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Using Anharmonic PAH Vibrational Spectra to Simulate Fully Anharmonic Cascade Emission Spectra

In recent years, we have developed vibrational second-order perturbation theory (VPT2) approaches that can be applied to very large molecules, such as polycyclic aromatic hydrocarbon (PAH) molecules. One of the main difficulties in applying standard VPT2 methods to PAHs is the large number of Fermi resonances that occur, especially in the C-H stretching region of the infrared spectrum. In order to properly account for these resonances, it is necessary to set up resonance polyads for each irreducible representation of the symmetry point group to which the molecule belongs, and for specific wavenumber regions, such as the C-H stretching region. Diagonalization of the polyads allows us to determine vibrational band positions, the intensity sharing due to the resonances, and hence there will be many more vibrational bands present than there are C-H bonds. Using these data, a library of fully anharmonic temperature-dependent spectra, with proper treatment of polyad resonances, can be determined and subsequently used to model the cascade emission spectra of PAH molecules – the type of spectra directly observed by astronomers. The theoretical approach will be described, with comparison to experiment where possible, and the latest fully anharmonic PAH cascade emission spectra will be discussed.

Timothy J Lee↗
NASA NTRS2001

Ab Initio and Improved Empirical Potentials for the Calculation of the Anharmonic Vibrational States and Intramolecular Mode Coupling of N-Methylacetamide

The second-order Moller-Plesset ab initio electronic structure method is used to compute points for the anharmonic mode-coupled potential energy surface of N-methylacetamide (NMA) in the trans(sub ct) configuration, including all degrees of freedom. The vibrational states and the spectroscopy are directly computed from this potential surface using the Correlation Corrected Vibrational Self-Consistent Field (CC-VSCF) method. The results are compared with CC-VSCF calculations using both the standard and improved empirical Amber-like force fields and available low temperature experimental matrix data. Analysis of our calculated spectroscopic results show that: (1) The excellent agreement between the ab initio CC-VSCF calculated frequencies and the experimental data suggest that the computed anharmonic potentials for N-methylacetamide are of a very high quality; (2) For most transitions, the vibrational frequencies obtained from the ab initio CC-VSCF method are superior to those obtained using the empirical CC-VSCF methods, when compared with experimental data. However, the improved empirical force field yields better agreement with the experimental frequencies as compared with a standard AMBER-type force field; (3) The empirical force field in particular overestimates anharmonic couplings for the amide-2 mode, the methyl asymmetric bending modes, the out-of-plane methyl bending modes, and the methyl distortions; (4) Disagreement between the ab initio and empirical anharmonic couplings is greater than the disagreement between the frequencies, and thus the anharmonic part of the empirical potential seems to be less accurate than the harmonic contribution;and (5) Both the empirical and ab initio CC-VSCF calculations predict a negligible anharmonic coupling between the amide-1 and other internal modes. The implication of this is that the intramolecular energy flow between the amide-1 and the other internal modes may be smaller than anticipated. These results may have important implications for the anharmonic force fields of peptides, for which N-methylacetamide is a model.

Gregurick, Susan K.↗
NASA NTRS2001

The Transition from Hydrogen Bonding to Ionization in (HCI)n(NH3)n and (HCI)n(H2O)n Clusters: Consequences for Anharmonic Vibrational Spectroscopy

Anharmonic vibrational frequencies and intensities are calculated for 1:1 and 2:2 (HCl)(sub n)(NH3)(sub n) and (HCl)(sub n)(H2O)(sub n) complexes, employing the correlation-corrected vibrational self-consistent field method with ab initio potential surfaces at the MP2/TZP computational level. In this method, the anharmonic coupling between all vibrational modes is included, which is found to be important for the systems studied. For the 4:4 (HCl)(sub n)(H2O)(sub n) complex, the vibrational spectra are calculated at the harmonic level, and anharmonic effects are estimated. Just as the (HCl)(sub n)(NH3)(sub n) structure switches from hydrogen-bonded to ionic for n=2, the (HCl)(sub n)(H2O)(sub n) switches to ionic structure for n=4. For (HCl)2(H2O)2, the lowest energy structure corresponds to the hydrogen-bonded form. However, configurations of the ionic form are separated from this minimum by a barrier of less than an O-H stretching quantum. This suggests the possibility of experiments on ionization dynamics using infrared excitation of the hydrogen-bonded form. The strong cooperative effects on the hydrogen bonding, and concomitant transition to ionic bonding, makes an accurate estimate of the large anharmonicity crucial for understanding the infrared spectra of these systems. The anharmonicity is typically of the order of several hundred wave numbers for the proton stretching motions involved in hydrogen or ionic bonding, and can also be quite large for the intramolecular modes. In addition, the large cooperative effects in the 2:2 and higher order (HCl(sub n)(H2O)(sub n) complexes may have interesting implications for solvation of hydrogen halides at ice surfaces.

