Anharmonic Corrections Research Articles

Constraints on anharmonic corrections of fuzzy dark matter

The cold dark matter (CDM) scenario has proved successful in cosmology. However, we lack a fundamental understanding of its microscopic nature. Moreover, the apparent disagreement between CDM predictions and subgalactic-structure observations has prompted the debate about its behaviour at small scales. These problems could be alleviated if the dark matter is composed of ultralight fields m ∼ 10−22 eV, usually known as fuzzy dark matter (FDM). Some specific models, with axion-like potentials, have been thoroughly studied and are collectively referred to as ultralight axions (ULAs) or axion-like particles (ALPs). In this work we consider anharmonic corrections to the mass term coming from a repulsive quartic self-interaction. Whenever this anharmonic term dominates, the field behaves as radiation instead of cold matter, modifying the time of matter-radiation equality. Additionally, even for high masses, i.e. masses that reproduce the cold matter behaviour, the presence of anharmonic terms introduce a cut-off in the matter power spectrum through its contribution to the sound speed. We analyze the model and derive constraints using a modified version of class and comparing with CMB and large-scale structure data.

Rovibrational analysis of c-SiC2H2: Further evidence for out-of-plane bending issues in correlated methods.

While the issue of properly describing the out-of-plane bends (OPBs) in sp2 hybridized carbon atoms has reappeared for c-SiC2H2, the present quantum chemical study provides a new characterization of this molecule in order to aid in its potential detection in astrophysically relevant studies. Combining the previous, high-level approach with MP2-F12/aug-cc-pVDZ gives exceptionally accurate results for the comparison of experimental rotational constants and seemingly reliable vibrational frequencies. Most notably, the brightest fundamental vibrational frequency in c-SiC2H2, the b1 OPB, is predicted to lie at 673.4 cm-1, within 4.0 cm-1 of the previous matrix isolation experiment. As with c-C3H2, CCSD(T)-F12/aug-cc-pVTZ appears to be quite susceptible to over estimating the OPB anharmonic correction in c-SiC2H2 and may also do such for in-plane bends, as well. MP2-F12/aug-cc-pVDZ is less susceptible to these errors, and increasing the step size reduces this positive anharmonicity issue in both the cases. The OPB underestimation, however, likely still remains. Finally, estimates for some anharmonic vibrational frequencies are provided for the methylated form, c-SiC2HCH3, which is likely also a product of gas phase reactions of ·SiH with various alkynes.

High Accuracy Quantum Chemical and Thermochemical Network Data for the Heats of Formation of Fluorinated and Chlorinated Methanes and Ethanes.

Reliable heats of formation are reported for numerous fluorinated and chlorinated methane and ethane derivatives by means of an accurate thermochemical protocol, which involves explicitly correlated coupled-cluster calculations augmented with anharmonic, scalar relativistic, and diagonal Born-Oppenheimer corrections. The theoretical results, along with additional experimental data, are further enhanced with the help of the thermochemical network approach. For 28 species, out of 50, this study presents the best estimates, and discrepancies with previous reports are also highlighted. Furthermore, the effects of the less accurate theoretical data on the results yielded by thermochemical networks are discussed.

Toward accurate high temperature anharmonic partition functions

We use four different methods to calculate an anharmonic correction factor fvib to the conventional RRHO partition functions for H2O, HO2, 3CH2, H2O2, and CH4 over a temperature range up to 3000 K. The exact quantum mechanical method benchmarks the other three approximate methods that are based on classical Monte Carlo phase space integrals, on vibrational perturbation theory, and on conventional harmonic partition functions evaluated with fundamental, rather than harmonic, frequencies. The last two of these methods converge on the exact partition function below temperatures that vary from 1500 K for the least anharmonic system (H2O) to 250 K for the most anharmonic system (H2O2). For 3CH2 and H2O2, both these methods are qualitatively incorrect because they are insensitive to a low energy barrier for internal motion. The classical method qualitatively overestimates quantum mechanical results at low temperatures because of the exclusion of zero point energy. However, here anharmonic corrections are small. At high temperatures, our anharmonic corrections can be large (up to 40% for CH4 at 3000 K) and at high enough temperatures the classical and exact quantum results will converge. Comparing perturbation theory and the classical method, the classical method becomes the approximate method of choice above ∼750 K for H2O2 and CH4, ∼2100 K for 3CH2, ∼2700 K for HO2, and > 3000 K for H2O.

