices and with new experimental data for the crystalline state. Car-Parrinello dynamics simulations are also used to study temperature effects on the spectra of α-D-glucose and β-D-glucose and to predict their vibrational spectra at 50, 150, and 300 K. The effects of temperature on the spectral features are analyzed and compared with results of the VSCF calculations conducted at 0 K. The main results include: (i) new potential surfaces, constructed from Hartree-Fock, adjusted to fit harmonic frequencies from Møller-Plesset (MP2) calculations, that give very good agreement with gas phase, matrix, and solid state spectra; (ii) computed infrared spectra of the crystalline solid of α-glucose, which are substantially improved by including mimic groups that represent the effect of the solid environment on the sugar; and (iii) identification of a small number of combination-mode transitions, which are predicted to be strong enough for experimental observation. The results are used to assess the role of anharmonic effects in the spectra of the sugars in isolation and in the solid state and to discuss the spectroscopic accuracy of potentials from different electronic structure methods.

Vibrational spectroscopy and the development of new force fields for biological molecules

The role of vibrational spectroscopy in the testing of force fields of biological molecules and in the determination of improved force fields is discussed. Analysis shows that quantitative testing of potential energy surfaces by comparison with spectroscopic data generally requires calculations that include anharmonic couplings between different vibrational modes. Applications of the vibrational self‐consistent field (VSCF) method to calculations of spectroscopy of biological molecules are presented, and comparison with experiment is used to determine the merits and flaws of various types of force fields. The main conclusions include the following: (1) Potential surfaces from ab initio methods at the level of MP2 yield very satisfactory agreement with spectroscopic experimental data. (2) By the test of spectroscopy, ab initio force fields are considerably superior to the standard versions of force fields such as AMBER or OPLS. (3) Much of the spectroscopic weakness of AMBER and OPLS is due to incorrect description of anharmonic coupling between different vibrational modes. (4) Potential surfaces of the QM/MM (Quantum Mechanics/Molecular Mechanics) type, and potentials based on improved versions of semi‐empirical electronic structure theory, which are feasible for large biological molecules, yield encouraging results by the test of vibrational spectroscopy.

Vibrational spectroscopy of triacetone triperoxide (TATP): anharmonic fundamentals, overtones and combination bands.

The vibrational spectrum of triacetone triperoxide (TATP) is studied by the correlation-corrected vibrational self-consistent field (CC-VSCF) method which incorporates anharmonic effects. Fundamental, overtone, and combination band frequencies are obtained by using a potential based on the PM3 method and yielding the same harmonic frequencies as DFT/cc-pVDZ calculations. Fundamentals and overtones are also studied with anharmonic single-mode (without coupling) DFT/cc-pVDZ calculations. Average deviations from experiment are similar for all methods: 2.1-2.5%. Groups of degenerate vibrations form regions of numerous combination bands with low intensity: the 5600-5800 cm(-1) region contains ca. 70 overtones and combinations of CH stretches. Anharmonic interactions are analyzed.

First-principles calculations of anharmonic vibrational spectroscopy of large molecules

Publisher Summary This chapter describes the methods for computing directly the anharmonic vibrational spectra of polyatomic molecules from potential surface points obtained from electronic structure theory. The focus is laid on the state of the art of the methodology, on the approximations and the algorithms involved and their limitations, and on the scaling of the computational effort with the number of vibrational modes. The performance of different electronic structure methods in obtaining accurate vibrational spectra is assessed by comparing the theoretical predictions with experiment for various test cases. Vibrational spectroscopy is a tool of great importance for identifying molecular species, exploring their properties, and learning about their potential energy surfaces. A variety of methods for performing anharmonic vibrational spectroscopy computations were developed to address these and related systems. At the early stages, essentially all the methods were developed for potential surfaces available as explicit analytic functions of the coordinates. Some of the many open problems and challenges in this field have also been discussed in the chapter.

Revealing the hot bands in the regions of the N-H and C-H stretch fundamentals of pyrrole.

Photoacoustic Raman spectra of gaseous pyrrole in the 3504-3535 and 3068-3152 cm(-1) energetic windows were measured, to obtain new information about the hot bands in the vicinity of the N-H(ν1) and C-H(ν2) stretch fundamentals, respectively. The observed vibrational patterns are characterized by sharp Q-branches, where the strong bands reflect the fundamentals and the weaker ones, as established from their temperature dependence, are hot bands. From the simulation of the observed spectra, the band origins and nondiagonal anharmonicities were determined. Comparison of the latter values to the anharmonicities, x(ij) (i = 1, 2 and j = 16, 15, 14, 12, 11) obtained from anharmonic calculations at the B3LYP/6-311++G(d,p), B3LYP/cc-pVQZ and MP2/cc-pVTZ levels, aided the tentative assignment of the hot bands. The retrieved parameters add new data to the extensive set of already known vibrational constants of pyrrole.

When a proton attacks cellobiose in the gas phase: ab initio molecular dynamics simulations

Investigations of reaction pathways between a proton and cellobiose (CB), a glucose disaccharide of importance, were carried out in cis and trans CB using Ab Initio Molecular Dynamics (AIMD) simulations starting from optimized configurations where the proton is initially placed near groups with affinity for it. Near and above 300 K, protonated CB (H(+)CB) undergoes several transient reactions including charge transfer to the sugar backbone, water formation and dehydration, ring breaking and glycosidic bond breaking events as well as mutarotation and ring puckering events, all on a 10 ps timescale. cis H(+)CB is energetically favoured over trans H(+)CB in vacuo, with an energy gap larger than for the neutral CB.