Zero-point Vibrational Corrections Research Articles

High-Resolution Spectroscopy and Structure of Heavy Carbon Subchalcogenides: Tricarbon Selenide, C3Se.

Linear tricarbon selenide, C3Se, has been studied spectroscopically for the first time using a combination of high-resolution infrared and microwave techniques. Probing laser ablation products from carbon-selenium targets in a free jet expansion with He, initial spectroscopic detection was accomplished in the infrared at a wavelength of 5 μm in search of the ν1 vibrational fundamental. Along with the band of the most abundant isotopic species C380Se found centered at about 2039 cm-1, the corresponding bands of the C382Se, C378Se, C376Se, and C377Se isotopologues were also detected. Pure rotational spectra of the five C3Se isotopologues in the 8-18 GHz frequency range were observed in a supersonic jet expansion using chirped-pulse microwave spectroscopy of the discharge products of selenophene, c-C4H4Se. Spectroscopic analyses were guided by results from high-level quantum-chemical calculations carried out at the coupled-cluster level of theory using large correlation-consistent basis sets. Using the experimentally derived ground-state rotational constants of five isotopologues and calculated zero-point vibrational corrections, an accurate semiexperimental equilibrium carbon-selenium bond length is derived.

Accurate thermochemistry of covalent and ionic solids from spin-component-scaled MP2.

We study the performance of spin-component-scaled second-order Møller-Plesset perturbation theory (SCS-MP2) for the prediction of the lattice constant, bulk modulus, and cohesive energy of 12 simple, three-dimensional covalent and ionic semiconductors and insulators. We find that SCS-MP2 and the simpler scaled opposite-spin MP2 (SOS-MP2) yield predictions that are significantly improved over the already good performance of MP2. Specifically, when compared to experimental values with zero-point vibrational corrections, SCS-MP2 (SOS-MP2) yields mean absolute errors of 0.015 (0.017) Å for the lattice constant, 3.8 (3.7) GPa for the bulk modulus, and 0.06 (0.08) eV for the cohesive energy, which are smaller than those of leading density functionals by about a factor of two or more. We consider a reparameterization of the spin-scaling parameters and find that the optimal parameters for these solids are very similar to those already in common use in molecular quantum chemistry, suggesting good transferability and reliable future applications to surface chemistry on insulators.

Vibrational Corrections to NMR Spin-Spin Coupling Constants from Relativistic Four-Component DFT Calculations.

Zero-point vibrational (ZPV) corrections to the nuclear spin–spin coupling constants have been calculated using four-component Dirac–Kohn–Sham DFT for H2X (where X = O, S, Se, Te, Po), XH3 (where X = N, P, As, Sb, Bi), and XH4 (where X = C, Si, Ge, Sn, and Pb) molecules and for HC≡CPbH3. The main goal was to study the influence of relativistic effects on the ZPV corrections and thus results calculated at relativistic and nonrelativistic approaches have been compared. The effects of relativity become notable for the ZPV corrections to the spin–spin coupling constants for compounds with lighter elements (selenium and germanium) than for the spin–spin coupling constants themselves. In the case of molecules containing heavier atoms, for instance BiH3 and PbH4, relativistic effects play a crucial role on the results and approximating ZPV corrections by the nonrelativistic results may lead to larger errors than omitting ZPV corrections altogether.

Conformational stability of cyclopropanecarboxaldehyde is ruled by vibrational effects

Cyclopropanecarboxaldehyde (CPCA) has two main conformers, syn and anti, that are renowned for being very close in energy. The stability order of these two main species is constantly reversed by changing the level of theory or the experimental technique employed in its determination. The anti conformer is predicted to be the most favoured in condensed states of matter, but uncertainty still remains on the relative stability in the gas phase. To gain further insights into this issue, the investigation of the rotational spectrum of both syn- and anti-CPCA has been extended in the 246–294 GHz frequency region and complemented by a detailed computational study of both conformers. A fit incorporating the recorded rotational transitions as well as those reported in the literature led to the accurate determination of the rotational parameters, also including high-order centrifugal distortion constants. Accurately computed vibrational frequencies were used to re-analyse the infrared spectrum of both conformers, thereby allowing a re-assignment of two vibrational bands, namely of anti-CPCA and of the syn conformer. While our state-of-the-art computations favour the anti conformer in the stability order, estimates from analysis of rotational spectra are rather controversial and are strongly affected by several factors, such as the zero-point vibrational correction.