Experimental vibrational spectroscopy (FTIR and FT-Raman) of D-tryptophan and its anharmonic theoretical studies using density functional theory

The present work has explored the anharmonic vibrational spectroscopy of D-tryptophan (DTRP) with the help of the FTIR (4000-400 cm−1) and FT-Raman (4000-50 cm−1) spectra as well as DFT calculations. Anharmonic corrections are computed within the generalized vibrational perturbation theory (GVPT2) approach using the DFT/6-31G(d,p) quantum-mechanical model. The anharmonic frequencies calculated at GVPT2 level is found to be in remarkable agreement with experimental results and show a significant improvement over the harmonic approximation. The effect of intermolecular interaction (OH⋅⋅⋅⋅⋅O) on the geometrical parameters and vibrational frequencies are analyzed by the calculations on the dimeric structure of the title molecule. Further, the electronic spectrum in DMSO solvent has been analyzed using TD-DFT approach and it is compared with experimental results. Moreover, other molecular properties such as frontier molecular orbitals and nonlinear optical (NLO) properties are also investigated.

Revisit the landscape of protonated water clusters H+(H2O)n with n = 10-17: An ab initio global search.

Using a genetic algorithm incorporated with density functional theory, we explore the ground state structures of protonated water clusters H+(H2O)n with n = 10-17. Then we re-optimize the isomers at B97-D/aug-cc-pVDZ level of theory. The extra proton connects with a H2O molecule to form a H3O+ ion in all H+(H2O)10-17 clusters. The lowest-energy structures adopt a monocage form at n = 10-16 and core-shell structure at n = 17 based on the MP2/aug-cc-pVTZ//B97-D/aug-cc-pVDZ+ZPE single-point-energy calculation. Using second-order vibrational perturbation theory, we further calculate the infrared spectra with anharmonic correction for the ground state structures of H+(H2O)10-17 clusters at the PBE0/aug-cc-pVDZ level. The anharmonic correction to the spectra is crucial since it reproduces the experimental results quite well. The extra proton weakens the O-H bond strength in the H3O+ ion since the Wiberg bond order of the O-H bond in the H3O+ ion is smaller than that in H2O molecules, which causes a red shift of the O-H stretching mode in the H3O+ ion.

Direct dynamics simulations of the unimolecular dissociation of dioxetane: Probing the non-RRKM dynamics.

In a previous UB3LYP/6-31G* direct dynamics simulation, non-Rice-Ramsperger-Kassel-Marcus (RRKM) unimolecular dynamics was found for vibrationally excited 1,2-dioxetane (DO); [R. Sun et al., J. Chem. Phys. 137, 044305 (2012)]. In the work reported here, these dynamics are studied in more detail using the same direct dynamics method. Vibrational modes of DO were divided into 4 groups, based on their characteristic motions, and each group excited with the same energy. To compare with the dynamics of these groups, an additional group of trajectories comprising a microcanonical ensemble was also simulated. The results of these simulations are consistent with the previous study. The dissociation probability, N(t)/N(0), for these excitation groups were all different. Groups A, B, and C, without initial excitation in the O-O stretch reaction coordinate, had a time lag to of 0.25-1.0 ps for the first dissociation to occur. Somewhat surprisingly, the C-H stretch Group A and out-of-plane motion Group C excitations had exponential dissociation probabilities after to, with a rate constant ∼2 times smaller than the anharmonic RRKM value. Groups B and D, with excitation of the H-C-H bend and wag, and ring bend and stretch modes, respectively, had bi-exponential dissociation probabilities. For Group D, with excitation localized in the reaction coordinate, the initial rate constant is ∼7 times larger than the anharmonic RRKM value, substantial apparent non-RRKM dynamics. N(t)/N(0) for the random excitation trajectories was non-exponential, indicating intrinsic non-RRKM dynamics. For the trajectory integration time of 13.5 ps, 9% of these trajectories did not dissociate in comparison to the RRKM prediction of 0.3%. Classical power spectra for these trajectories indicate they have regular intramolecular dynamics. The N(t)/N(0) for the excitation groups are well described by a two-state coupled phase space model. From the intercept of N(t)/N(0) with random excitation, the anharmonic correction to the RRKM rate constant is approximately a factor of 1.5.

