Effects Of Vibrational Anharmonicity Research Articles

Perturbative treatment of anharmonic vibrational effects on bond distances: An extended langevin dynamics method

In this work, we first review the perturbative treatment of an oscillator with cubic anharmonicity. It is shown that there is a quantum-classical correspondence in terms of mean displacement, mean-squared displacement, and the corresponding variance in the first-order perturbation theory, provided that the amplitude of the classical oscillator is fixed at the zeroth-order energy of quantum mechanics EQM (0). This correspondence condition is realized by proposing the extended Langevin dynamics (XLD), where the key is to construct a proper driving force. It is assumed that the driving force adopts a simple harmonic form with its amplitude chosen according to EQM (0), while the driving frequency chosen as the harmonic frequency. The latter can be improved by using the natural frequency of the system in response to the potential if its anharmonicity is strong. By comparing to the accurate numeric results from discrete variable representation calculations for a set of diatomic species, it is shown that the present method is able to capture the large part of anharmonicity, being competitive with the wave function-based vibrational second-order perturbation theory, for the whole frequency range from ∼4400 cm(-1) (H2 ) to ∼160 cm(-1) (Na2 ). XLD shows a substantial improvement over the classical molecular dynamics which ceases to work for hard mode when zero-point energy effects are significant.

Polymorphism and melt in high-pressure tantalum

Recent small-cell (150 atom) quantum molecular dynamics (QMD) simulations for Ta based on density functional theory (DFT) have predicted a hexagonal \ensuremath{\omega} (hex-\ensuremath{\omega}) phase more stable than the normal bcc phase at high temperature ($T$) and pressure ($P$) above 70 GPa [Burakovsky et al., Phys. Rev. Lett. 104, 255702 (2010)]. Here we examine possible high-$T,P$ polymorphism in Ta with complementary DFT-based model generalized pseudopotential theory (MGPT) multi-ion interatomic potentials, which allow accurate treatment of much larger system sizes (up to \ensuremath{\sim}80 000 atoms). We focus on candidate bcc, A15, fcc, hcp, and hex-\ensuremath{\omega} phases for the high-$T,P$ phase diagram to 420 GPa, studying the mechanical and relative thermodynamic stability of these phases for both small and large computational cells. Our MGPT potentials fully capture the $T=0$ DFT energetics of these phases, while MGPT-MD simulations demonstrate that the higher-energy fcc, hcp, and hex-\ensuremath{\omega} structures are only mechanically stabilized at high temperature by large, size-dependent, anharmonic vibrational effects, with the stability of the hex-\ensuremath{\omega} phase also being found to be a sensitive function of its $c/a$ ratio. Both two-phase and Z-method melting techniques have been used in MGPT-MD simulations to determine relative phase stability and its size dependence. In the large-cell limit, the two-phase method yields accurate equilibrium melt curves for all five phases, with bcc producing the highest melt temperatures at all pressures and hence being the most stable phase of those considered. The two-phase bcc melt curve is also in good agreement with dynamic experimental data as well as with the MGPT melt curve calculated from bcc and liquid free energies. In contrast, we find that the Z method produces only an upper bound to the equilibrium melt curve in the large-cell limit. For the bcc and hex-\ensuremath{\omega} structures, however, this is a close upper bound within 5$%$ of the two-phase results, although for the A15, fcc, and hcp structures, the Z-melt curves are 25$%$--35$%$ higher in temperature than the two-phase results. Nonetheless, the Z method has allowed us to study melt size effects in detail. We find these effects to be either small or modest for the cubic bcc, A15, and fcc structures, but to have a large impact on the hexagonal hcp and hex-\ensuremath{\omega} melt curves, which are dramatically pushed above that of bcc for simulation cells less than 150 atoms. The melt size effects are driven by and closely correlated with similar size effects on the mechanical stability and the vibrational anharmonicity. We further show that for the same simulation cell sizes and choice of $c/a$ ratio, the MGPT-MD bcc and hex-\ensuremath{\omega} melt curves are in good agreement with the QMD results, so the QMD prediction is confirmed in the small-cell limit. But in the large-cell limit, the MGPT-MD hex-\ensuremath{\omega} melt curve is always lowered below that of bcc for any choice of $c/a$, so bcc is the most stable phase. We conclude that for the non-bcc Ta phases studied, one requires simulation cells of at least 250--500 atoms to be free of size effects impacting mechanical and thermodynamic phase stability.