H/D Isotope Effects in Keto-Enol Tautomerism of β-Dicarbonyl Compounds —Importance of Nuclear Quantum Effects of Hydrogen Nuclei—

Abstract Deuterium isotope effects in the keto-enol tautomerism of β-dicarbonyl compounds (malonaldehyde, acetylacetone, dibenzoylmethane, and avobenzone) have been studied using a B3LYP+D functional level of multi-component density functional theory (MC_DFT), which can directly take nuclear quantum effects (NQEs) of the hydrogen nuclei into account. We clearly show that the keto-enol energy difference becomes smaller by deuterium substitution, which is in reasonable agreement with the corresponding experimental evidence. Our MC_DFT study also reveals the hydrogen/deuterium (H/D) isotope effect in geometries and shows that the deuterium substitution weakens the intramolecular hydrogen-bonded interaction in the enol form. Direct treatment of NQEs of hydrogen nuclei via the MC_DFT method is essential for analyzing the H/D isotope effect in keto-enol tautomerism of β-dicarbonyl compounds. Such isotope effects cannot be reproduced in the conventional DFT scheme with harmonic zero-point vibrational corrections.

Phosphorus mononitride: A difficult case for theory

AbstractPhosphorus nitride (PN) is the simplest molecule formed solely by phosphorus and nitrogen. It represents an interesting model for materials, where phosphorus is directly attached to nitrogen. Nevertheless, both theoretical and experimental studies often provide an incomplete picture on the structural, electronic, and spectral properties of PN. Theoretical predictions often suffer from insufficient level of theory, incomplete basis set, or from neglecting several effects, for example, zero‐point vibrational correction (ZPVC). Therefore, we performed an extensive benchmark study on structural, electronic, and spectral properties of PN at the Hartree‐Fock, density functional theory (DFT), or even the coupled‐cluster levels. We paid special attention to the basis set effect. We tested three variants of Dunning's aug‐cc‐pVXZ basis sets with the size from double‐ζ to sextuple‐ζ, as well as Jensen's aug‐pc‐n, aug‐pcJ‐n, and aug‐pcSseg‐n basis sets, where n = 1‐4. Obtained energetics, PN distance, dipole moment, vibrational frequencies, and nuclear magnetic resonance (NMR) parameters were extrapolated to the complete basis set limit (CBS) using three‐ or two‐parameter formulas. The 31P NMR shieldings estimated with the aug‐cc‐pVXZ and aug‐cc‐pV(X + d)Z basis sets strongly depend on the basis set size providing scattered convergence patterns toward CBS. The Hartree‐Fock self‐consistent field (HF‐SCF) NMR parameters evinced similar behavior as the coupled‐cluster data. The only smooth convergence was achieved using the aug‐cc‐pCVXZ basis sets that include core‐valence effects. The KT3 functional underestimated the phosphorus CBS shieldings by about 12 ppm compared to coupled cluster with singles and doubles (CCSD) (T). Nevertheless, KT3 unambiguously surpasses the HF‐SCF and CCSD levels that provide 31P shieldings that are lower by about 150 ppm and 24 ppm compared to CCSD(T). The convergence of nitrogen shieldings was regular for all basis set hierarchies and all theoretical methods. Relativistic and vibrational effects on selected properties were also discussed.

Ab initio investigation of cationic water cluster (H2O)+13 via particle swarm optimization algorithm

The configurations of cationic water cluster (H2O) 13 + have been explored through the particle swarm optimization algorithm conjunct with computational quantum chemistry approaches. Geometry optimization and vibrational analysis for the 15 possible low-lying clusters were calculated at the MPW1K/6–31++G** level as well as infrared spectrum calculation. Through various hybrid exchange–correlation functionals of density functional theory in combination with zero-point vibrational energies correction, we can definitely get the relative stable configurations and discuss the effect on the relative energy order of these clusters caused by different functionals in detail. Given the effect of temperature, it is found that as the temperature rises, the configuration with irregular shape will become more stable. By analyzing the infrared spectra, the structure and vibration analysis of these clusters are studied in detail. Based on topological analysis, we study the relationship between structural characteristics and the bonding strengths, and analyze the strength of hydrogen bonding at the bond critical points.