Dissociation Energy of the H2O···HF Dimer.

Even though (H2O)2 and (HF)2 are arguably the most thoroughly characterized prototypes for hydrogen bonding, their heterogeneous analogue H2O···HF has received relatively little attention. Here we report that the experimental dissociation energy ( D0) of this important paradigm for heterogeneous hydrogen bonding is too large by 2 kcal mol-1 or 30% relative to our computed value of 6.3 kcal mol-1. For reference, computational procedures similar to those employed here to compute D0 (large basis set CCSD(T) computations with anharmonic corrections from second-order vibrational perturbation theory) provide results within 0.1 kcal mol-1 of the experimental values for (H2O)2 and (HF)2. Near the CCSD(T) complete basis set limit, the electronic dissociation energy for H2O···HF is ∼4 kcal mol-1 larger than those for (H2O)2 and (HF)2 (∼9 kcal mol-1 for the heterogeneous dimer vs ∼5 kcal mol-1 for the homogeneous dimers). Results reported here from symmetry-adapted perturbation theory computations suggest that this large difference is primarily due to the induction contribution to the interaction energy.

Theoretical calculation of enthalpy of formation of multiconformational molecules: 1,2-ethanediol, propanediols, and glycerol

The gas-phase enthalpies of formation of four molecules with high flexibility, which leads to the existence of a large number of low-energy conformers, were calculated with the G4 method to see whether the lowest energy conformer is sufficient to achieve high accuracy in the computed values. The calculated values were in good agreement with the experiment, whereas adding the correction for conformer distribution makes the agreement worse. The reason for this effect is a large anharmonicity of low-frequency torsional motions, which is ignored in the calculation of ZPVE and thermal enthalpy. It was shown that the approximate correction for anharmonicity estimated using a free rotor model is of very similar magnitude compared with the conformer correction but has the opposite sign, and thus almost fully compensates for it. Therefore, the common practice of adding only the conformer correction is not without problems.

Anharmonic Rovibrational Partition Functions for Fluxional Species at High Temperatures via Monte Carlo Phase Space Integrals.

Monte Carlo phase space integration (MCPSI) is used to compute full dimensional and fully anharmonic, but classical, rovibrational partition functions for 22 small- and medium-sized molecules and radicals. Several of the species considered here feature multiple minima and low-frequency nonlocal motions, and efficiently sampling these systems is facilitated using curvilinear (stretch, bend, and torsion) coordinates. The curvilinear coordinate MCPSI method is demonstrated to be applicable to the treatment of fluxional species with complex rovibrational structures and as many as 21 fully coupled rovibrational degrees of freedom. Trends in the computed anharmonicity corrections are discussed. For many systems, rovibrational anharmonicities at elevated temperatures are shown to vary consistently with the number of degrees of freedom and with temperature once rovibrational coupling and torsional anharmonicity are accounted for. Larger corrections are found for systems with complex vibrational structures, such as systems with multiple large-amplitude modes and/or multiple minima.

