Polarization and experimental configuration analyses of sum frequency generation vibrational spectra, structure, and orientational motion of the air/water interface

Here we report a detailed study on spectroscopy, structure, and orientational distribution, as well as orientational motion, of water molecules at the air/water interface, investigated with sum frequency generation vibrational spectroscopy (SFG-VS). Quantitative polarization and experimental configuration analyses of the SFG data in different polarizations with four sets of experimental configurations can shed new light on our present understanding of the air/water interface. Firstly, we concluded that the orientational motion of the interfacial water molecules can only be in a limited angular range, instead of rapidly varying over a broad angular range in the vibrational relaxation time as suggested previously. Secondly, because different vibrational modes of different molecular species at the interface has different symmetry properties, polarization and symmetry analyses of the SFG-VS spectral features can help the assignment of the SFG-VS spectra peaks to different interfacial species. These analyses concluded that the narrow 3693 cm(-1) and broad 3550 cm(-1) peaks belong to C(infinityv) symmetry, while the broad 3250 and 3450 cm(-1) peaks belong to the symmetric stretching modes with C2v symmetry. Thus, the 3693 cm(-1) peak is assigned to the free OH, the 3550 cm(-1) peak is assigned to the singly hydrogen-bonded OH stretching mode, and the 3250 and 3450 cm(-1) peaks are assigned to interfacial water molecules as two hydrogen donors for hydrogen bonding (with C2v symmetry), respectively. Thirdly, analysis of the SFG-VS spectra concluded that the singly hydrogen-bonded water molecules at the air/water interface have their dipole vector directed almost parallel to the interface and is with a very narrow orientational distribution. The doubly hydrogen-bonded donor water molecules have their dipole vector pointing away from the liquid phase.     

Towards fast computations of correlated vibrational wave functions: vibrational coupled cluster response excitation energies at the two-mode coupling level

An efficient implementation of vibrational coupled cluster theory with two-mode excitations and a two-mode Hamiltonian is described. The algorithm is shown to scale cubically with respect to the number of modes which is identical to the scaling of the corresponding vibrational configuration interaction algorithm. This is achieved through the use of special intermediates. The same algorithm can also be used in vibrational M?ller-Plesset calculations. To improve performance, screening techniques have been implemented as well. Test calculations on polyaromatic hydrocarbons with up to 264 coupled modes and model systems with up to 1140 modes are used to illustrate the various features of the algorithm.     

Ab initio calculations of anharmonic vibrational spectroscopy for hydrogen fluoride (HF)n (n = 3, 4) and mixed hydrogen fluoride/water (HF)n(H2O)n (n = 1, 2, 4) clusters

Anharmonic vibrational frequencies and intensities are computed for hydrogen fluoride clusters (HF)n, with n = 3, 4 and mixed clusters of hydrogen fluoride with water (HF)n(H2O)n where n = 1, 2. For the (HF)4(H2O)4 complex, the vibrational spectra are calculated at the harmonic level, and anharmonic effects are estimated. Potential energy surfaces for these systems are obtained at the MP2/TZP level of electronic structure theory. Vibrational states are calculated from the potential surface points using the correlation-corrected vibrational self-consistent field method. The method accounts for the anharmonicities and couplings between all vibrational modes and provides fairly accurate anharmonic vibrational spectra that can be directly compared with experimental results without a need for empirical scaling. For (HF)n, good agreement is found with experimental data. This agreement shows that the M?ller-Plesset (MP2) potential surfaces for these systems are reasonably reliable. The accuracy is best for the stiff intramolecular modes, which indicates the validity of MP2 in describing coupling between intramolecular and intermolecular degrees of freedom. For (HF)n(H2O)n experimental results are unavailable. The computed intramolecular frequencies show a strong dependence on cluster size. Intensity features are predicted for future experiments.     