Normal modes for probing the local solvation environment of nitrate anion during step wise hydration: A theoretical study

We investigate structural, energetic and spectroscopic aspects of the finite size hydrated NO3-·nH2O (n=1–8) clusters based on the first principles electronic structure calculations. It is observed that the geometrical parameters at MP2/6-311++G(d,p) level are almost equal to that of calculated at B3LYP/6-311++G(d,p) level for the higher size of clusters (n>3). Our results reveal that total interaction energy and its components do vary linearly with the size of the clusters. Two types of scaling factors are implemented in two different regions to account the effect of anharmonic vibrations. The degeneracy of in-plane bending and asymmetric NO stretching mode in nitrate system is lifted due to hydration. An excellent agreement is observed between the present calculated H2O bending and asymmetric NO stretching frequencies with the experimental results (within 4% w.r.t. experimentally measured values). Understanding the nature of normal modes of vibration at the molecular level provides information of the local hydration environment during stepwise solvation.

Theoretical Unimolecular Kinetics for CH4 + M ⇄ CH3 + H + M in Eight Baths, M = He, Ne, Ar, Kr, H2, N2, CO, and CH4

Ensembles of classical trajectories are used to study collisional energy transfer in highly vibrationally excited CH(4) for eight bath gases. Several simplifying assumptions for the CH(4) + M interaction potential energy surface are tested against full dimensional direct dynamics trajectory calculations for M = He, Ne, and H(2). The calculated energy transfer averages are confirmed to be sensitive to the shape of the repulsive wall of the intermolecular potential, with an exponential repulsive wall required for quantitative predictions. For the diatomic baths, the usual "separable pairwise" approximation for the interaction potential is unable to describe the orientation dependence of the interaction potential accurately, and the ambiguity in the resulting parametrizations contributes an additional uncertainty to the predicted energy transfer averages of 20-40%. On the other hand, the energy transfer averages are shown to be insensitive to the level of theory used to describe the intramolecular CH(4) potential, with a computationally efficient semiempirical tight binding potential for hydrocarbons performing equally well as an MP2 potential. The relative collisional energy transfer efficiencies of the eight bath gases are discussed and shown to be a function of temperature. The ensemble-averaged energy transferred in deactivating collisions <ΔE(d)> for each bath is used to parametrize a single-exponential-down model for collisional energy transfer in master equation calculations. The predicted decomposition rate coefficients for CH(4) agree well with available experimental rate coefficients for M = He, Ar, Kr, and CH(4). The effect of vibrational anharmonicity on the predicted rate coefficients is considered briefly.

Time-correlation function approach to molecular anharmonicity in hyperthermal atom-molecule collisions

In hyperthermal atom-molecule collisions, differential cross sections for vibrational and rotational excitation are related to correlation functions of the positions of the atoms that constitute the target. We present a new approach to the evaluation of the correlation functions that encompasses the effects of anharmonic vibrations of the polyatomic. By means of cumulant expansion techniques, the vibrational correlation function is expressed in terms of displacement—displacement correlation functions, which are obtained from the corresponding double-time Green functions. The displacement-displacement Green functions are evaluated by decoupling their hierarchy of equations of motion with a linearization procedure that includes anharmonic forces to infinite order. Results for cubic and quartic anharmonicities in N2, CO, and in the bending mode of CO2 indicate that, at hyperthermal collision energies, anharmonic forces contribute less than 1% to the vibrational energy transferred to these targets.

Anomalously Strong Effect of the Ion Sign on the Thermochemistry of Hydrogen Bonded Aqueous Clusters of Identical Chemical Composition

The sign preference of hydrogen bonded aqueous ionic clusters X±(H2O)i (n =1–5, X = F; Cl; Br) has been investigated using the Density Functional Theory and ab initio MP2 method. The present study indicates the anomalously large difference in formation free energies between cations and anions of identical chemical composition. The effect of vibrational anharmonicity on stepwise Gibbs free energy changes has been investigated, and possible uncertainties associated with the harmonic treatment of vibrational spectra have been discussed.

