Direct calculation of anharmonic vibrational states of polyatomic molecules using density functional theory: spectroscopic tests of recently developed functionals

New developments of a multifrequency virtual spectrometer: stereo-electronic, dynamical, and environmental effects on chiroptical spectra

Computational spectroscopy has recently evolved from a field reserved for specialists toward a general tool allowing interpretations and analyses of experimental results. However, the current practice of providing tables of transitions for rigid geometries, possibly tuned by phenomenological broadening, is by far too naive. In order to improve this situation in the last few years we have been developing a general, robust, and user-friendly virtual spectrometer (VS) able to complement experimental studies for complex systems in condensed phases. The VS is based on flexible graphical pre- and postprocessing tools interfaced with general number-crunching software. This last tool is rooted in several electronic structure methodologies (DFT, TD-DFT, post-Hartree-Fock), powerful discrete/continuum models for describing environmental effects, and general vibrational and vibronic models. These last topics are the main focus of this work, which sketches our latest developments related to effective inclusion of anharmonic contributions, together with time-independent and/or time-dependent descriptions of vibronic transitions including Franck-Condon, Herzberg-Teller, and Duschinsky effects. Some test cases are described in some detail with the aim of showing the role of different effects in ruling vibrational (VCD) and electronic (ECD, CPL) chiral spectroscopies.

Optimized Structure and Vibrational Properties by Error Affected Potential Energy Surfaces

The precise theoretical determination of the geometrical parameters of molecules at the minima of their potential energy surface and of the corresponding vibrational properties are of fundamental importance for the interpretation of vibrational spectroscopy experiments. Quantum Monte Carlo techniques are correlated electronic structure methods promising for large molecules, which are intrinsically affected by stochastic errors on both energy and force calculations, making the mentioned calculations more challenging with respect to other more traditional quantum chemistry tools. To circumvent this drawback in the present work, we formulate the general problem of evaluating the molecular equilibrium structures, the harmonic frequencies, and the anharmonic coefficients of an error affected potential energy surface. The proposed approach, based on a multidimensional fitting procedure, is illustrated together with a critical evaluation of systematic and statistical errors. We observe that the use of forces instead of energies in the fitting procedure reduces the statistical uncertainty of the vibrational parameters by 1 order of magnitude. Preliminary results based on variational Monte Carlo calculations on the water molecule demonstrate the possibility to evaluate geometrical parameters and harmonic and anharmonic coefficients at this level of theory with an affordable computational cost and a small stochastic uncertainty (<0.07% for geometries and <0.7% for vibrational properties).

A second-order perturbation theory route to vibrational averages and transition properties of molecules: general formulation and application to infrared and vibrational circular dichroism spectroscopies

A general formulation to compute anharmonic vibrational averages and transition properties at the second-order of perturbation theory is derived from the Rayleigh-Schrödinger development. This approach is intended to be applicable to any property expanded as a Taylor series up to the third order with respect to normal coordinates or their associated momenta. The equations are straightforward to implement and can be easily adapted to various properties, as illustrated for the case of electric and magnetic dipole moments. From those, infrared and vibrational circular dichroism spectra can be readily obtained. This fully automatic procedure has been applied to several chiral molecules of small-to-medium sizes and compared to the standard double harmonic approximation and to experimental data.

Infrared spectroscopy of the alanine dipeptide analog in liquid water with DFT-MD. Direct evidence for P(II)/beta conformations

Following our previous work [J. Phys. Chem. B. Lett., 2009, 113, 10059], DFT-based molecular dynamics (DFTMD) simulations of 2-Ala peptide (i.e. Ac-Ala-NHMe dialanine peptide analog with methyl group caps at the extremities) immersed in liquid water at room temperature are reported. Our goal here is the theoretical calculation of the infrared spectrum of aqueous 2-Ala, in order to provide a definitive understanding of the average conformation adopted by this peptide in the liquid phase, taking into account solute and solvent at the same theoretical level of representation. We find that the experimental Amide I-II band predominantly results from a mixture of partially unfolded P(II) and unfolded beta conformational equilibrium of aqueous 2-Ala at room temperature.