An empirical approach to the bond additivity model in quantitative interpretation of sum frequency generation vibrational spectra

Knowledge of the ratios between different polarizability betai'j'k' tensor elements of a chemical group in a molecule is crucial for quantitative interpretation and polarization analysis of its sum frequency generation vibrational spectroscopy (SFG-VS) spectrum at interface. The bond additivity model (BAM) or the hyperpolarizability derivative model along with experimentally obtained Raman depolarization ratios has been widely used to obtain such tensor ratios for the CH3, CH2, and CH groups. Successfully, such treatment can quantitatively reproduce the intensity polarization dependence in SFG-VS spectra for the symmetric (SS) and asymmetric (AS) stretching modes of CH3 and CH2 groups, respectively. However, the relative intensities between the SS and AS modes usually do not agree with each other within this model even for some of the simplest molecular systems, such as the air/methanol interface. This fact certainly has cast uncertainties on the effectiveness and conclusions based on the BAM. One of such examples is that the AS mode of CH3 group has never been observed in SFG-VS spectra from the air/methanol interface, while this AS mode is usually very strong for SFG-VS spectra from the air/ethanol interface, other short chain alcohol, as well as long chain surfactants. In order to answer these questions, an empirical approach from known Raman and IR spectra is used to make corrections to the BAM. With the corrected ratios between the betai'j'k' tensor elements of the SS and AS modes, all features in the SFG-VS spectra of the air/methanol and air/ethanol interfaces can be quantitatively interpreted. This empirical approach not only provides new understandings of the effectiveness and limitations of the bond additivity model but also provides a practical way for its application in SFG-VS studies of molecular interfaces.     

C-H stretching vibrations of methyl, methylene and methine groups at the vapor/alcohol (N = 1-8) interfaces

In IR and Raman spectral studies, the congestion of the vibrational modes in the C-H stretching region between 2800 and 3000 cm(-1) has complicated spectral assignment, conformational analysis, and structural and dynamics studies, even with quite a few of the simplest molecules. To resolve these issues, polarized spectra measurement on a well aligned sample is generally required. Because the liquid interface is generally ordered and molecularly thin, and sum frequency generation vibrational spectroscopy (SFG-VS) is an intrinsically coherent polarization spectroscopy, SFG-VS can be used for discerning details in vibrational spectra of the interfacial molecules. Here we show that, from systematic molecular symmetry and SFG-VS polarization analysis, a set of polarization selection rules could be developed for explicit assignment of the SFG vibrational spectra of the C-H stretching modes. These polarization selection rules helped assignment of the SFG-VS spectra of vapor/alcohol (n = 1-8) interfaces with unprecedented details. Previous approach on assignment of these spectra relied on IR and Raman spectral assignment, and they were not able to give such detailed assignment of the SFG vibrational spectra. Sometimes inappropriate assignment was made, and consequently misleading conclusions on interfacial structure, conformation and even dynamics were reached. With these polarization rules in addition to knowledge from IR and Raman studies, new structural information and understanding of the molecular interactions at these interfaces were obtained, and some new spectral features for the C-H stretching modes were also identified. Generally speaking, these new features can be applied to IR and Raman spectroscopic studies in the condensed phase. Therefore, the advancement on vibrational spectra assignment may find broad applications in the related fields using IR and Raman as vibrational spectroscopic tools.     

The specific vibrational modes of GTP in solution and bound to Ras: a detailed theoretical analysis by QM/MM simulations

The hydrolysis of guanosine triphosphate (GTP) in general, and especially by GTPases like the Ras protein, is in the focus of biological investigations. A huge amount of experimental data from Fourier-transformed infrared studies is currently available, and many vibrational bands of free GTP, GTP·Mg(2+), and Ras·GTP·Mg(2+) in solution have been assigned by isotopic labeling. In the Ras environment, bands between 800 cm(-1) and 1300 cm(-1) have already been assigned, but not those below 800 cm(-1). The combination of quantum and molecular mechanics (QM/MM) methods takes the quantum effects for selected relevant atoms into account. This provides structural details, vibrational frequencies and electron distributions of the region of interest. We therefore used MM and QM/MM simulations to investigate the normal vibrational modes of GTP, GTP·Mg(2+), and Ras·GTP·Mg(2+) in solution, and assigned the vibrational frequencies for each normal vibration mode. In this study, the quantum box contains the nucleoside and the Mg(2+). The comparison of calculated and experimental vibrational spectra provides a very good control for the quality of the calculations. Structurally, MM and QM/MM simulations reveal a stable tridentate coordination of the Mg(2+) by GTP in water, and a stable bidentate coordination by GTP in complex with Ras. For validation, we compare the calculated frequencies and isotopic shifts with the experimental results available in the range of 800 cm(-1) to 1300 cm(-1). For the first time we suggest band assignments of the vibrational modes below 800 cm(-1) by comparison of calculated and experimental spectra.     

