Vibrational Corrections Research Articles

The Lennard-Jones Potential Revisited: Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices.

Analytical formulas are derived for the zero-point vibrational energy and anharmonicity corrections of the cohesive energy and the mode Grüneisen parameter within the Einstein model for the cubic lattices (sc, bcc, and fcc) and for the hexagonal close-packed structure. This extends the work done by Lennard-Jones and Ingham in 1924, Corner in 1939, and Wallace in 1965. The formulas are based on the description of two-body energy contributions by an inverse power expansion (extended Lennard-Jones potential). These make use of three-dimensional lattice sums, which can be transformed to fast converging series and accurately determined by various expansion techniques. We apply these new lattice sum expressions to the rare gas solids and discuss associated critical points. The derived formulas give qualitative but nevertheless deep insight into vibrational effects in solids from the lightest (helium) to the heaviest rare gas element (oganesson), both presenting special cases because of strong quantum effects for the former and strong relativistic effects for the latter.

A simple way to novel 2‐dichloromethyl‐5‐aryl‐2H‐tetrazoles

AbstractA series of 2‐dichloromethyl‐5‐aryl‐2H‐tetrazoles (3a–i) were synthesized by the reaction of 5‐aryl‐NH‐tetrazoles with trichloromethane in strong organic basic condition. The reaction represents a single‐stage access to a new class of promising compounds, which not only can have biological activity, but can also serve as intermediates for further alkylation of halogen and the introduction of various fragments into the structure. The compounds obtained were fully characterized by means of ESI–MS, 1H and 13C{1H} NMR spectroscopies, as well as by single‐crystal X‐ray diffraction (for 3b) the structural parameters as well as the vibrational corrections to enthalpies and total energies of the investigated systems were calculated using DFT B3LYP/6‐31+G** approach.

Unlocking the Water Trimer Loop: Isotopic Study of Benzophenone‐(H2O)1–3Clusters with Rotational Spectroscopy

AbstractExamined here are the structures of complexes of benzophenone microsolvated with up to three water molecules by using broadband rotational spectroscopy and the cold conditions of a molecular jet. The analysis shows that the water molecules dock sideways on benzophenone for the water monomer and dimer moieties, and they move above one of the aromatic rings when the water cluster grows to the trimer. The rotational spectra shows that the water trimer moiety in the complex adopts an open‐loop arrangement. Ab initio calculations face a dilemma of identifying the global minimum between the open loop and the closed loop, which is only solved when zero‐point vibrational energy correction is applied. An OH⋅⋅⋅π bond and a Bürgi‐Dunitz interaction between benzophenone and the water trimer are present in the cluster. This work shows the subtle balance between water–water and water–solute interactions when the solute molecule offers several different anchor sites for water molecules.

Unlocking the Water Trimer Loop: Isotopic Study of Benzophenone-(H2 O)1-3 Clusters with Rotational Spectroscopy.

Examined here are the structures of complexes of benzophenone microsolvated with up to three water molecules by using broadband rotational spectroscopy and the cold conditions of a molecular jet. The analysis shows that the water molecules dock sideways on benzophenone for the water monomer and dimer moieties, and they move above one of the aromatic rings when the water cluster grows to the trimer. The rotational spectra shows that the water trimer moiety in the complex adopts an open‐loop arrangement. Ab initio calculations face a dilemma of identifying the global minimum between the open loop and the closed loop, which is only solved when zero‐point vibrational energy correction is applied. An OH⋅⋅⋅π bond and a Bürgi‐Dunitz interaction between benzophenone and the water trimer are present in the cluster. This work shows the subtle balance between water–water and water–solute interactions when the solute molecule offers several different anchor sites for water molecules.

Efficient J‐oriented tin basis sets for the correlated calculations of indirect nuclear spin–spin coupling constants

New J-oriented tin basis sets, acvXz-J (X=2, 3, 4), have been developed at the level of the second-order polarization propagator approximation with the coupled-cluster single and double amplitudes, SOPPA (CCSD), for the purpose of correlated calculations of indirect nuclear spin-spin coupling constants involving tin nucleus. High-quality coupled-cluster calculations of several tin-proton and tin-carbon spin-spin coupling constants, performed with one of the newly developed basis sets, namely, the acv3z-J, taking into account relativistic, solvent, and vibrational corrections showed that the acv3z-J basis set is capable to provide reliable results, as compared with the experimental data.