Thermodynamics and dynamics of a monoatomic glass former. Constant pressure and constant volume behavior

We report constant-volume and constant-pressure simulations of the thermodynamic and dynamic properties of the low-temperature liquid and crystalline phases of the modified Stillinger-Weber (SW) model. We have found an approximately linear temperature increase of the effective Gaussian width of the distribution of inherent structures. This effect comes from non-Gaussianity of the landscape and is consistent with the predictions of the Gaussian excitations model representing the thermodynamics of the configurational manifold as an ensemble of excitations, each carrying an excitation entropy. The SW model provides us with both the configurational and excess entropies, with the difference mostly attributed to vibrational anharmonicity. We therefore can address the distinction between the excess thermodynamic quantities, often used to interpret experiments, and configurational thermodynamics used to describe the dynamics in the Adam-Gibbs (AG) equation. However we are limited computationally to work at temperatures above the "crossover" temperature at which the breakdown in the Adam-Gibbs relation has been identified in laboratory studies. We find a new break in the slope of the constant pressure AG plot (in the same sense but at much higher temperature than with laboratory data) when the excess entropy is used in the AG equation. This break, which we associate with anharmonic vibrational effects, is not seen when the configurational entropy is used. The simulation diffusivity data are equally well fitted by the AG equation and by a new equation, derived within the Gaussian excitations model, that emphasizes enthalpy over entropy as the thermodynamic control variable for transport in viscous liquids. We show that the modified SW model has close links to the behavior observed for bulk metallic glasses, both in its diffusional and in its thermodynamic properties.

Molecular structures of the two most stable conformers of free glycine

The equilibrium molecular structures of the two lowest-energy conformers of glycine, Gly-Ip and Gly-IIn, have been characterized by high-level ab initio electronic structure computations, including all-electron cc-pVTZ CCSD(T) geometry optimizations and 6-31G* MP2 quartic force fields, the latter to account for anharmonic zero-point vibrational effects to isotopologic rotational constants. Based on experimentally measured vibrationally averaged effective rotational constant sets of several isotopologues and our ab initio data for structural constraints and zero-point vibrational shifts, least-squares structural refinements were performed to determine improved Born-Oppenheimer equilibrium (r(e)) structures of Gly-Ip and Gly-IIn. Without the ab initio constraints even the extensive set of empirical rotational constants available for 5 and 10 isotopologues of Gly-Ip and Gly-IIn, respectively, cannot satisfactorily fix their molecular structure. Excellent agreement between theory and experiment is found for the rotational constants of both conformers, the rms residual of the final fits being 7.8 and 51.6 kHz for Gly-Ip and Gly-IIn, respectively. High-level ab initio computations with focal point extrapolations determine the barrier to planarity separating Gly-IIp and Gly-IIn to be 20.5 +/- 5.0 cm(-1). The equilibrium torsion angle tau(NCCO) of Gly-IIn, characterizing the deviation of its heavy-atom framework from planarity, is (11 +/- 2) degrees. Nevertheless, in the ground vibrational state the effective structure of Gly-IIn has a plane of symmetry.

Effect of anharmonic longitudinal and transverse vibrations with wave vector k = (2/3)(1, 1, 1) on the structural stability of β-Zr under pressure

The pressure and temperature dependences of the frequencies of a strongly anharmonic longitudinal and a transverse vibrational mode with wave vector k = (2/3)(1, 1, 1) in β-Zr are studied. The frequencies are calculated by solving a set of stochastic Langevin differential equations with a thermal bath of the white-noise type. In the calculations, a two-mode effective potential is used. This potential is found in the framework of the density-functional theory using the “frozen-phonon” model and assuming that the contribution from the electron entropy to the free energy is dependent on the atomic displacements. Based on the calculated pressure and temperature dependences of the spectral density of transverse vibrations, the region of stability of the bcc phase of zirconium is determined for pressures up to 35 GPa, and the result is in good agreement with the experimental data. The bcc lattice is found to be unstable with respect to atomic displacements characteristic of vibrations with wave vector k = (2/3)(1, 1, 1). This instability is of importance not only in the β → ω transition but also in the β → α transformation, which is observed to occur at pressures less than 5 GPa.