Note on the role of vibrational modes in molecular electronic transitions

A simple application of a readily available quantum chemistry program (AMPAC) permits an illuminating presentation of the role of vibrational modes in electronic transitions. A direct comparison of modal surfaces for different electronic states of the same molecule can be made by using a perspective plot of the Duschinsky matrix for the transition with mode indices or eigenvalue sequence, as the planar axes. The sum of squares of the off-diagonal elements of the Duschinsky matrix can be used to give a measure of the difference between vibrational modes of the initial and final states. Calculations indicate that, in biacetyl, the triplet state is closer vibrationally to the anion ground state than either the singlet or the neutral ground state, while in glyoxal the ground state neutral has greater vibrational similarity to the anion ground state. The measure also indicates little change in vibrational modes upon intersystem crossing in formaldehyde.     

Observation of sub-surface phenyl rings in polystyrene with vibrationally resonant sum-frequency generation

The use of vibrationally resonant sum-frequency generation (VR-SFG) spectroscopy to investigate the structure of surfaces and interfaces generally relies on the assumption that only the surface/interface is probed and that the vibrational mode assignments are known and correct. To make vibrational mode assignments, two fundamental aspects of the technique must be dealt with. First, not all vibrational modes observed in linear spectroscopic techniques, such as IR and Raman, are necessarily present in the VR-SFG spectrum. Second, while it is generally assumed that VR-SFG only probes the surface, this technique in actuality is sensitive to molecules in any environment with broken symmetry. Previously published assignments for the aromatic CH stretching modes of polystyrene surfaces are contradictory, and one purpose of this work is to revisit those assignments. In addition to thin films of polystyrene, we have collected VR-SFG spectra of dimethylphenyl silane, polystyrene covered with a layer of poly(methyl methacrylate) (PMMA), and plasma-treated polystyrene to aid our mode assignments. Density functional theory calculations were also performed on styrene oligomers. Based on these experimental and theoretical results, we have determined that not all the expected vibrational modes are observed in the VR-SFG spectrum of polystyrene. We have also found that one particular mode, the ν₂ symmetric stretch, accounts for two of the observed peaks, one from the exposed surface and a second feature from a subsurface layer within the polymer thin film. These two features appear at separate frequencies (11 cm⁻¹ separation) because this mode is very sensitive to the local density, which is higher in the bulk than at the surface. With these experimentally validated mode assignments, VR-SFG spectra in the aromatic CH stretching region can be interpreted more reliably. More importantly, these results demonstrate that great care must be taken in assigning VR-SFG spectra. These results also show that VR-SFG can be used to interrogate more than just free surfaces and buried interfaces; any area of broken symmetry is probed with this technique.     

Thermodynamic calculations for molecules with asymmetric internal rotors--application to 1,3-butadiene

We present quantum mechanical partition functions, free energies, entropies, and heat capacities of 1,3-butadiene derived from ab initio calculations. Our technique makes use of a reaction path-like Hamiltonian to couple all 23 vibrational modes to the large-amplitude torsion, which involves heavy asymmetric functional groups. Ab initio calculations were performed at the B3LYP, MP2, and CCSD(T) levels of theory and compared with experimental values as a reference case. By using the ab initio potentials and projected frequencies, simple perturbative expressions are presented for computing the couplings of all the vibrational modes to the large-amplitude torsion. The expressions are particularly suited for programming in the new STAR-P software platform which automatically parallelizes our codes with distributed memory via a familiar MATLAB interface. Using the efficient parallelization scheme of STAR-P, we obtain thermodynamic properties of 1,3-butadiene for temperatures ranging from 50 to 500 K. The free energies, entropies, and heat capacities obtained from our perturbative formulas are compared with conventional approximations and experimental values found in thermodynamic tables.     

Microscopic Investigation of Ethylene Carbonate Interface: A Molecular Dynamics and Vibrational Spectroscopic Study

