Zero-point Vibrational Effects Research Articles

Direct Probes of π-Delocalization in Prototypical Resonance-Stabilized Radicals: Hyperfine-Resolved Microwave Spectroscopy of Isotopic Propargyl and Cyanomethyl.

Delocalization of the unpaired electron in π-conjugated radicals has profound implications for their chemistry, but direct and quantitative characterization of this electronic structure in isolated molecules remains challenging. We apply hyperfine-resolved microwave rotational spectroscopy to rigorously probe π-delocalization in propargyl, CH2CCH, a prototypical resonance-stabilized radical and key reactive intermediate. Using the spectroscopic constants derived from the high-resolution cavity Fourier transform microwave measurements of an exhaustive set of 13C- and 2H-substituted isotopologues, together with high-level ab initio calculations of zero-point vibrational effects, we derive its precise semiexperimental equilibrium geometry and quantitatively characterize the spatial distribution of its unpaired electron. Our results highlight the importance of considering both spin-polarization and orbital-following contributions when interpreting the isotropic hyperfine coupling constants of π radicals. These physical insights are strengthened by a parallel analysis of the isoelectronic species cyanomethyl, CH2CN, using new 13C measurements also reported in this work. A detailed comparison of the structure and electronic properties of propargyl, cyanomethyl, and other closely related species allows us to correlate trends in their chemical bonding and electronic structure with critical changes in their reactivity and thermochemistry.

Cyclo[18]carbon including zero-point motion: ground state, first singlet and triplet excitations, and hole transfer.

Recent synthesis of cyclo[18]carbon has spurred increasing interest in carbon rings. We focus on a comparative inspection of ground and excited states, as well as of hole transfer properties of cumulenic and polyynic cyclo[18]carbon via Density Functional Theory (DFT), time-dependent DFT (TD-DFT) and real-time time-dependent DFT (RT-TDDFT). Zero-point vibrations are also accounted for, using a Monte Carlo sampling technique and a less exact, yet mode-resolved, quadratic approximation. The inclusion of zero-point vibrations leads to a red-shift on the HOMO-LUMO gap and the first singlet and triplet excitation energies of both conformations, correcting the values of the 'static' configurations by 9% to 24%. Next, we oxidize the molecule, creating a hole at one carbon atom. Hole transfer along polyynic cyclo[18]carbon is decreased in magnitude compared to its cumulenic counterpart and lacks the symmetric features the latter displays. Contributions by each mode to energy changes and hole transfer between diametrically opposed atoms vary, with specific bond-stretching modes being dominant.

On the impact of zero-point vibrations in calcium carbonate

ABSTRACT By performing calculations based on density functional theory (DFT), while adopting different exchange and correlations functionals, we have investigated pressure-induced phase transitions in calcium carbonate (CaCO3) up to 30 GPa. We have focused on the effect of zero-point vibrations on the stability sequence of three CaCO3 polymorphs, i.e. calcite-III, calcite-IIIb and calcite-VI, as well as on the evolution of their elastic properties. Our results show that the zero-point vibrations have a minor effect on the bulk modulus of the three CaCO3 polymorphs, in the inspected pressure range. However, we demonstrate that the zero-point vibrations have a major impact on phase transitions leading to the following polymorphic sequence: calcite-IIIb→calcite-III→calcite-VI, where transitions of the first order occur at 4 and 18 GPa. The obtained sequence shows that the boundary phase of calcite-II is calcite-IIIb; and the latter doesn't reappear at higher pressure, as previously predicted by theory.

Anharmonicity of the acoustic modes of graphene

The anharmonicity of the acoustic phonon dispersion of graphene has been studied by the harmonic linear response (HLR) approach at finite temperature. This is a non-perturbative method based on the linear response of the system to applied forces, as derived from equilibrium computer simulations. Anharmonic shifts are analyzed in the long-wavelength limit at room temperature, with emphasis in the effect of applied tensile or compressive in-plane stress. The simulation results are compared with available analytical models, based either on first-order perturbation theory or on a description by anomalous exponents. The simulations show better agreement to the expectations of the perturbational approach. The effect of temperature and zero-point vibrations on the acoustic out-of-plane anharmonic shifts of graphene are briefly reviewed.