Accurate calculation of electron affinity for S3**Project supported by the National Natural Science Foundation of China (Grant Nos. 11874179, 11447194,11574114, and 11874177) and the Natural Science Foundation of Jilin Province, China (Grant No. 20180101289JC).

The accurate equilibrium structures of S3 and are determined by the coupled-cluster method with single, double excitation and perturbative triple excitation (CCSD(T)) with basis sets of aug-cc-pV(n + d)Z (n = T, Q, 5, or 6), complete basis set extrapolation functions with two-parameters and three-parameters, together with considering the contributions due to the core-valence electron correlation, scalar relativistic effects, spin–orbit coupling, and zero-point vibrational corrections. Our calculations show that both the neutral S3 and anion have open forms with C2v symmetry. On the basis of the stable geometries, the adiabatic electron affinity of S3 is determined to be 19041(11) cm−1, which is in excellent agreement with the experimental data (19059(7) cm−1). The dependence of geometries and electron affinity on the computation level and physical corrections is discussed. The present computational results are helpful to the experimental molecular spectroscopy and bonding of S3.

On the geometric dependence of the molecular dipole polarizability in water: A benchmark study of higher-order electron correlation, basis set incompleteness error, core electron effects, and zero-point vibrational contributions.

In this work, we investigate how geometric changes influence the static dipole polarizability (α) of a water molecule by explicitly computing the corresponding dipole polarizability surface (DPS) across 3125 total (1625 symmetry-unique) geometries using linear response coupled cluster theory including single, double, and triple excitations (LR-CCSDT) and the doubly augmented triple-ζ basis set (d-aug-cc-pVTZ). Analytical formulae based on power series expansions of this ab initio surface are generated using linear least-squares analysis and provide highly accurate estimates of this quantity as a function of molecular geometry (i.e., bond and angle variations) in a computationally tractable manner. An additional database, which consists of 25 representative molecular geometries and incorporates a more thorough treatment of both basis sets and core electron effects, is provided as a current benchmark for this quantity and the corresponding leading-order C 6 dispersion coefficient. This database has been utilized to assess the importance of these effects as well as the relative accuracy that can be obtained using several quantum chemical methods and a library of density functional approximations. In addition to high-level electron correlation methods (like CCSD) and our analytical least-squares formulae, we find that the SCAN0, PBE0, MN15, and B97-2 hybrid functionals yield the most accurate descriptions of the molecular polarizability tensor in H2O. Using first-order perturbation theory, we compute the zero-point vibrational correction to α at the CCSDT/d-aug-cc-pVTZ level and find that this correction contributes approximately 3% to the isotropic (α iso) and nearly 50% to the anisotropic (α aniso) polarizability values. In doing so, we find that α iso = 9.8307 bohr3, which is in excellent agreement with the experimental value of 9.83 ± 0.02 bohr3 provided by Russell and Spackman. The DPS reported herein provides a benchmark-quality quantum mechanical estimate of this fundamental quantity of interest and should find extensive use in the development (and assessment) of next-generation force fields and machine-learning based approaches for modeling water in complex condensed-phase environments.

Electronic and Vibrational Hyperpolarizabilities of Lithium Substituted (Aza)benzenes and (Aza)naphthalenes

In this article we report results for the electronic and vibrational hyperpolarizabilities of ten molecules: Li@benzene, Li@pyridine, Li@pyrimidine, and Li@pyrazine; Li@naphthalene, Li@quinoline, Li@isoquinoline, Li@cinnolin, Li@quinazoline, and Li@quinoxaline. An electron correlation study shows that second-order many-body perturbation theory and density functional theory with CAM-B3LYP and M05-2X functionals give results for the electronic hyperpolarizabilities in good agreement with coupled cluster with single and doubles reference values. Static and dynamic vibrational corrections were computed through the perturbation theoretical method of Bishop and Kirtman and using a variational approach. In general, we obtained notable discrepancies between the results obtained by the two methods for the pure vibrational corrections because of the deficiency of the perturbation method to properly treat low-frequency normal modes present in the investigated systems. However, both methods give results similar to the zero-point vibrational average corrections.