Ethylene carbonate(EC) liquid and its vapor-liquid interface were investigated using a combination of molecular dynamics(MD)simulation and vibrational IR, Raman and sum frequency generation(SFG)spectroscopies. The MD simulation was performed with a flexible and polarizable model of the EC molecule newly developed for the computation of vibrational spectra. The internal vibration of the model was described on the basis of the harmonic couplings of vibrational modes, including the anharmonicity and Fermi resonance coupling of C=O stretching. The polarizable model was represented by the charge response kernel(CRK),which is based on ab initio molecular orbital calculations and can be readily applied to other systems. The flexible and polarizable model can also accurately reproduce the structural and thermodynamic properties of EC liquid. Meanwhile, a comprehensive set of vibrational spectra of EC liquid, including the IR and Raman spectra of the bulk liquid as well as the SFG spectra of the liquid interface, were experimentally measured and reported. The set of experimental vibrational spectra provided valuable information for validating the model, and the MD simulation using the model comprehensively elucidates the observed vibrational IR, Raman, and SFG spectra of EC liquid. Further MD analysis of the interface region revealed that EC molecules tend to orientate themselves with the C=O bond parallel to the interface. The MD simulation explains the positive Im[χ~((2))](ssp) band of the C=O stretching region in the SFG spectrum in terms of the preferential orientation of EC molecules at the interface. This work also elucidates the distinct lineshapes of the C=O stretching band in the IR, Raman, and SFG spectra. The lineshapes of the C=O band are split by the Fermi resonance of the C=O fundamental and the overtone of skeletal stretching. The Fermi resonance of C=O stretching was fully analyzed using the empirical potential parameter shift analysis(EPSA) method. The apparently different lineshapes of the C=O stretching band in the IR, Raman, and SFG spectra were attributed to the frequency shift of the C=O fundamental in different solvation environments in the bulk liquid and at the interface. This work proposes a systematic procedure for investigating the interface structure and SFG spectra, including general modeling procedure based on ab initio calculations, validation of the model using available experimental data, and simultaneous analysis of molecular orientation and SFG spectra through MD trajectories. The proposed procedure provides microscopic information on the EC interface in this study, and can be further applied to investigate other interface systems, such as liquid-liquid and solid-liquid interfaces.     

The role of CN and CO ligands in the vibrational relaxation dynamics of model compounds of the [FeFe]-hydrogenase enzyme

The vibrational dynamics of (μ-propanedithiolate)Fe(2)(CO)(4)(CN)(2)(2-), a model compound of the active site of the [FeFe]-hydrogenase enzyme, have been examined via ultrafast 2D-IR spectroscopy. The results indicate that the vibrational coupling between the stretching modes of the CO and CN ligands is small and restricted to certain modes but the slow growth of off-diagonal peaks is assigned to population transfer processes occurring between these modes on timescales of 30-40 ps. Analysis of the dynamics in concert with anharmonic density functional theory simulations shows that the presence of CN ligands alters the vibrational relaxation dynamics of the CO modes in comparison to all-carbonyl model systems and suggests that the presence of these ligands in the enzyme may be an important feature in terms of directing the vibrational relaxation mechanism.     

A QM-MM interface between CHARMM and TURBOMOLE: implementation and application to systems in bulk phase and biologically active systems

The implementation of a hybrid QM-MM approach combining ab initio and density functional methods of TURBOMOLE with the molecular mechanics program package CHARMM is described. An interface has been created to allow data exchange between the two applications. With this method the efficient multiprocessor capabilities of TURBOMOLE can be utilized with CHARMM running as a single processor application. Therefore, features of nonparallel running code in CHARMM like the TRAVEL module for locating saddle points or VIBRAN for the calculation of second derivatives can be exploited by running the CPU intensive QM calculations in parallel. To test the methodology, several small systems are studied with both Hartree-Fock and density functional methods and varying QM-MM boundaries. Also, the computationally efficient RI-J method has been examined for use in QM-MM applications. A B(12) cofactor containing cobalt has been studied, to examine systems with a large QM region and transition metals. All tested methods perform satisfactory in comparison with pure quantum calculations. Additionally, algorithms for the characterization of saddle points have been tested for their potential use in QM-MM problems. The TRAVEL module of CHARMM has been applied to the Menshutkin reaction in the condensed phase, and a saddle point was located. This saddle point was verified by calculation of a steepest descent path connecting educt, transition state, and product, and by calculation of vibrational modes.     

A theoretical anharmonic study of the infrared absorption spectra of FHF-, FDF-, OHF-, and ODF- anions