Molecular vibrations reduce the maximum achievable photovoltage in organic solar cells

The low-energy edge of optical absorption spectra is critical for the performance of solar cells, but is not well understood in the case of organic solar cells (OSCs). We study the microscopic origin of exciton bands in molecular blends and investigate their role in OSCs. We simulate the temperature dependence of the excitonic density of states and low-energy absorption features, including low-frequency molecular vibrations and multi-exciton hybridisation. For model donor-acceptor blends featuring charge-transfer excitons, our simulations agree very well with temperature-dependent experimental absorption spectra. We unveil that the quantum effect of zero-point vibrations, mediated by electron-phonon interaction, causes a substantial exciton bandwidth and reduces the open-circuit voltage, which is predicted from electronic and vibronic molecular parameters. This effect is surprisingly strong at room temperature and can substantially limit the OSC’s efficiency. Strategies to reduce these vibration-induced voltage losses are discussed for a larger set of systems and different heterojunction geometries.

Coordination corrected ab initio formation enthalpies

The correct calculation of formation enthalpy is one of the enablers of ab-initio computational materials design. For several classes of systems (e.g. oxides) standard density functional theory produces incorrect values. Here we propose the “coordination corrected enthalpies” method (CCE), based on the number of nearest neighbor cation–anion bonds, and also capable of correcting relative stability of polymorphs. CCE uses calculations employing the Perdew, Burke and Ernzerhof (PBE), local density approximation (LDA) and strongly constrained and appropriately normed (SCAN) exchange correlation functionals, in conjunction with a quasiharmonic Debye model to treat zero-point vibrational and thermal effects. The benchmark, performed on binary and ternary oxides (halides), shows very accurate room temperature results for all functionals, with the smallest mean absolute error of 27(24) meV/atom obtained with SCAN. The zero-point vibrational and thermal contributions to the formation enthalpies are small and with different signs—largely canceling each other.

From dimers to the solid-state: Distributed intermolecular force-fields for pyridine.

An anisotropic atom-atom force-field for pyridine, using distributed atomic multipoles, polarizabilities, and dispersion coefficients and an anisotropic atom-atom repulsion model derived from symmetry-adapted perturbation theory (density functional theory) dimer calculations, is used to model pyridine crystal structures. Here we show that this distributed intermolecular force-field (DIFF) models the experimental crystal structures as accurately as modelling all but the electrostatic term with an isotropic repulsion-dispersion potential that has been fitted to experimental crystal structures. In both cases, the differences are comparable to the changes in the crystal structure with temperature, pressure, or neglect of zero-point vibrational effects. A crystal structure prediction study has been carried out, and the observed polymorphs contrasted with hypothetical thermodynamically competitive crystal structures. The DIFF model was able to identify the structure of an unreported high pressure phase of pyridine, unlike the empirically fitted potential. The DIFF model approach therefore provides a model of the underlying pair potential energy surface that we have transferred to the crystalline phase with a considerable degree of success, though the treatment of the many-body terms needs improvement and the pair potential is slightly over-binding. Furthermore, this study of a system that exhibits isotopic polymorphism highlights that the use of an empirical potential has partially absorbed temperature and zero-point motion effects as well as the intermolecular forces not explicitly represented in the functional form. This study therefore highlights the complexity in modelling crystallization phenomena from a realistic pair potential energy surface.

Estimating the intrinsic limit of the Feller-Peterson-Dixon composite approach when applied to adiabatic ionization potentials in atoms and small molecules