Binding Matter with Antimatter: The Covalent Positron Bond.

We report sufficient theoretical evidence of the energy stability of the e+ ⋅H22- molecule, formed by two H- anions and one positron. Analysis of the electronic and positronic densities of the latter compound undoubtedly points out the formation of a positronic covalent bond between the otherwise repelling hydride anions. The lower limit for the bonding energy of the e+ ⋅H22- molecule is 74 kJ mol-1 (0.77 eV), accounting for the zero-point vibrational correction. The formation of a non electronic covalent bond is fundamentally distinct from positron attachment to stable molecules, as the latter process is characterized by a positron affinity, analogous to the electron affinity.

Stability of endo- and exohedral complexes of all-boron fullerene B 40

Abstract In a recent publication [Nature Chemistry, 6, 727 (2014)] the synthesis and properties of a new all-boron fullerene analog, B40, have been reported, and a possibility of utilizing the B40 molecule as a hydrogen storage has been postulated. Therefore, in this contribution we study the stability of endo- and exohedral complexes with the hydrogen molecule and several other small molecules, such as N2, H2O, and CO2. The examination of binding and interaction energies obtained by symmetry-adapted perturbation theory and by supermolecular approaches shows that among the studied endohedral complexes only the one with H2 inside the cage is possibly weakly stabilized by the complexation, while all other molecules clearly exhibit too large repulsion, which cannot be counterweighted by attractive components of the interaction energy. An addition of the zero-point vibrational correction to the H2@B40 binding energy changes the balance of the attractive and repulsive contributions in favor of repulsion, so that finally also this endohedral complex is thermodynamically unstable at zero Kelvin. The exohedral minima are stable in all the cases, and are mostly bound by dispersion.

Comparison of measured and predicted specific optical rotation in gas and solution phases: A test for the polarizable continuum model of solvation.

A comparative theoretical and experimental study of dispersive optical activity is presented for a set of small, rigid organic molecules in gas and solution phases. Target species were chosen to facilitate wavelength-resolved measurements of specific rotation in rarefied vapors and in organic solvents having different polarities, while avoiding complications due to conformational flexibility. Calculations were performed with two density functionals (B3LYP and CAM-B3LYP) and with the coupled-cluster singles and doubles (CCSD) ansatz, and solvent effects were included through use of the polarizable continuum model (PCM). Across the various theoretical methods surveyed, CCSD with the modified velocity gauge provided the best overall performance for both isolated and solvated conditions. Zero-point vibrational corrections to equilibrium calculations of chiroptical response tended to improve agreement with gas-phase experiments, but the quality of performance realized for solutions varied markedly. Direct comparison of measured and predicted specific-rotation suggests that PCM, in general, is not able to reproduce attendant solvent shifts (neither between gas and solution phases nor among solvents) and fares better in estimating actual medium-dependent values of this property (although the error is rather system dependent). Thus, more elaborate solvation models seem necessary for a proper theoretical description of solvation in dispersive optical activity.

Ab Initio Prediction of NMR Spin Relaxation Parameters from Molecular Dynamics Simulations.

1H-15N NMR spin relaxation and relaxation dispersion experiments can reveal the time scale and extent of protein motions across the ps-ms range, where the ps-ns dynamics revealed by fundamental quantities R1, R2, and heteronuclear NOE can be well-sampled by molecular dynamics simulations (MD). Although the principles of relaxation prediction from simulations are well-established, numerous NMR-MD comparisons have hitherto focused upon the aspect of order parameters S2 due to common artifacts in the prediction of transient dynamics. We therefore summarize here all necessary components and highlight existing and proposed solutions, such as the inclusion of quantum mechanical zero-point vibrational corrections and separate MD convergence of global and local motions in coarse-grained and all-atom force fields, respectively. For the accuracy of the MD prediction to be tested, two model proteins GB3 and Ubiquitin are used to validate five atomistic force fields against published NMR data supplemented by the coarse-grained force field MARTINI+EN. In Amber and CHARMM-type force fields, quantitative agreement was achieved for structured elements with minimum adjustment of global parameters. Deviations from experiment occur in flexible loops and termini, indicating differences in both the extent and time scale of backbone motions. The lack of systematic patterns and water model dependence suggests that modeling of the local environment limits prediction accuracy. Nevertheless, qualitative accuracy in a 2 μs CHARMM36m Stam2 VHS domain simulation demonstrates the potential of MD-based interpretation in combination with NMR-measured dynamics, increasing the utility of spin relaxation in integrative structural biology.