Analysis and Comparison of the Vibration Correction Accuracy of Different Optimization Objectives for the Classical Absolute Gravimeter

Accurate absolute gravimeters are important instruments in applications, such as metrology, geophysics, and geological exploration. Vibration is one of the limiting factors that cause deterioration in measurement accuracy, which includes trueness and precision. The vibration correction method, in which a seismometer is used to record the vibration, provides an effective method to deal with the disturbances. The theoretical analysis shows that the ultimate correction accuracy is limited by the inherent frequency performance of the seismometer. The correction algorithm is an optimization problem to achieve this ultimate accuracy. The selection of the optimization objectives affects the correction accuracy dramatically. Although the real gravitational acceleration is unknown before the measurement is taken, minimization of the standard deviation of the fitting residual for a single drop (SDFRSD) is proven to realize better trueness. Enhanced precision is achieved through minimization of the Type A uncertainty of gravitational accelerations for all drops (UGAAD). Simulations and experimental measurements with the T-1 absolute gravimeter verify the theoretical analysis results. In addition, the results also show that the SDFRSD correction contains the real gravitational acceleration value, while the UGAAD correction exceeds the valid range. Therefore, the SDFRSD correction approach provides better comprehensive accuracy than the UGAAD correction method.

A Vertical Seismometer With Built-In Retroreflector for Absolute Gravimetry

Classical absolute gravimeters are widely used in many areas, including metrology, seismology, geophysics, and exploration. These gravimeters apply a free-fall method to measure absolute gravitational acceleration using a laser interferometer. In practice, the measurement precision is affected by ground vibrations. Vibration correction is an important way to deal with these ground vibrations for absolute gravity measurement. Most vibration correction methods use a commercial seismometer to measure the motion of a reference retroreflector indirectly. A vertical seismometer with a built-in retroreflector is designed to directly measure the motion of the retroreflector, which is fixed on the proof mass of the seismometer. The motion of the retroreflector relative to the ground vibration is measured through capacitance detection. A voice coil actuator is employed to drive the retroreflector to track the ground vibration. The sensitivity of the homemade vertical seismometer is approximately 15751 V/g. The bandwidth of the system is 80 Hz. The homemade vertical seismometer is integrated into the homemade T-1 absolute gravimeter to test its performance. The standard deviation of the measurement results is reduced by a factor of 16, when compared with the results obtained without any vibration treatment. Absolute gravimeters with the homemade vertical seismometer are expected to be used in field measurements.

Analysis of vibration correction performance of vibration sensor for absolute gravity measurement

Analysis of vibration correction performance of vibration sensor for absolute gravity measurement

Equilibrium molecular structure of orotic acid from gas-phase electron diffraction data and quantum-chemical calculations

The accurate equilibrium structures of planar anti and syn orotic acid conformers with different positions of the carboxyl group with respect to the C=C bond were determined from gas-phase electron diffraction data using the dynamic model and taking into account anharmonic vibrational corrections calculated with ab initio force field. The high accuracy of coupled-cluster computations was exploited in the analysis of structural effects due to electron-acceptor substituents.

An Optimized Vibration Correction Method for Absolute Gravimetry

Accurate observations of the gravitational acceleration ( $g$ , about 9.8 m/s2) provide important geophysical data for use in geophysics, metrology, and geodesy. At present, the most widely used absolute gravimeter determines the value of $g$ by tracking a falling retroreflector in a vacuum using a laser interferometer. The precision and accuracy of the measurement are mainly affected by ground vibration noise. When compared with a vibration isolator, vibration correction offers a simple and convenient way to reduce the influence of ground vibrations. Previous correction methods have used a low-noise seismometer as a detector. However, their performance is limited by the seismometer’s bandwidth (which usually ranges from 0.01 to 60 Hz). An optimized correction method combined with digital filtering is proposed here to increase the seismometer’s bandwidth numerically. Experimental results show that the accuracy and precision of the corrected results using the optimized method are improved in both relatively quiet and complex vibration environments. And better improvement is shown in complex vibration environment. Therefore, both the feasibility and the superiority of the proposed method have been verified. Further improvements can be achieved by using a higher-order digital filter.

Zero-point energies prevent a trigonal to simple cubic transition in high-pressure sulfur

Recently published density functional theory results using the PBE functional (Whaley-Baldwin and Needs 2020 New J. Phys. 22 023020) suggest that elemental sulfur does not adopt the simple-cubic (SC) phase at high pressures, in disagreement with previous works (Rudin and Liu 1999 Phys. Rev. Lett. 83 3049--52; Gavryushkin et al 2017 Phys. Status Solidi B 254 1600857). We carry out an extensive set of calculations using a variety of different exchange–correlation functionals (both local and non-local), and show that even though under LDA and PW91 a high-pressure SC phase does indeed become favourable at the static lattice level, when zero-point energies (ZPEs) are included, the transition to the SC phase is suppressed in every case, owing to the larger ZPE of the SC phase; thus confirming the transition sequence as BCC, with no intervening SC phase. We reproduce these findings with pseudopotentials that explicitly include core electronic states, and show that even at these high pressures, only the n = 3 valence shell contributes to bonding in sulfur. We then compare our findings against the all-electron code ELK, which is in excellent agreement with our pseudopotential results, and examine the roles of the exchange and correlation contributions to the total energy. We further calculate anharmonic vibrational corrections to the ZPEs of the two phases, and find that such corrections are several orders of magnitude smaller than the ZPEs and are thus negligible. The effect of finite temperatures is also considered, and we show that the phase becomes even more unfavourable with an increase in temperature. Finally, the experimental consequences of our results on the equation of state of sulfur and its superconducting critical temperature are explicitly calculated.