Benchmark adiabatic ionization potentials were obtained with the Feller-Peterson-Dixon (FPD) theoretical method for a collection of 48 atoms and small molecules. In previous studies, the FPD method demonstrated an ability to predict atomization energies (heats of formation) and electron affinities well within a 95% confidence level of ±1 kcal/mol. Large 1-particle expansions involving correlation consistent basis sets (up to aug-cc-pV8Z in many cases and aug-cc-pV9Z for some atoms) were chosen for the valence CCSD(T) starting point calculations. Despite their cost, these large basis sets were chosen in order to help minimize the residual basis set truncation error and reduce dependence on approximate basis set limit extrapolation formulas. The complementary n-particle expansion included higher order CCSDT, CCSDTQ, or CCSDTQ5 (coupled cluster theory with iterative triple, quadruple, and quintuple excitations) corrections. For all of the chemical systems examined here, it was also possible to either perform explicit full configuration interaction (CI) calculations or to otherwise estimate the full CI limit. Additionally, corrections associated with core/valence correlation, scalar relativity, anharmonic zero point vibrational energies, non-adiabatic effects, and other minor factors were considered. The root mean square deviation with respect to experiment for the ionization potentials was 0.21 kcal/mol (0.009 eV). The corresponding level of agreement for molecular enthalpies of formation was 0.37 kcal/mol and for electron affinities 0.20 kcal/mol. Similar good agreement with experiment was found in the case of molecular structures and harmonic frequencies. Overall, the combination of energetic, structural, and vibrational data (655 comparisons) reflects the consistent ability of the FPD method to achieve close agreement with experiment for small molecules using the level of theory applied in this study.

Static polarizabilities and C6 dispersion coefficients using the algebraic-diagrammatic construction scheme for the complex polarization propagator

An implementation of the damped linear response function, or complex polarization propagator, using the algebraic-diagrammatic construction (ADC) scheme has been developed and utilized for the calculation of electric-dipole polarizabilities and C6 dispersion coefficients. Four noble gases (He, Ne, Ar, and Kr), five n-alkanes (methane, ethane, propane, butane, and pentane), three carbonyls (formaldehyde, acetaldehyde, and acetone), and three unsaturated hydrocarbons (ethene, acetylene, and benzene) have been treated with the hierarchical set of models ADC(2), ADC(2)-x, and ADC(3/2), and comparison has been made to results obtained with damped linear response Hartree–Fock (HF) and coupled cluster singles and doubles (CCSD) theory as well as high-quality experimental estimates via the dipole oscillator strength distribution approach. This study marks the first ADC calculations of C6 dispersion coefficients and the first ADC(3/2) calculations of static polarizabilities. Results at CCSD and ADC(3/2) levels of theory are shown to be of similar quality, with electron correlation effects increasing the molecular property values for all calculations except CCSD considerations of ethene and acetylene (attributed to an overestimation of bond electron density at HF level of theory). The discrepancies between CCSD and ADC(3/2) are partially due to ADC overestimating anisotropies, and discrepancies with respect to experimental values are partially due to the lack of zero-point vibrational effects in the present study.

Binding energies and interaction origins between nonclassical single-electron hydrogen, sodium and lithium bonds and neutral boron-containing radicals: a theoretical investigation

Nonclassical single electron hydrogen, sodium and lithium bonds (SEHBs, SENaBs and SELiBs) between single electron acceptors X–A (A=H, Na, Li; X=CN, HCC, HO, NC, CF3) and neutral radicals BY2 (Y=H, OH, CH3) and have been systematically investigated by high level theoretical methods, such as second-order Moller-Plesset perturbation theory (MP2), spin-component-scaled Moller-Plesset theory (SCS-MP2), the coupled cluster method with perturbative triples (CCSD(T)), and the correlation consistent composite approach (ccCA). Binding energies have been corrected for zero-point vibrational effects and (when applicable) basis set superposition error. The quantum theory of atoms in molecules (AIM) and natural bond orbital (NBO) analyses were also employed to qualitatively characterize the single electron bond interactions. The stabilization energy was partitioned via the localized molecular orbital energy decomposition analysis (LMO-EDA) method, and both electrostatic and exchange interactions were seen to be major driving forces for the complex stabilization. Interestingly, the sum of the energy contributors of exchange (EEX), repulsion (EREP), polarization (EPOL), dispersion (EDIS) is close to zero and the changes in the interaction energy follow the trend of the electrostatic energy (EES). We observe several linear relationships among the optimized intermolecular parameters and the interaction energies of the various complexes.