The influence of vibrations of polyatomic molecules on dipole moment and static dipole polarizability: theoretical study

Dipole moment and static dipole polarizability surfaces for 50 polyatomic molecules, that are important for material science, combustion, and atmospheric chemistry, are explored in the vicinity of their equilibrium nuclear configurations by using density functional theory. The effective values of dipole moment and static polarizability of these molecules in individual vibrational states are determined using the calculated data on the electric properties and potential energy surfaces. Special attention is paid to the effect of the zero-point vibrations on the electric properties. The simple approximation scheme, allowing low-cost estimation of the zero-point vibrational corrections to polarizability, applicable for wide range of polyatomic compounds, are developed on the basis of the obtained data. The influence of the excitation of vibrational states on the dipole moment and dipole polarizability of polyatomic molecules are discussed with respect to the possible change of some important properties of molecular gases, such as refractive index, diffusion coefficients, and rates of chemical reactions.

Microscopic description of the competition between spontaneous fission and α-decay in neutron-rich Ra, U and Pu nuclei

Constrained mean-field calculations, based on the Gogny-D1M energy density functional, have been carried out to describe fission in Ra, U and Pu nuclei with neutron number 144 ≤ N ≤ 176. Fission paths, collective masses and zero-point quantum vibrational and rotational corrections are used to compute the spontaneous fission half-lives. We also pay attention to isomeric states along the considered fission paths. Alpha decay half-lives have also been computed using a parametrization of the Viola-Seaborg formula. Though there exists a strong variance of the predicted fission rates with respect to the details involved in their computation a robust trend is obtained indicating, that with increasing neutron number fission dominates over α-decay. Our results also suggest that a dynamical treatment of pairing correlations is required within the microscopic studies of the fission process in heavy nuclear systems.

Benchmarking Density Functionals for Chemical Bonds of Gold

Gold plays a major role in nanochemistry, catalysis, and electrochemistry. Accordingly, hundreds of studies apply density functionals to study chemical bonding with gold, yet there is no systematic attempt to assess the accuracy of these methods applied to gold. This paper reports a benchmark against 51 experimental bond enthalpies of AuX systems and seven additional polyatomic and cationic molecules. Twelve density functionals were tested, covering meta functionals, hybrids with variable HF exchange, double-hybrid, dispersion-corrected, and nonhybrid GGA functionals. The defined benchmark data set probes all types of bonding to gold from very electronegative halides that force Au+ electronic structure, via covalently bonded systems, hard and soft Lewis acids and bases that either work against or complement the softness of gold, the Au2 molecule probing gold's bond with itself, and weak bonds between gold and noble gases. Zero-point vibrational corrections are relatively small for Au-X bonds, ∼ 11-12 kJ/mol except for Au-H bonds. Dispersion typically provides ∼5 kJ/mol of the total bond enthalpy but grows with system size and is 10 kJ/mol for AuXe and AuKr. HF exchange and LYP correlation produce weaker bonds to gold. Most functionals provide similar trend accuracy, though somewhat lower for M06 and M06L, but very different numerical accuracy. Notably, PBE and TPSS functionals with dispersion display the smallest numerical errors and very small mean signed errors (0-6 kJ/mol), i.e. no bias toward over- or under-binding. Errors are evenly distributed versus atomic number, suggesting that relativistic effects are treated fairly; the mean absolute error is almost halved from B3LYP (45 kJ/mol) to TPSS and PBE (23 kJ/mol, including difficult cases); 23 kJ/mol is quite respectable considering the diverse bonds to gold and the complication of relativistic effects. Thus, studies that use DFT with effective core potentials for gold chemistry, with no alternative due to computational cost, are on solid ground using TPSS-D3 or PBE-D3.