Vibrational anharmonicity effects in electronic tunneling through molecular bridges

Effects of anharmonic bridge vibrations on electronic tunneling in donor-bridge-acceptor complexes are studied using a model of anharmonic bridge vibration coupled nonlinearly to an electronic degree of freedom. An anharmonicity parameter is introduced, enabling to reproduce the standard harmonic model with linear coupling as a limiting case. The frequency of electronic tunneling oscillations between the donor and acceptor sites is shown to be sensitive to the nuclear anharmonicity, where stretching and compression modes have an opposite effect on the electronic frequency. This phenomenon, that cannot be accounted for within the harmonic approximation, is analyzed and explained.

Semispectroscopic and Quantitative Structure−Property Relationship Estimates of the Equilibrium and Vibrationally Averaged Structure and Dipole Moment of 1-Buten-3-yne

Systematic quantum chemical calculations have been performed to obtain precise estimates of the equilibrium and vibrationally averaged molecular structure and electric dipole moment of vinylacetylene (VA, 1-buten-3-yne). Anharmonic (cubic and semi-diagonal quartic) MP2/cc-pVTZ force fields in normal coordinates were computed to account for anharmonic vibrational effects, including zero-point contributions to the rotational constants and the electric dipole moment. A simultaneous weighted least-squares structural refinement was performed, resulting in the best semispectroscopic estimate of the re structure of VA. The refinement was based on experimentally measured ground-state rotational constants of two isotopologs of VA corrected to equilibrium values using MP2/cc-pVTZ vibration-rotation interaction constants and all-electron CCSD(T)/aug-cc-pVTZ structural constraints. The semispectroscopic re structure of VA agrees excellently with the high-level CCSD(T)/aug-cc-pVTZ ab initio structure. The most dependable, CCSD(T)/cc-pVQZ//CCSD(T)/aug-cc-pVTZ equilibrium electric dipole moment of VA, in D, is mua= 0.4088, mub= 0.0004, and muc= 0. The vibrationally corrected a-component of 0.4214 D is in excellent agreement with one of the available experimental values. The present analysis shows that mub is negligible even after vibrational correction. A simple quantitative structure-property relationship (QSPR) model resulted in a highly similar estimate, 0.45 D, for the electric dipole moment of VA.

Molecular Structure of Proline

The molecular structures of the two lowest-energy conformers of proline, Pro-I and Pro-II, have been characterized by ab initio electronic structure computations. An extensive MP2/6-31G* quartic force field for Pro-I, containing 62,835 unique elements in the internal coordinate space, was computed to account for anharmonic vibrational effects, including total zero-point contributions to isotopomeric rotational constants. New re and improved r0 least-squares structural refinements were performed to determine the heavy-atom framework of Pro-I, based on experimentally measured (A. Lesarri, S. Mata, E. J. Cocinero, S. Blanco, J. C. Lopez, J. L. Alonso, Angew. Chem. 2002, 114, 4867; Angew. Chem. Int. Ed. 2002, 41, 4673) rotational constant sets of nine isotopomers and our ab initio data for structural constraints and zero-point vibrational (ZPV) shifts. Without the ab initio constraints, even the extensive set of empirical rotational constants cannot satisfactorily fix the molecular structure of the most stable conformer of proline, a 17-atom molecule with no symmetry. After imposing the ab initio constraints, excellent agreement between theory and experiment is found for the heavy-atom geometric framework, the root-mean-square (rms) residual of the empirical rotational constant fit being cut in half by adding ZPV corrections. The most significant disparity, about 0.07 A, between the empirical and the best ab initio structures, concerns the r(N...H) distance of the intramolecular hydrogen bond. Some of the experimental quartic centrifugal distortion constants assigned to Pro-II have been corrected based on data obtained from a theoretical force field.