Theoretical spectroscopy of floppy peptides at room temperature. A DFTMD perspective: gas and aqueous phase

Theoretical spectroscopy is mandatory for a precise understanding and assignment of experimental spectra recorded at finite temperature. We review here room temperature DFT-based molecular dynamics simulations for the purpose of interpreting finite temperature infrared spectra of peptides of increasing size and complexity, in terms of temperature-dependent conformational dynamics and flexibility, and vibrational anharmonicities (potential energy surface anharmonicities, vibrational mode couplings and dipole anharmonicities). We take examples from our research projects in order to illustrate the main key-points and strengths of dynamical spectra modeling in that context. The calculations are presented in relation to room temperature gas phase IR-MPD experiments and room temperature liquid phase IR absorption experiments. These illustrations of floppy polypeptides have been chosen in order to convey the following ideas: temperature-dependent spectra modeling is pivotal for a precise understanding of gas phase spectra recorded at room temperature, including conformational dynamics and vibrational anharmonicities; harmonic spectroscopy (as commonly performed in the literature) can be misleading and even erroneous for a proper interpretation of spectra recorded at finite temperature; taking into account vibrational anharmonicities is pivotal for a proper interplay between theory and experiments; amide I-III bands are not necessarily the most relevant fingerprints for unraveling the local structures of peptides and more complex systems; liquid phase simulations have unraveled relationships between the zwitterionic properties of the peptide bonds and infrared signatures. The review presents a state-of-the-art account of the domain and offers perspectives and new developments for future still more challenging applications.

Vibrational spectroscopy of (SO42−)∙(H2O)n clusters, n=1–5: Harmonic and anharmonic calculations and experiment

The vibrational spectroscopy of (SO4(2-)).(H2O)n is studied by theoretical calculations for n=1-5, and the results are compared with experiments for n=3-5. The calculations use both ab initio MP2 and DFT/B3LYP potential energy surfaces. Both harmonic and anharmonic calculations are reported, the latter with the CC-VSCF method. The main findings are the following: (1) With one exception (H2O bending mode), the anharmonicity of the observed transitions, all in the experimental window of 540-1850 cm(-1), is negligible. The computed anharmonic coupling suggests that intramolecular vibrational redistribution does not play any role for the observed linewidths. (2) Comparison with experiment at the harmonic level of computed fundamental frequencies indicates that MP2 is significantly more accurate than DFT/B3LYP for these systems. (3) Strong anharmonic effects are, however, calculated for numerous transitions of these systems, which are outside the present observation window. These include fundamentals as well as combination modes. (4) Combination modes for the n=1 and n=2 clusters are computed. Several relatively strong combination transitions are predicted. These show strong anharmonic effects. (5) An interesting effect of the zero point energy (ZPE) on structure is found for (SO4(2-)).(H2O)(5): The global minimum of the potential energy corresponds to a C(s) structure, but with incorporation of ZPE the lowest energy structure is C2v, in accordance with experiment. (6) No stable structures were found for (OH-).(HSO4-).(H2O)n, for n<or=5.

Anharmonic vibrational properties by a fully automated second-order perturbative approach

This paper describes the implementation of a fully automated code for the building of anharmonic force constants and their use in a second-order perturbative evaluation of vibrorotational parameters. Next, a number of test applications are discussed, which show the strengths and limits of various computational levels.

Ab Initio Study of the Isomeric Equilibrium of the HCN···H2O and H2O···HCN Hydrogen-Bonded Clusters

An ab initio study of the stability, spectroscopic properties, and isomeric equilibrium of the hydrogen-bonded HCN...H2O and H2O...HCN isomers is presented. Density functional theory and perturbative second-order MP2 and coupled-cluster CCSD(T) calculations were carried out and binding energies obtained with correlation-consistent basis sets including extrapolation to the infinity basis set level. At the best theoretical level, CCSD(T), the H2O...HCN complex is more stable than the HCN...H2O complex by ca. 6.3 kJ mol(-1). Rotational and vibrational spectra, including anharmonic corrections, are calculated. These calculated spectroscopic data are used to obtain thermochemical contributions to the thermodynamic functions and hence the Gibbs free energy. The relative free energies are used to estimate the equilibrium constant for isomerism. We find that under typical conditions of supersonic expansion experiments (T < 150 K) H2O...HCN is essentially the only isomer present. Furthermore, our calculations indicate that the hydrogen-bonded cluster becomes favorable over the separated moieties at temperatures below 200 K.

Prediction of accurate anharmonic experimental vibrational frequencies for water clusters, (H2O)n, n=2-5

Accurate anharmonic experimental vibrational frequencies for water clusters consisting of 2-5 water molecules have been predicted on the basis of comparing different methods with MP2/aug-cc-pVTZ calculated and experimental anharmonic frequencies. The combination of using HF/6-31G* scaled frequencies for intramolecular modes and anharmonic frequencies for intermolecular modes gives excellent agreement with experiment for the water dimer and trimer and are as good as the expensive anharmonic MP2 calculations. The water trimer, the cyclic Ci and S4 tetramers, and the cyclic pentamer all have unique peaks in the infrared spectrum between 500 and 800 cm-1 and between 3400 and 3700 cm-1. Under the right experimental conditions these different clusters can be uniquely identified using high-resolution IR spectroscopy.