Chaban, Galina M.↗
NASA NTRS2016

High-Resolution IR Absorption Spectroscopy of Polycyclic Aromatic Hydrocarbons: The Realm of Anharmonicity

We report on an experimental and theoretical investigation of the importance of anharmonicity in the 3 micrometers CH stretching region of Polycyclic Aromatic Hydrocarbon (PAH) molecules. We present mass-resolved, high-resolution spectra of the gas-phase cold ((is) approximately 4K) linear PAH molecules naphthalene, anthracene, and tetracene. The measured IR spectra show a surprisingly high number of strong vibrational bands. For naphthalene, the observed bands are well separated and limited by the rotational contour, revealing the band symmetries. Comparisons are made to the harmonic and anharmonic approaches of the widely used Gaussian software. We also present calculated spectra of these acenes using the computational program SPECTRO, providing anharmonic predictions enhanced with a Fermi-resonance treatment that utilizes intensity redistribution. We demonstrate that the anharmonicity of the investigated acenes is strong, dominated by Fermi resonances between the fundamental and double combination modes, with triple combination bands as possible candidates to resolve remaining discrepancies. The anharmonic spectra as calculated with SPECTRO lead to predictions of the main modes that fall within 0.5% of the experimental frequencies. The implications for the Aromatic Infrared Bands, specifically the 3-m band are discussed.

Astrochemistry↗
NASA NTRS2001

Ab Initio Calculations of Anharmonic Vibrational Spectroscopy for Hydrogen Fluoride (HF)n (n=3,4) and Mixed Hydrogen Fluoride/Water (HF)n(H20)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 (CC-VSCF) 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 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.

Chaban, Galina M.↗
NASA NTRS2002

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 Moller-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.

Water/chemistry↗
NASA NTRS1997

Positive Anharmonicities: The Oxonide Anion as an Example

An accurate ab initio quartic force field for the ozonide anion has been determined at the singles and doubles coupled-cluster level of theory that includes a perturbational estimate of the effects of connected triple excitations, denoted CCSD(T), using the augmented valence triple-zeta correlation consistent one-particle basis set. Convergence of the harmonic frequencies with respect to the one-particle basis set has been demonstrated by computing quadratic force fields at the CCSD(T) level using augmented valence double-zeta and quadruple-zeta basis sets. Fundamental vibrational frequencies have been determined via second-order ro-vibrational perturbation theory and also using exact variational methods. Agreement is very good, and they both show that the antisymmetric O-O stretch, v 3, possesses a positive anharmonic correction (that is, the fundamental frequency is predicted to be higher in energy than the harmonic frequency). Comparison of the O_3 and O3 quartic force fields shows that the positive anharmonic correction is the result of a particularly large F3333 symmetry internal coordinate force constant. The reasonableness of this force constant has been tested by computing both F33 and F3333 at the CCSD, CCSD(T), and CASPT2 levels of theory. A discussion of known positive anharmonicities for stretching modes is presented.

Lee, Timothy J.↗
NASA NTRS2003

Anharmonic Vibrational Spectroscopy of the F-(H20)n, complexes, n=1,2

We report anharmonic vibrational spectra (fundamentals, first overtones) for the F-(H(sub 2)O) and F-(H(sub 2)O)2 clusters computed at the MP2 and CCSD(T) levels of theory with basis sets of triple zeta quality. Anharmonic corrections were estimated via the correlation-corrected vibrational self-consistent field (CC-VSCF) method. The CC-VSCF anharmonic spectra obtained on the potential energy surfaces evaluated at the CCSD(T) level of theory are the first ones reported at a correlated level beyond MP2. We have found that the average basis set effect (TZP vs. aug-cc-pVTZ) is on the order of 30-40 cm(exp -1), whereas the effects of different levels of electron correlation [MP2 vs. CCSD(T)] are smaller, 20-30 cm(exp -1). However, the basis set effect is much larger in the case of the H-bonded O-H stretch of the F-(H(sub 2)O) cluster amounting to 100 cm(exp -1) for the fundamentals and 200 cm (exp -1) for the first overtones. Our calculations are in agreement with the limited available set of experimental data for the F-(H(sub 2)O) and F-(H(sub 2)O)2 systems and provide additional information that can guide further experimental studies.