Reinterpreting the infrared spectrum of H + HCN: Methylene amidogen radical and its coproducts

The methylene amidogen radical (H2CN) plays a role in high-energy material combustion and extraterresterial atmospheres. Recent theoretical work has struggled to match experimental assignments for its CN and antisymmetric CH2 stretching frequencies (ν2 and ν5), which were reported to occur at 1725 and 3103 cm-1. Herein, we compute the vibrational energy levels of this molecule by extrapolating quadruples-level coupled-cluster theory to the complete basis limit and adding corrections for vibrational anharmonicity. This level of theory predicts that ν2 and ν5 should occur at 1646 and 2892 cm-1, at odds with the experimental assignments. To investigate the possibility of defects in our theoretical treatment, we analyze the sensitivity of our approach to each of its contributing approximations. Our analysis suggests that the observed deviation from experiment is too large to be explained as an accumulation of errors, leading us to conclude that these transitions were misassigned. To help resolve this discrepancy, we investigate possible byproducts of the H + HCN reaction, which was the source of H2CN in the original experiment. In particular, we predict vibrational spectra for cis-HCNH, trans-HCNH, and H2CNH using high-level coupled-cluster computations. Based on these results, we reassign the transition at 1725 cm-1 to ν3 of trans-HCNH, yielding excellent agreement. Supporting this identification, we assign a known contaminant peak at 886 cm-1 to ν5 of the same conformer. Our computations suggest that the peak observed at 3103 cm-1, however, does not belong to any of the aforementioned species. To facilitate further investigation, we use structure and bonding arguments to narrow the range of possible candidates. These arguments lead us to tentatively put forth formaldazine [(H2CN)2] as a suggestion for further study, which we support with additional computations.

Detailed kinetics of tetrafluoroethene ozonolysis.

The C2F4 + O3 reaction plays an important role in the oxidation process of perfluoroalkenes in the atmosphere. The detailed reaction mechanism was explored using the accurate electronic structure method, CCSD(T)/CBS//B3LYP/aug-cc-pVTZ. The 1,3-cycloaddition of O3 with C2F4 to form the primary ozonide was found to be the rate-determining step of the oxidation process with a small barrier (i.e., 7.3 kcal mol-1 at 0 K). The temperature- and pressure-dependent behaviors of the title reaction were characterized in the range of 200-1000 K & 0.1-760 Torr using the integrated deterministic and stochastic master equation/Rice-Ramsperger-Kassel-Marcus (ME/RRKM) rate model with the inclusion of the corrections for anharmonicity and tunneling treatments. It is found that the anharmonic effect plays a role in the kinetic behaviors (e.g., lower the rate by a factor of ∼ two at 298 K) while the tunneling correction is insignificant. The total rate constants were found to be pressure-independent under the considered conditions, shown as ktot(T) = 4.80 × 10-23 × T2.69 × exp(-2983.4 K/T) (cm3 per molecule per s), which confirms the latest experimental data by Acerboni et al. (G. Acerboni, N. R. Jensen, B. Rindone and J. Hjorth, Chem. Phys. Lett., 1999, 309, 364-368); thus this study helps to resolve a long-term controversy among the previous measurements. The sensitivity analyses on the derived rate coefficients and time-resolved species mole fraction with respect to the ab initio input parameters were also performed to further understand as well as quantify the kinetic behaviors for the title reaction.

Quantum Emulation of Molecular Force Fields: A Blueprint for a Superconducting Architecture

In this work, we propose a flexible architecture of microwave resonators with tunable couplings to perform quantum simulations of problems from the field of molecular chemistry. The architecture builds on the experience of the D-Wave design, working with nearly harmonic circuits instead of qubits. This architecture, or modifications of it, can be used to emulate molecular processes such as vibronic transitions. Furthermore, we discuss several aspects of these emulations, such as dynamical ranges of the physical parameters, quenching times necessary for diabaticity, and, finally, the possibility of implementing anharmonic corrections to the force fields by exploiting certain nonlinear features of superconducting devices.

Anharmonicity and the isotope effect in superconducting lithium at high pressures: A first-principles approach

Recent experiments [Schaeffer 2015] have shown that lithium presents an extremely anomalous isotope effect in the 15-25 GPa pressure range. In this article we have calculated the anharmonic phonon dispersion of $\mathrm{^7Li}$ and $\mathrm{^6Li}$ under pressure, their superconducting transition temperatures, and the associated isotope effect. We have found a huge anharmonic renormalization of a transverse acoustic soft mode along $\Gamma$K in the fcc phase, the expected structure at the pressure range of interest. In fact, the anharmonic correction dynamically stabilizes the fcc phase above 25 GPa. However, we have not found any anomalous scaling of the superconducting temperature with the isotopic mass. Additionally, we have also analyzed whether the two lithium isotopes adopting different structures could explain the observed anomalous behavior. According to our enthalpy calculations including zero-point motion and anharmonicity it would not be possible in a stable regime.