Experimental infrared spectra of Cl−(ROH) (R = H, CH3, CH3CH2) complexes in the gas-phase

Infrared multiple photon dissociation spectra for the chloride ion solvated by either water, methanol or ethanol have been recorded using an FTICR spectrometer coupled to a free-electron laser, and are presented here along with assignments to the observed bands. The assignments made to the Cl(-)/H(2)O, Cl(-)(CH(3)OH), and Cl(-)(CH(3)CH(2)OH) spectra are based on comparison with the neutral H(2)O, CH(3)OH, and CH(3)CH(2)OH spectra, respectively. This work confirms that a band observed around 1400 cm(-1) in the Cl(-)(H(2)O) spectrum is not due to the Ar tag in Ar predissociation spectra. The carrier of this band is, most likely, the first overtone of the OHCl bend. Based on the position of the overtone in the IRMPD spectrum, 1375 cm(-1), the fundamental must occur very close to 700 cm(-1) and observation of this band should aid theoretical treatments of the spectrum of this complex. B3LYP/6-311++G(2df,2pd) calculations are shown to reproduce the IRMPD spectra of all three solvated chloride species. They also predict that attaching one or two Ar atoms to the Cl(-)(H(2)O) complex results in a shift of no more than a few wavenumbers in the fundamental bands for the bare complex, in agreement with previous experiment. For both alcohol-Cl(-) complexes, the S(N)2 "backside attack" isomers are not observed and Cl(-) is predicted theoretically, and confirmed experimentally, to be bound to the hydroxyl hydrogen. For Cl(-)(CH(3)CH(2)OH), the trans and gauche conformers are similar in energy, with the gauche conformer predicted to be thermodynamically favoured. The experimental infrared spectrum agrees well with that predicted for the gauche conformer but a mixture of gauche and anti conformers cannot be ruled out based on the experimental spectra nor on the computed thermochemistry.

Ab Initio Vibrational Calculations for H2SO4 and H2SO4·H2O: Spectroscopy and the Nature of the Anharmonic Couplings

Vibrational frequencies for fundamental, overtone, and combination excitations of sulfuric acid (H2SO4) and of sulfuric acid monohydrate cluster (H2SO4 x H2O) are computed directly from ab initio MP2/TZP potential surface points using the correlation-corrected vibrational self-consistent field (CC-VSCF) method, which includes anharmonic effects. The results are compared with experiment. The computed transitions show in nearly all cases good agreement with experimental data and consistent improvement over the harmonic approximation. The CC-VSCF improvements over the harmonic approximation are largest for the overtone and combination excitations and for the OH stretching fundamental. The agreement between the calculations and experiment also supports the validity of the MP2/TZP potential surfaces. Anharmonic coupling between different vibrational modes is found to significantly affect the vibrational frequencies. Analysis of the mean magnitude of the anharmonic coupling interactions between different pairs of normal modes is carried out. The results suggest possible mechanisms for the internal flow of vibrational energy in H2SO4 and H2SO4 x H2O.

Vibrational zero-point energies and thermodynamic functions beyond the harmonic approximation

This paper compares harmonic and anharmonic zero-point energies and thermodynamic functions for a number of molecules of small and medium size. Anharmonic corrections cannot be neglected for quantitative studies, but can be obtained quite effectively by a perturbative treatment including cubic force constants to the second order and semidiagonal quartic constants to the first order. Simple finite difference equations provide all the necessary terms by at most 6N-11 Hessian evaluations, where N is the number of atoms in the system. Accurate values are obtained by this method using the Becke three parameter Lee-Yang-Parr functional, medium size basis sets, and, when needed, proper treatment of internal rotations. The whole model has been completely automated in the Gaussian package.

Fast vibrational self-consistent field calculations through a reduced mode–mode coupling scheme

We present a new methodology to perform fast correlation-corrected vibrational self-consistent field (CC-VSCF) calculations using ab initio potential energy points calculated on the fly. Our method is based on the replacement of all-electron basis sets with a pseudo-potential basis for heavy atoms, and on an efficient reduction of the number of pair-coupling elements used in the CC-VSCF procedure. The method is applied to several test systems: H2O, NH3, and CH4, where it proves to be efficient, providing a speedup factor of 2 compared to a standard CC-VSCF calculation. We also apply our technique to the simulation of the vibrational spectrum of ethane and show that very accurate results can be obtained with a substantial speedup for this system.

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.