Rovibrational effects on NMR shieldings in a heavy-element system: XeF2

Fully quantum-mechanical treatment of the effects of thermal rovibrational motion in a heavy-element molecule with relativistic effects is carried out for the heavy (129/131)Xe and light (19)F nuclear shieldings in the linear XeF(2) molecule. More importantly, purely quantum-mechanical, intramolecular phenomena, the primary and secondary isotope effect on these shieldings, respectively, are treated with including both the zero-point vibrational and finite-temperature effects. While large solvent effects influence the experimental absolute shielding constants and chemical shifts (thereby making comparison of experiment and theory very difficult), they are not significant for the isotope shifts. We study the role of electron correlation at both nonrelativistic (NR) and relativistic [Breit-Pauli perturbational theory (BPPT) as well as 4-component Dirac theory] level. We obtain quantitative agreement with the nearly solvent-independent experimental (19)F secondary isotope shifts. This implies a promising accuracy for our predictions of the experimentally so far non-existing primary Xe isotope shift and the temperature dependence of Xe and F chemical shifts corresponding to a low pressure gas phase. To achieve this, a combination of high-level ab initio NR shielding surface is found necessary, in the present work supplemented by relativistic corrections by density-functional theory (DFT). Large errors are demonstrated to arise due to DFT in the NR shielding surface, explaining findings in recent computational studies of heavy-element isotope shifts. Besides a high-quality property hypersurface, the inclusion of thermal effects (in addition to zero-point motion) is also necessary to compare with experimental results. The geometry dependence of the different relativistic influences on the wave function, Zeeman interaction, and hyperfine interaction, as well as their role in the temperature dependence of both the Xe and F shielding constants and their isotope shifts, are discussed. The relativistic rovibrational effects arise from the same individual contributions as previously found for the chemical shifts and shielding anisotropies. In general, the spin-orbit interactions are more sensitive to rovibrational motion than the scalar relativistic contributions. A previously suggested third-order BPPT contribution to shielding anisotropy is shown to be important for a better agreement with experiment.

Characterization of the t-Butyl Radical and Its Elusive Anion.

The t-butyl radical and its anion are studied theoretically using state-of-the-art quantum mechanical methods including coupled cluster theory with full single, double, and triple excitations (CCSDT) and CCSDT with perturbative quadruple excitations [CCSDT(Q)], in concert with large correlation-consistent cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5) basis sets. The relative energies are extrapolated to the complete basis set limit (CBS). The lowest energy structure of the t-butyl radical has a nonplanar carbon backbone with overall C3v symmetry. Low-lying C3h and Cs symmetry transition states, for pyramidal inversion and methyl group rotation, respectively, between equivalent C3v minima are investigated. The barriers for these interconversions are both less than 1 kcal mol(-1), but the corresponding barriers on the anion potential energy surface are more pronounced. Using the focal point analysis technique, we obtain a value of -0.48 kcal mol(-1) for the t-butyl radical adiabatic electron affinity at the CCSDT(Q)/CBS level of theory, where the negative sign indicates that the formation of the t-butyl anion is adiabatically unfavorable. We show that the electron affinity, whose sign has been the subject of debate, is very sensitive to both the basis set and the correlation treatment, and previous experimental and theoretical estimates of its value bracket the value computed herein. Our results indicate that the t-butyl anion is classically metastable with a vertical detachment energy of over 10 kcal mol(-1) to reach the neutral potential energy surface. However, the inclusion of the zero-point vibrational effects seems to favor its nonexistence.

Quantum Monte Carlo study of pressure-inducedB3−B1phase transition in GaAs

We have investigated the transition pressure ${p}_{t}$ of bulk GaAs from the zinc-blende ($B3$) to the rocksalt ($B1$) structure using the local-density approximation (LDA), Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA), and diffusion Monte Carlo (DMC). We took into account finite temperature effects (zero-point vibrational effects) as well as finite-size corrections. Our DMC calculation using GGA trial nodal surface supports the higher value of the transition pressure, $\ensuremath{\sim}$17 GPa, than the lower value of $\ensuremath{\sim}$12 GPa, both of which are experimentally reported values. This projection increases the transition pressure ${p}_{t}$ from DFT predictions, being of the same tendency as that for Si bulk crystal. The choice of the exchange-correlation functional in DFT was found to significantly determine the phase-transition pressure, while DMC gave more accurate results for this transition pressure.