Radiative transition probabilities for the main diatomic electronic systems of N2, [formula omitted], NO, O2, CO, CO+, CN, C2 and H2 produced in plasma of atmospheric entry

Accurate radiative transition probabilities of diatomic electronic systems are required to calculate the discrete radiation of plasmas. However, most of the published transition probabilities are obtained using older spectroscopic constants and electronic transition moment functions (ETMFs), some of which deviates greatly from experimental data. Fortunately, a lot of new spectroscopic constants that include more anharmonic correction terms than the earlier ones have been published over the past few years. In this work, the Einstein coefficients, Franck–Condon factors and absorption band oscillator strengths are calculated for important diatomic radiative transition processes of N2-O2, CO2-N2 and H2 plasmas produced in entering into the atmosphere of Earth, Mars and Jupiter. The most up-to-date spectroscopic constants are selected to reconstruct the potential energy curves by the Rydberg–Klein–Rees (RKR) method. Then the vibrational wave functions are calculated through the resolution of the radial Schrödinger equation for such potential energy curves. These results, together with the latest “ab-initio” ETMFs derived from the literature are used to compute the square of electronic-vibrational transition moments, Einstein coefficients and absorption band oscillator strengths. Moreover, the Franck–Condon factors are determined with the obtained vibrational wave functions. In the supplementary material we present tables of the radiative transition probabilities for 40 band systems of N2, N2+, NO, O2, CO, CO+, CN, C2 and H2 molecules. In addition, the calculated radiative lifetimes are systematically validated by available experimental results.

Toward reliable modeling of S-nitrosothiol chemistry: Structure and properties of methyl thionitrite (CH3SNO), an S-nitrosocysteine model.

Methyl thionitrite CH3SNO is an important model of S-nitrosated cysteine aminoacid residue (CysNO), a ubiquitous biological S-nitrosothiol (RSNO) involved in numerous physiological processes. As such, CH3SNO can provide insights into the intrinsic properties of the -SNO group in CysNO, in particular, its weak and labile S-N bond. Here, we report an ab initio computational investigation of the structure and properties of CH3SNO using a composite Feller-Peterson-Dixon scheme based on the explicitly correlated coupled cluster with single, double, and perturbative triple excitations calculations extrapolated to the complete basis set limit, CCSD(T)-F12/CBS, with a number of additive corrections for the effects of quadruple excitations, core-valence correlation, scalar-relativistic and spin-orbit effects, as well as harmonic zero-point vibrational energy with an anharmonicity correction. These calculations suggest that the S-N bond in CH3SNO is significantly elongated (1.814 Å) and has low stretching frequency and dissociation energy values, νS-N = 387 cm-1 and D0 = 32.4 kcal/mol. At the same time, the S-N bond has a sizable rotation barrier, △E0≠ = 12.7 kcal/mol, so CH3SNO exists as a cis- or trans-conformer, the latter slightly higher in energy, △E0 = 1.2 kcal/mol. The S-N bond properties are consistent with the antagonistic nature of CH3SNO, whose resonance representation requires two chemically opposite (antagonistic) resonance structures, CH3-S+=N-O- and CH3-S-/NO+, which can be probed using external electric fields and quantified using the natural resonance theory approach (NRT). The calculated S-N bond properties slowly converge with the level of correlation treatment, with the recently developed distinguished cluster with single and double excitations approximation (DCSD-F12) performing significantly better than the coupled cluster with single and double excitations (CCSD-F12), although still inferior to the CCSD(T)-F12 method that includes perturbative triple excitations. Double-hybrid density functional theory (DFT) calculations with mPW2PLYPD/def2-TZVPPD reproduce well the geometry, vibrational frequencies, and the S-N bond rotational barrier in CH3SNO, while hybrid DFT calculations with PBE0/def2-TZVPPD give a better S-N bond dissociation energy.