Tritium adsorption and desorption on/from nuclear graphite edge by a first-principles study

The removal of tritium from irradiated nuclear graphite is one of the key targets of nuclear graphite decontamination. Here, we employ first principle density functional theory (DFT) to study its adsorption and molecular desorption on the most common edges and their reconstructions. The calculated adsorption energy ranges from −2.6 to - 5 eV, depending on the edge structure and the hydrogenation level, and are much larger than on the bulk of graphite. The hydrogenation level increases with the increase of hydrogen partial pressure, and drops rapidly at high temperature. The pathways to fully saturated edges are then determined for each edge variant and the activation energy (Eac) for molecular desorption computed by properly accounting for vibrational zero-point energy corrections (ΔEZPE). Our results showed that, there are three different stages for the desorption of hydrogen isotopes from nuclear graphite, namely stage 1 (200–300 °C), stage 2 (500–700 °C), stage 3 (1000–1100 °C). Our results can provide a theoretical basis for the tritium removal experiment from nuclear graphite.

Discovering the Elusive Global Minimum in a Ternary Chiral Cluster: Rotational Spectra of Propylene Oxide Trimer

AbstractThe chirality controlled conformational landscape of the trimer of propylene oxide (PO), a prototypical chiral molecule, was investigated using rotational spectroscopy and a range of theoretical tools for conformational searches and for evaluating vibrational contributions to effective structures. Two sets of homochiral (PO)3 rotational transitions were assigned and the associated conformers identified with theoretical support. One set of heterochiral (PO)3 transitions was assigned, but no structures generated by one of the latest, advanced conformational search codes could account for them. With the aid of a Python program, the carbon atom backbone and then the heterochiral (PO)3 structure were generated using 13C isotopic data. Excellent agreement between theoretical and experimental rotational constants and relative dipole moment components of all three conformers was achieved, especially after applying vibrational corrections to the rotational constants.

Discovering the Elusive Global Minimum in a Ternary Chiral Cluster: Rotational Spectra of Propylene Oxide Trimer.

The chirality controlled conformational landscape of the trimer of propylene oxide (PO), a prototypical chiral molecule, was investigated using rotational spectroscopy and a range of theoretical tools for conformational searches and for evaluating vibrational contributions to effective structures. Two sets of homochiral (PO)3 rotational transitions were assigned and the associated conformers identified with theoretical support. One set of heterochiral (PO)3 transitions was assigned, but no structures generated by one of the latest, advanced conformational search codes could account for them. With the aid of a Python program, the carbon atom backbone and then the heterochiral (PO)3 structure were generated using 13C isotopic data. Excellent agreement between theoretical and experimental rotational constants and relative dipole moment components of all three conformers was achieved, especially after applying vibrational corrections to the rotational constants.

DFT Investigation of Hydrogen Atom Abstraction from NHC-Boranes by Methyl, Ethyl and Cyanomethyl Radicals-Composition and Correlation Analysis of Kinetic Barriers.

Understanding the hydrogen atom abstraction (HAA) reactions of N-heterocyclic carbene (NHC)-boranes is essential for extending the practical applications of boron chemistry. In this study, density functional theory (DFT) computations were performed for the HAA reactions of a series of NHC-boranes attacked by •CH2CN, Me• and Et• radicals. Using the computed data, we investigated the correlations of the activation and free energy barriers with their components, including the intrinsic barrier, the thermal contribution of the thermodynamic reaction energy to the kinetic barriers, the activation Gibbs free energy correction and the activation zero-point vibrational energy correction. Furthermore, to describe the dependence of the activation and free energy barriers on the thermodynamic reaction energy or reaction Gibbs free energy, we used a three-variable linear model, which was demonstrated to be more precise than the two-variable Evans–Polanyi linear free energy model and more succinct than the three-variable Marcus-theory-based nonlinear HAA model. The present work provides not only a more thorough understanding of the compositions of the barriers to the HAA reactions of NHC-boranes and the HAA reactivities of the substrates but also fresh insights into the suitability of various models for describing the relationships between the kinetic and thermodynamic physical quantities.