Relativistic and Non‐Relativistic Electronic Molecular‐Structure Calculations for Dimers of 4p‐, 5p‐, and 6p‐Block Elements

We report results of non-relativistic and two-component relativistic single-reference coupled-cluster with single and double and perturbative triple excitations [CCSD(T)] treatments for the 4p-block dimers Ga(2) to Br(2) , the 5p-block dimers In(2) to I(2) , and their atoms. Extended basis sets up to pentuple zeta are employed and energies extrapolated to the complete basis-set limit. Relativistic and non-relativistic results for the dissociation energy D(e) are in close agreement with each other and previously published data, provided non-relativistic or scalar-relativistic results are corrected for spin-orbit contributions taken from the literature. An exception is Te(2) where theoretical results scatter by 0.085 eV. By virtue of this agreement it is unexpected that comparison with the experimental D(0) or D(e) dissociation energies (zero-point vibrational effects are negligible in this context) reveal errors larger than 0.1 eV for Ga(2), Ge(2), and Sb(2). Only relativistic treatments are presented for the 6p-block cases Tl(2) to At(2). Sufficient agreement with experimental data is found only for Pb(2) and Bi(2), the deviation of the computed and experimental D(0) values for Po(2) is again larger than 0.1 eV. Deviations of 0.1 eV between the computed and experimental D(0) values are a major reason for concern and call for additional investigations in both fields to clarify the situation.

Effects of vibrational averaging on coupled cluster calculations of spin–spin coupling constants for hydrocarbons

We present vibrationally corrected nuclear spin–spin coupling constants for four hydrocarbons with different types of carbon–carbon bonds calculated with coupled cluster (CC) theory. First, we perform a systematic basis set investigation on acetylene for all of the four contributions (Fermi-contact, spin-dipole, para- and diamagnetic spin–orbit) to the spin–spin coupling constants and subsequently choose basis sets of sufficient flexibility to describe converged electronic properties. Then, in order to describe the effects of vibrational motion for the studied molecules we perform a Taylor expansion in the normal coordinates up to second order – a method that is well known for both its quality and efficiency – and rigorously estimate the resulting contribution for all types of spin–spin coupling constants. Combined, this allows us to obtain highly accurate benchmark estimates of the spin–spin coupling constants for acetylene, ethylene, ethane, and cyclopropane. This work provides one of the first systematic benchmarks of zero-point vibrational contributions to spin–spin coupling constants in poly-atomic molecules using the reliable CC theory and it is thus an important reference for further research within in-silico spin–spin coupling constant determination. We note that earlier computational estimates of zero-point vibrational effects agree well with those presented here (for acetylene, ethylene, and cyclopropane) while vibrational corrections for ethane are reported for the first time.

A HIGH-RESOLUTION ISOTOPIC STUDY OF THE ROTATIONAL SPECTRUM OF c -C 3 H 2

The rotational spectra of the normal and seven isotopic species of cyclopropenylidene c-C{sub 3}H{sub 2} have been measured at high spectral resolution by Fourier transform microwave spectroscopy of a supersonic molecular beam between 10 and 43 GHz. Deuterium quadrupole coupling and carbon-13 spin-rotation hyperfine constants were determined in addition to the rotational constants. Quartic and sextic centrifugal distortion constants derived from 28 lines between 150 and 316 GHz of the doubly deuterated species c-C{sub 3}D{sub 2} allow the rotational spectrum to be calculated to 0.5 km s{sup -1} or better in equivalent radial velocity up to 500 GHz. Spectroscopic constants determined from four centimeter-wave and 19 millimeter-wave lines of the normal species c-C{sub 3}H{sub 2}, including 15 with sharp Lamb-dips, allow prediction of the most important astronomical transitions (i.e., those with {Delta}J = 1 and K{sub a} {<=} 3) to 0.05 km s{sup -1} or better at 500 GHz. The doubly deuterated species is a good candidate for detection in cold dark clouds, because deuterium fractionation is high in c-C{sub 3}H{sub 2} and lines of C{sub 3}HD are fairly intense in these sources. An accurate empirical equilibrium structure of c-C{sub 3}H{sub 2}, derived from the experimental rotational constants of normalmore » and isotopic c-C{sub 3}H{sub 2}, corrected for zero-point vibrational effects, is compared with previously reported structures.« less

From Dimer to Crystal: Calculating the Cohesive Energy of Rare Gas Solids

An upper-level undergraduate project is described in which students perform high-level ab initio computational scans of the potential energy curves for Ne2 and Ar2 and obtain the respective Lennard-Jones (LJ) potential parameters σ and e for the dimers. Using this information, along with the summation of pairwise interactions in the face-centered cubic structures of the crystalline solids, the students determine the cohesive energies of solid Ne and Ar. By applying the Debye theory of solids, they then adjust these values to take zero-point vibrational effects into account after obtaining the respective Debye temperatures from published low-temperature heat capacity data. The students also calculate the lattice parameters and solid densities. An assessment of their work is made by comparing their results with experimental data.