Microscopic description of fission in nobelium isotopes with the Gogny-D1M energy density functional

Constrained mean-field calculations, based on the Gogny-D1M energy density functional, have been carried out to describe fission in the isotopes $^{250-260}$No. The even-even isotopes have been considered within the standard Hartree-Fock-Bogoliobov (HFB) framework while for the odd-mass ones the Equal Filling Approximation (HFB-EFA) has been employed. Ground state quantum numbers and deformations, pairing energies, one-neutron separation energies, inner and outer barrier heights as well as fission isomer excitation energies are given. Fission paths, collective masses and zero-point quantum vibrational and rotational corrections are used to compute the systematic of the spontaneous fission half-lives t$_\mathrm{SF}$ both for even-even and odd-mass nuclei. Though there exists a strong variance of the predicted fission rates with respect to the details involved in their computation, it is shown that both the specialization energy and the pairing quenching effects, taken into account within the self-consistent HFB-EFA blocking procedure, lead to larger t$_\mathrm{SF}$ values in odd-mass nuclei as compared with their even-even neighbors. Alpha decay lifetimes have also been computed using a parametrization of the Viola-Seaborg formula. The high quality of the Gogny-D1M functional regarding nuclear masses leads to a very good reproduction of $Q_{\alpha}$ values and consequently of lifetimes.

Improving on equilibrium isotropic nuclear shielding constants

AbstractIsotropic nuclear shielding constants at the equilibrium molecular structure σeq and zero‐point vibrational corrections (ZPVCs) to σeq are evaluated using the B3LYP/aug‐cc‐pVTZ level of theory, as well as the KT2/aug‐cc‐pVTZ level of theory. Various scaling factors and systematic corrections are obtained by linear regression to experimental shielding constants. Comparisons of the scaled and systematically corrected equilibrium and vibrationally averaged shielding constants reveal that, at the 99% confidence level, the ZPVCs via second‐order perturbation theory do not improve the agreement of B3LYP/aug‐cc‐pVTZ and KT2/aug‐cc‐pVTZ calculated shielding constants with experiment. This holds true when the same analysis is applied to CCSD(T)/aug‐cc‐pCV[TQ]Z calculated σeq of Teale et al. [Journal of Chemical Physics 2013, 138, 024111]. In addition, at the 99% confidence level, B3LYP/aug‐cc‐pVTZ and KT2/aug‐cc‐pVTZ scaled and systematically corrected shielding constants are found to be statistically no different from CCSD(T)/aug‐cc‐pCV[TQ]Z calculated σeq. The use of scaling factors and systematic corrections could thus provide a cheaper but yet reasonably accurate alternative for the study of nuclear shielding constants of larger systems.

On the convergence of zero-point vibrational corrections to nuclear shieldings and shielding anisotropies towards the complete basis set limit in water

ABSTRACTThe method and basis set dependence of zero-point vibrational corrections (ZPVCs) to nuclear magnetic resonance shielding constants and anisotropies has been investigated using water as a test system. A systematic comparison has been made using the Hartree–Fock, second-order Møller–Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) and Kohn–Sham density functional theory with the B3LYP exchange-correlation functional methods in combination with the second-order vibrational perturbation theory (VPT2) approach for the vibrational corrections. As basis sets, the correlation consistent basis sets cc-pVXZ, aug-cc-pVXZ, cc-pCVXZ and aug-cc-pCVXZ with X = D, T, Q, 5, 6 and the polarisation consistent basis sets aug-pc-n and aug-pcS-n with n = 1, 2, 3, 4 were employed. Our results show that basis set convergence of the vibrational corrections is not monotonic and that very large basis sets are needed before a reasonable extrapolation to the basis set limit can be performed. Furthermore, our results suggest that coupled cluster methods and a decent basis set are required before the error of the electronic structure approach is lower than the inherent error of the VPT2 approximation.