Hydrogen-bonding between the hydrogen peroxide molecule and the hydroperoxy radical (H 2O 2–HO 2): the global minimum

Spectroscopic properties of H 2O 2–HO 2 have been re-investigated by post Hartree–Fock methods including anharmonic vibrational effects through a second order perturbative approach. The results have been compared to recent experimental data. The very low barrier height computed for the conversion of the five-membered complex into its more stable six-membered counterpart (27 cm −1) explains why only the six-membered hydrogen-bonded complex is observed in argon matrices. The calculated anharmonic frequencies of the latter complex are in excellent agreement with experimental data.

Hydrogen-bonding between the hydrogen peroxide molecule and the hydroperoxy radical (H2O2?HO2): the global minimum

Spectroscopic properties of H 2 O 2 –HO 2 have been re-investigated by post Hartree–Fock methods including anharmonic vibrational effects through a second order perturbative approach. The results have been compared to recent experimental data. The very low barrier height computed for the conversion of the five-membered complex into its more stable six-membered counterpart (27 cm −1 ) explains why only the six-membered hydrogen-bonded complex is observed in argon matrices. The calculated anharmonic frequencies of the latter complex are in excellent agreement with experimental data.

Hydrogen in aluminum: First-principles calculations of structure and thermodynamics

Despite decades of study, several key aspects of the Al-H system remain the subject of considerable debate. In an effort to elucidate some of these unknowns, we perform a systematic study of this system using first-principles density-functional calculations. We show that generalized gradient approximation (GGA) calculations provide an accurate picture of energetics, phase stability and structure, diffusion, and defect binding in the Al-H system. A series of calculations for hydrides in the M-H systems (M=Al, Ba, Ca, K, Mg, La, Li, Na, Ni, Pd, Sc, Sr, Ti, V, and Y) also shows that the GGA calculations are a quantitatively accurate predictor of hydride formation energies. For Al-H, we find: (i) In agreement with experiment, the observed metastable hydride, ${\mathrm{AlH}}_{3}$ is found to have a small, negative formation enthalpy at ambient conditions, but a strongly positive formation free energy. (ii) Linear response calculations of ${\mathrm{AlH}}_{3}$ yield vibrational frequencies, phonon densities of states (DOS), and heat capacities in excellent agreement with experimental measurements, and suggest the need for a reinterpretation of measured phonon DOS. (iii) Atomic relaxation and anharmonic vibrational effects both play an important role in the tetrahedral versus octahedral interstitial site preference of H in Al. (iv) The calculated heat of solution of H in the preferred tetrahedral site is large and positive (+0.71 eV), consistent with experimental solubility data and with Al as an endothermic hydrogen absorber. (v) Interstitial H interacts strongly with Al vacancies $(\ensuremath{\square}),$ with a calculated H-$\ensuremath{\square}$ binding energy of 0.33 eV. (vi) In the absence of vacancies, the calculated migration energy of H between the tetrahedral and octahedral interstitial sites is 0.18 eV, but for H migrating away from an Al vacancy, the migration energy increases to 0.54 eV. Vacancy trapping of H can therefore provide an explanation for observed disparate H migration barriers.

Equilibrium structure and large amplitude motion investigation of 1,4-disilacyclohexa-2,5-diene by means of electron diffraction, vibrational spectroscopic data, and ab initio calculations

Equilibrium and thermal average structure of 1,4-disilacyclohexa-2,5-diene (DSCHD) was determined by applying procedures that have been recently developed for joint treatment of gas phase electron diffraction and molecular spectroscopy data guided by ab initio calculations. Both large amplitude motion and anharmonic vibrational effects were taken into account. Similar structural results were obtained by considering DSCHD molecule as a unique equilibrium conformer and as a set of quasi-conformers describing large amplitude motion. The determined equilibrium structural parameters for DSCHD (planar configuration) are: r e ( Si– C)=1.861(2) A ̊ , r e ( CC)=1.346(3) A ̊ , r e ( Si– H)=1.498(10) A ̊ , r e ( C– H)=1.074(10) A ̊ , ∠(C–Si–C)=109.9(3)°, ∠(H–CC)=116.7(10)°, and ∠(H–Si–H)=107.9(10)°. Uncertainties given in parentheses include three times standard deviation and a systematic error.