Anharmonic vibrational spectra and mode-mode couplings analysis of 2-aminopyridine

Vibrational spectra of 2-aminopyridine (2AP) have been analyzed using the vibrational self-consistence field theory (VSCF), correlated corrected vibrational self-consistence field theory (CC-VSCF) and vibrational perturbation theory (VPT2) at B3LYP/6-311G(d,p) framework. The mode-mode couplings affect the vibrational frequencies and intensities. The coupling integrals between pairs of normal modes have been obtained on the basis of quartic force field (2MR-QFF) approximation. The overtone and combination bands are also assigned in the FTIR spectrum with the help of anharmonic calculation at VPT2 method. A statistical analysis of deviations shows that estimated anharmonic frequencies are closer to the experiment over harmonic approximation. Furthermore, the anharmonic correction has also been carried out for the dimeric structure of 2AP. The fundamental vibration bands have been assigned on the basis of potential energy distribution (PED) and visual look over the animated modes. Other important molecular properties such as frontier molecular orbitals and molecular electrostatics potential mapping have also been analyzed.

Study of molecular structure, anharmonic vibrational dynamic and electronic properties of sulindac using spectroscopic techniques integrated with quantum chemical calculations

In the present investigation, spectroscopic techniques (FTIR, FT-Raman and UV–Vis) and quantum chemical calculations are employed for exploring vibrational and electronic spectra of sulindac compound. The calculations are performed on most stable conformer of the sulindac molecule using density functional theory (DFT). Anharmonic corrections are made to frequencies using vibrational second-order perturbation theory (VPT2). The effect of intermolecular interactions on the vibrational dynamics has been analyzed using dimeric structure of sulindac molecule. Hirshfeld surface analysis and 2D fingerprint plots are utilized to investigate the nature of interaction present in the crystal system. To account for electronic spectra in different solvents, an integral equation formalism of polarizable continuum model (IEFPCM) at TD-DFT/B3LYP/6-31G(d,p) level of theory has been employed. An excellent agreement between the theoretical and experimental data over the entire spectral region is observed. In addition, natural bond orbital (NBO) analysis, frontier molecular orbitals, nonlinear optical properties (NLO) and molecular electrostatic potential (MEP) analysis are also reported.

Accurate Anharmonic Zero-Point Energies for Some Combustion-Related Species from Diffusion Monte Carlo.

Full-dimensional analytic potential energy surfaces based on CCSD(T)/cc-pVTZ calculations have been determined for 48 small combustion-related molecules. The analytic surfaces have been used in Diffusion Monte Carlo calculations of the anharmonic zero-point energies. The resulting anharmonicity corrections are compared to vibrational perturbation theory results based both on the same level of electronic structure theory and on lower-level electronic structure methods (B3LYP and MP2).

Hydrogen bonded dimers of small alkyl substituted amides: Structures, energetics, and spectral analyses based on density functional theory calculations

We have performed a density functional theory (DFT) study on the hydrogen bonding patterns for the dimers of small alkyl substituted amides, including formamide, acetamide, and propionamide, as well as their N-methyl substituted counterparts. The dispersion-corrected ωB97X-D exchange-correlation density functional with the aug-cc-pVDZ basis set has been employed in the energy and frequency calculations. To calibrate the DFT calculated binding energies for these dimeric complexes, we perform a benchmark calculation with the coupled cluster with single, double and perturbative triple excitations method at the complete basis set limit [CCSD(T)/CBS]. The binding energies are further analyzed by the energy decomposition method based on the symmetry adapted perturbation theory. The infrared spectra for the alkyl substituted amides and their dimers are simulated with explicit anharmonicities included, and compared with the representative experimental data. Both the dimer formations and the anharmonic corrections have significant effects on the principal spectral features related to hydrogen bonding, while the substitution effects are comparatively marginal.