Parity-nonconserving interactions of electrons in chiral molecules with cosmic fields

Pseudoscalar or pseudovector cosmic fields, that serve as a source of parity ($\mathcal{P}$) violation, are invoked in different models for cold dark matter or in the standard model extension that allows for Lorentz invariance violation. A direct detection of the timelike-component of such fields requires a direct measurement of $\mathcal{P}$-odd potentials or their evolution over time. Herein, advantageous properties of chiral molecules, in which $\mathcal{P}$-odd potentials lead to resonance frequency differences between enantiomers, for direct detection of such $\mathcal{P}$-odd cosmic fields are demonstrated. Scaling behavior of electronic structure enhancements of such interactions with respect to nuclear charge number and the fine-structure constant is derived analytically. This allows a simple estimate of the effect sizes for arbitrary molecules. The analytical derivation is supported by quasi-relativistic numerical calculations in the molecules H$_2$X$_2$ and H$_2$XO with X $=$ O, S, Se, Te, Po. Parity violating effects due to cosmic fields on the C--F stretching mode in CHBrClF are compared to electroweak parity violation and influences of non-separable anharmonic vibrational corrections are discussed. On this basis it was estimated from a twenty year old experiment with CHBrClF that bounds on Lorentz invariance violation as characterized by the parameter $|b^\mathrm{e}_0|$ can be pushed down to the order of $10^{-17}\,\mathrm{GeV}$ in modern experiments with suitably selected molecular system, which will be an improvement of the current best limits by at least two orders of magnitude. This serves to highlight the particular opportunities that precision spectroscopy of chiral molecules provides in the search for new physics beyond the standard model.

Molecular structure of 5-fluorouracil from gas-phase electron diffraction data and quantum-chemical calculations

The accurate equilibrium molecular structure of a canonical tautomer of 5-fluorouracil was determined by electron diffraction taking into account anharmonic vibrational corrections calculated with ab initio force field. This structure was applied to benchmark the results of CCSD(T) computations used for the analysis of substitution effects in uracil derivatives.

Resolving Anharmonic Lattice Dynamics in Molecular Crystals with X-Ray Diffraction and Terahertz Spectroscopy.

Molecular crystals are increasingly being used for advanced applications, ranging from pharmaceutics to organic electronics, with their utility dictated by a combination of their three-dimensional structures and molecular dynamics-with anharmonicity in the low-frequency vibrations crucial to numerous bulk phenomena. Through the use of temperature-dependent x-ray diffraction and terahertz time-domain spectroscopy, the structures and dynamics of a pair of isomeric molecular crystals exhibiting nearly free rotation of a CF_{3} functional group at ambient conditions are fully characterized. Using a recently developed solid-state anharmonic vibrational correction, and applying it to a molecular crystal for the first time, the temperature-dependent spatial displacements of atoms along particular terahertz modes are obtained, and are found to be in excellent agreement with the experimental observations, including the assignment of a previously unexplained absorption feature in the low-frequency spectrum of one of the solids.

A New Basis Set for the Calculation of 13C NMR Chemical Shifts within a Non-empirical Correlated Framework.

A new basis set of triple-ζ quality for carbon, 3z-S, is developed and tested at the DFT, MP2, and CCSD(T) levels, taking into account solvent and vibrational corrections for a number of molecules ranging from the smallest fluoromethane, CH3F, to the largest 5,10,15,20-tetraphenylporphyrin, C44H30N4. The proposed highly economical 3z-S basis set has been proven to provide very good accuracy in all examinations, comparable to that of the NMR-oriented Jensen's pcS-2 basis set, which is about 50% larger than 3z-S.

On temperature effects on the structural phase transitions of GaP

In this presentation by employing a combination of calculations based on Density Functional Theory (DFT) and Molecular Dynamics simulations (MD), we show that temperature has an unquestionable role in the behavior of Gallium Phosphide under pressure, shedding a new light in the controversial interpretation of experimental results. For example, we justify the absence of some structures predicted by early theoretical works, which remained up to now misunderstood. Moreover, we predict transitions to new structures at high temperature that may encourage new experiments. The differences in the observed transition sequences at low and high temperatures indicate that the vibrational corrections we included in the DFT calculations are fundamental to the description of the stability of higher pressure structures, and may be employed on other materials. Additionally, the good agreement between DFT and MD shows the suitability of the classical effective many-body interaction potential used to describe the different high-pressure phases of GaP in the Molecular Dynamics simulations. Finally, we discuss the behavior of GaP under extreme conditions for temperatures up to 1400 K and pressures up to 50 GPa, predicting new phases.