Anharmonic effects on photo-induced electron transfer: A Redfield approach

Photo-induced electron transfer experiments examine intrinsically nonequilibrium processes. A theoretical description of photoinduced processes should take into account the fact that the approximations and assumptions made for equilibrium electron transfer need not be appropriate. Under nonequilibrium conditions, anharmonic distortions in the potential energy surfaces of nuclear motion coupled to the electron transfer may effect the dynamics. This work is a study of the effects of anharmonicity on photo-induced electron transfer reactions for condensed phase systems where one vibrational mode is strongly coupled to the electron transfer and a stochastic bath. For this vibrational mode, both harmonic and anharmonic potential energy surfaces for the excited states are considered and the electron transfer dynamics is monitored in a range of system–bath coupling regimes. The study focuses on two effects due to anharmonic distortions of the intramolecular modes: changes to the system Hamiltonian, and differences in the dephasing processes caused by the anharmonic distortions. These calculations show that for small differences in the donor and acceptor state energies, the effects of vibrational anharmonicity is very small. However, when this energy difference is large, the dynamics for anharmonic and harmonic modes is significant. The relative role played by the competing physical processes is easily understood by examining the vibronic state populations obtained using a multistate Redfield approach.

Gas-Phase Infrared Spectrum of the Coronene Cation

The gas-phase infrared spectrum of the coronene cation in the 700-1700 cm-1 range is presented. The spectrum is obtained via multiphoton dissociation spectroscopy of ionic coronene stored in a quadrupole ion trap using the intense and narrowband infrared radiation of a free electron laser. The spectrum shows main absorption peaks at 849, 1327, and 1533 cm-1 along with some weak and barely resolved features, in good agreement with density functional calculations if the effects of vibrational anharmonicity are accounted for. Relative line intensities show remarkable differences with respect to matrix isolation data. The novel experimental technique applied here leads in a natural way to an absorption spectrum of highly excited species. Hence, measured absorption spectra can be compared rather directly to interstellar emission spectra, negating to some extent the need for detailed model calculations.

Theoretical investigations of proton-bound cluster ions.

Several proton-bound cluster ions have been studied by means of coupled cluster calculations with large basis sets. Among these are complexes of a krypton or xenon atom with the cations HCO+, HN2+ and HNCH+. Various spectroscopic properties have been calculated in all cases. Effects of vibrational anharmonicity are particularly pronounced for the intramolecular stretching vibrations of Kr...HN2+ and Xe...HN2+. The proton stretching vibration of (N2)H+(N2) is predicted around 800 cm-1, with a large transition dipole moment of 1.15 D. Both (N2)H+(N2) and (HCN)H+(NCH) have linear centrosymmetric equilibrium structures. Those of (OC)H+(CO) and (HCC-)H+(CCH-) are asymmetric with barrier heights to the centrosymmetric saddle points of 382 and 2323 cm-1, respectively. The dissociation energy of the anionic complex Cl-...HCCH is calculated to be Do = 3665 cm-1, 650 cm-1 larger than the corresponding value for Br-...HCCH. The complex between a fluoride ion and acetylene is more strongly bound and shows strongly anharmonic behaviour, similar to the bihalides FHF- or ClHCl-. Strong Fermi resonance interaction is predicted between nu 3 (approximately proton stretch) and 2 nu 4 (first overtone of intermolecular stretch).

The hydrogen-bonded cluster anions Br-···HCCH and I-···HCCH: results of coupled cluster calculations

Large-scale coupled cluster calculations at the CCSD(T) level of approximation have been carried out for the anionic complexes Br−···HCCH and I−···HCCH, both of which have a linear equilibrium structure. The equilibrium dissociation energies (De) are predicted to be 3126 and 2550 cm−1, respectively. Agreement with available experimental data, obtained through predissociation infrared spectroscopy, is very good. In addition, many predictions are made for spectroscopic properties of various isotopomers of the two species. Particular emphasis is given to the effects of vibrational anharmonicity, conveniently expressed by anharmonicity constants Xij and vibration–rotation coupling constants αr. Transition dipole moments were calculated for various stretching vibrational transitions.