Structural and zero-point vibrational effects on the electric dipole moments and static dipole polarizabilities of sodium clusters

The electric dipole moments of small Na${}_{n}$ clusters have been recently measured [J. Bowlan, A. Liang, and W. A. de Heer, Phys. Rev. Lett. 106, 043401 (2011)] and found to be essentially zero, a distinguishing feature of metallicity. Previous theoretical calculations fail in describing this fundamental nanoscale property. In this paper, we resolve the discrepancy by employing density functional calculations in conjunction with a highly accurate, nonlocal, van der Waals density functional. We show that knowing the correct global minimum structures is indispensable for reproducing the observed dipole moments. We also show that the dipoles are highly fluxional due to their strong coupling with zero-point vibrations, which contribute significantly to the dipole moment and polarizability values.

The pure rotational spectrum of HPS ($\tilde{\rm X}^1 {\rm A}^{\prime}$X̃1A′): Chemical bonding in second-row elements

The pure rotational spectrum of HPS, as well as its (34)S and D isotopologues, has been recorded at microwave, millimeter, and submillimeter wavelengths, the first observation of this molecule in the gas phase. The data were obtained using a combination of millimeter direct absorption, Fourier transform microwave (FTMW), and microwave-microwave double-resonance techniques, which cover the total frequency range from 15 to 419 GHz. Quantum chemical calculations at the B3LYP and CCSD(T) levels were also performed to aid in spectral identification. HPS was created in the direct absorption experiment from a mixture of elemental phosphorus, H(2)S, and Ar carrier gas; DPS was produced by adding D(2). In the FTMW study, these species were generated in a pulsed discharge nozzle from PH(3) and H(2)S or D(2)S, diluted in neon. The spectra recorded for HPS and its isotopologues exhibit clear asymmetric top patterns indicating bent structures; phosphorus hyperfine splittings were also observed in HPS, but not DPS. Analysis of the data yielded rotation, centrifugal distortion, and phosphorus nuclear spin-rotation parameters for the individual species. The r(m) ((1)) structure for HPS, calculated from the rotational constants, is r(H-P) = 1.438(1) Å, r(P-S) = 1.9320(1) Å, and θ(H-P-S) = 101.85(9)°. Empirically correcting for zero-point vibrational effects yields the geometry r(e)(H-P) = 1.4321(2) Å, r(e)(P-S) = 1.9287(1) Å, and θ(e)(H-P-S) = 101.78(1)°, in close agreement with the r(m) ((1)) structure. A small inertial defect was found for HPS indicating a relatively rigid molecule. Based on these data, the bonding in this species is best represented as H-P=S, similar to the first-row analog HNO, as well as HNS and HPO. Therefore, substitution of phosphorus and sulfur for nitrogen and oxygen does not result in a dramatic structural change.

Laboratory detection of protonated SO2 in two isomeric forms

By means of Fabry-Pérot Fourier transform microwave spectroscopy, the rotational spectrum of protonated sulfur dioxide in two distinct isomeric forms, a cis- and a trans-geometry, is reported. The search for both isomers was based on theoretical structures obtained at the CCSD(T)/cc-pwCVQZ level of theory corrected for zero-point vibrational effects. At a similarly high level of theory, the cis-isomer is calculated to be the global minimum on the potential energy surface, but the trans-isomer is predicted to lie only a few kcal/mol higher in energy. A total of seven lines, including a- and b-type transitions, has been observed for both isomers, and precise rotational constants have been derived. Because sulfur dioxide, SO(2), is a widespread and very abundant astronomical species, and because it possesses a large proton affinity, HOSO(+) is an excellent candidate for radioastronomical detection.