Anharmonic vibrational frequencies, equilibrium bond lengths, rotational constants, and vibrational absorption spectra have been calculated for the triatomic anions, FHF(-) and OHF(-), and the heavier isotopomers FDF(-) and ODF(-). The triatomic anions are assumed to maintain a collinear configuration throughout all calculations, so only the symmetric (nu(1)) and asymmetric (nu(3)) stretching modes are considered. The two-dimensional permanent dipole surfaces and potential energy surfaces are then constructed along bond coordinates, using high-level ab initio methods. Fundamental and combination bands are obtained from the vibrational eigenfunctions, resulting in anharmonic frequencies, which can be compared with the available theoretical and experimental data. The agreement is very good, especially for the pure symmetric modes, while the asymmetric ones show larger discrepancies, presumably due to the neglected coupling between stretching and bending modes. Strong inverse anharmonicity is found in the level spacing of the asymmetric modes, for both FHF(-) and OHF(-) anions. The calculated mixed modes (nnu(1)+mnu(3), n, m=0-3) also agree reasonably with the few available experimental data, supporting our model. Based on the vibrational eigenfunctions, isotope effects are also rationalized. Infrared absorption spectra are calculated from the dipole autocorrelation function for FHF(-) and FDF(-), and for OHF(-) and ODF(-). Peak locations and relative intensities are assigned in terms of the fundamental and mixed transitions.     

Vibrational projection analysis: New tool for quantitatively comparing vibrational normal modes of similar molecules

A new method for quantitatively comparing calculated vibrational modes is described that relies on projecting the vectors describing the normal modes of one molecule onto those of a basis molecule. The procedure virtually automates the assignment of vibrational modes from one molecule to a second, structurally similar one. We illustrate the concept by using the classical Wilson modes of benzene as a basis for describing normal modes of the monosubstituted benzene derivatives phenol, phenol-d5, and phenol radical cation. These examples demonstrate the method's power for accurately assigning and comparing the normal modes of molecules perturbed by chemical substitution, isotopic substitution, or oxidation state. The vibrational projection analysis method—a special case of vector projection analysis—is compared and contrasted with total energy distribution analysis, perhaps the most commonly used technique for quantitatively comparing vibrational modes, and is found superior in each case when comparing normal modes. Vibrational projection analysis need not be limited to single molecules and quantum calculations, because normal modes may be obtained for much larger systems using molecular mechanics or molecular dynamics techniques. The method should therefore prove useful for interpreting the normal modes of ordered periodic solids and structures perturbed by noncovalent contacts, including proteins and polymers. The method may also prove useful in evaluating new computational methods by allowing direct, quantitative comparison of the vibrational modes obtained from different techniques. The power of this technique will make vibrational projection analysis a valuable tool for computational chemists as well as those using calculations to complement vibrational spectroscopic measurements. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1663–1674, 1998     

Calculations of intermode coupling constants and simulations of amide I,II, and III vibrational spectra of dipeptides

Amide I, II, and III vibrations of polypeptides are important marker modes whose vibrational spectra can provide critical information on structure and dynamics of proteins in solution. The extent of delocalization and vibrational properties of amide normal mode can be described by the amide local mode frequencies and intermode coupling constants between a pair of amide local modes. To determine these fundamental quantities, the previous Hessian matrix reconstruction method has been generalized here and applied to the density functional theory results for various dipeptide conformers. The calculation results are then used to simulate IR absorption, vibrational circular dichroism, and 2D IR spectra of dipeptides. The relationships between dipeptide backbone conformations and these vibrational spectra are discussed. It is believed that the present computational method and results will be of use to quantitatively simulate vibrational spectra of complicated polypeptides beyond simple dipeptides     

Simulations of vibrational spectra from classical trajectories: calibration with ab initio force fields

An algorithm allowing simulating vibrational spectra from classical time-dependent trajectories was applied for infrared absorption, vibrational circular dichroism, Raman, and Raman optical activity of model harmonic systems. The implementation of the theory within the TINKER molecular dynamics (MD) program package was tested with ab initio harmonic force fields in order to determine the feasibility for more extended MD simulations. The results suggest that sufficiently accurate frequencies can be simulated with integration time steps shorter than about 0.5 fs. For a given integration time step, lower vibrational frequencies ( approximately 0-2000 cm(-1)) could be reproduced with a higher accuracy than higher-frequency vibrational modes (e.g., O-H and C-H stretching). In principle, the algorithm also provides correct intensities for ideal systems. In applied simulations, however, the intensity profiles are affected by an unrealistic energy distribution between normal modes and a slow energy relaxation. Additionally, the energy fluctuations may cause weakening of the intensities on average. For ab initio force fields, these obstacles could be overcome by an arbitrary normal mode energy correction. For general MD simulations, averaging of many shorter MD trajectories started with randomly distributed atomic velocities provided the best spectral shapes. alpha-pinene, D-gluconic acid, formaldehyde dimer, and the acetylprolineamide molecule were used in the tests.