Chaban, Galina M.↗
NASA NTRS1974

Vibration-translation energy transfer in anharmonic diatomic molecules. 1: A critical evaluation of the semiclassical approximation

The semiclassical approximation is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Mckenzie, R. L.↗
NASA NTRS1975

Vibration-translation energy transfer in anharmonic diatomic molecules. I - A comparative evaluation of the semiclassical approximation

The semiclassical approximation (quantum oscillator, classical path) is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Mckenzie, R. L.↗
NASA NTRS1982

Anharmonic properties of solids from measurements of the stress acoustic constant

The equations of elastic motion and their solutions are generalized in order to include nonzero homogeneous initial stresses and redefine the stress acoustic constants to include the effect of initial stress. In deriving the relationship between the stress acoustic constants and the strain-generalized Gruneisen parameters, implications in material anharmonicity and nonlinear thermoelasticity are discovered. It is found that the linear change in velocity obtained from these measurements is a nonlinear process resulting from anharmonicity in the interatomic potential. In addition, the thermal expansion coefficient can also be expressed in terms of linear combinations.

Cantrell, J. H., Jr.↗
NASA NTRS1987

Anharmonicity and the interstellar polycyclic aromatic hydrocarbon infrared emission spectrum

The hypothesis that interstellar infrared emission originates from vibrationally excited polycyclic aromatic hydrocarbons (PAHs) requires that emission can arise from all vibrational levels that are energetically accessible. Due to anharmonicity, the emission from the upper vibrational levels is shifted to longer wavelengths from that of the v = 1-0 transition. It is shown that structure in the 3-micron region is readily and quantitatively explained by emission from upper vibrational levels of excited PAHs that contain a maximum of 20-30 carbon atoms. The asymmetrical broadening of the 11.3-micron emission band may also be due to anharmonicity.

Barker, John R.↗
NASA NTRS1988

Anharmonic and screening corrections to the melting of a two-dimensional charged colloidal crystal

The Kosterlitz-Thouless-Halperin-Nelson-Young theory of melting is applied to a two-dimensional charged colloidal crystal. The renormalization of elastic constants due to anharmonic and dislocation pair-screening effects is calculated. For colloidal spheres ('polyballs') suspended in a thin film of water confined between two glass plates whose surfaces are highly charged, as in recent experimental configurations, the corrections to the harmonic results simply require an altered effective polyball charge to reproduce virtually the identical melting curve of the harmonic approximation (which agrees well with experiment). The effect on the melting curve of added salt is also calculated; the corresponding experiments have yet to be performed. For a film between uncharged surfaces the anharmonic correction again softens the lattice significantly. Dislocation pair screening causes an additional but minor reduction of the elastic constants. Neither correction eliminates a nonmelting behavior characteristic of the two-dimensional screened Coulomb system in this configuration.

Chang, Enson↗
NASA NTRS1995

Finite-element time evolution operator for the anharmonic oscillator

The finite-element approach to lattice field theory is both highly accurate (relative errors approximately 1/N(exp 2), where N is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is H = p(exp 2)/2 + lambda q(exp 4)/4. Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a results for the anharmonic oscillator ground state energy accurate to better than 1 percent, while a two-state approximation reduces the error to less than 0.1 percent.

Milton, Kimball A.↗
NASA NTRS1995

The Anharmonic Force Field of Ethylene, C2H4, by Means of Accurate Ab Initio Calculations

The quartic force field of ethylene, C2H4, has been calculated ab initio using augmented coupled cluster, CCSD(T), methods and correlation consistent basis sets of spdf quality. For the C-12 isotopomers C2H4, C2H3D, H2CCD2, cis-C2H2D2, trans-C2H2D2, C2HD3, and C2D4, all fundamentals could be reproduced to better than 10 per centimeter, except for three cases of severe Fermi type 1 resonance. The problem with these three bands is identified as a systematic overestimate of the Kiij Fermi resonance constants by a factor of two or more; if this is corrected for, the predicted fundamentals come into excellent agreement with experiment. No such systematic overestimate is seen for Fermi type 2 resonances. Our computed harmonic frequencies suggest a thorough revision of the accepted experimentally derived values. Our computed and empirically corrected re geometry differs substantially from experimentally derived values: both the predicted rz geometry and the ground-state rotational constants are, however, in excellent agreement with experiment, suggesting revision of the older values. Anharmonicity constants agree well with experiment for stretches, but differ substantially for stretch-bend interaction constants, due to equality constraints in the experimental analysis that do not hold. Improved criteria for detecting Fermi and Coriolis resonances are proposed and found to work well, contrary to the established method based on harmonic frequency differences that fails to detect several important resonances for C2H4 and its isotopomers. Surprisingly good results are obtained with a small spd basis at the CCSD(T) level. The well-documented strong basis set effect on the v8 out-of-plane motion is present to a much lesser extent when correlation-optimized polarization functions are used. Complete sets of anharmonic, rovibrational coupling, and centrifugal distortion constants for the isotopomers are available as supplementary material to the paper.

Martin, Jan M. L.↗