Zero-point Effects Research Articles

On the accuracy of commonly used density functional approximations in determining the elastic constants of insulators and semiconductors.

We have performed density functional calculations using a range of local and semi-local as well as hybrid density functional approximations of the structure and elastic constants of 18 semiconductors and insulators. We find that most of the approximations have a very small error in the lattice constants, of the order of 1%, while the errors in the elastic constants and bulk modulus are much larger, at about 10% or better. When comparing experimental and theoretical lattice constants and bulk modulus we have included zero-point phonon effects. These effects make the experimental reference lattice constants 0.019 Å smaller on average while making the bulk modulus 4.3 GPa stiffer on average. According to our study, the overall best performing density functional approximations for determining the structure and elastic properties are the PBEsol functional, the two hybrid density functionals PBE0 and HSE (Heyd, Scuseria, and Ernzerhof), as well as the AM05 functional.

Temperature dependence of the electronic structure of semiconductors and insulators.

The renormalization of electronic eigenenergies due to electron-phonon coupling (temperature dependence and zero-point motion effect) is sizable in many materials with light atoms. This effect, often neglected in ab initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the recent progresses in this field and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a slowly converging q-point integration. For non-zero Born effective charges, we show that a divergence appears in the electron-phonon matrix elements at q → Γ, leading to a divergence of the adiabatic renormalization at band extrema. This problem is exacerbated by the slow convergence of Born effective charges with electronic wavevector sampling, which leaves residual Born effective charges in ab initio calculations on materials that are physically devoid of such charges. Here, we propose a solution that improves this convergence. However, for materials where Born effective charges are physically non-zero, the divergence of the renormalization indicates a breakdown of the adiabatic harmonic approximation, which we assess here by switching to the non-adiabatic harmonic approximation. Also, we study the convergence behavior of the renormalization and develop reliable extrapolation schemes to obtain the converged results. Finally, the adiabatic and non-adiabatic theories, with corrections for the slow Born effective charge convergence problem (and the associated divergence) are applied to the study of five semiconductors and insulators: α-AlN, β-AlN, BN, diamond, and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening, and the renormalized electronic band structure.

Zero-Point Effects on Phase Transitions of Thorium Dihydride under High Pressure

The crystalline structures of thorium dihydride, ThH2, under pressure are investigated by using an unbiased structure searching method coupled with ab initio calculations. Three low-enthalpy phases are found as the thermodynamic ground states of ThH2 up to 200 GPa, including an experimentally observed I4/mmm phase and two newly predicted monoclinic phases (C2/m and C/2c phase). ThH2 is predicted to undergo I4/mmm → C2/m → C/2c phase transitions without zero-point (ZP) effects, whereas it directly transforms from the I4/mmm phase to the C2/c phase with ZP effects. Phonon calculations show that these competitive phases are thermodynamically stable. There is a strengthening of the metallic characters of the chemical bonding with increased pressure. Our results highlight the role of ZP effects in the high-pressure behaviors of metal hydrides and provide insight into further studies of other compounds containing light elements under pressure.

ChemInform Abstract: Generalized Theory of Spin Fluctuations in Itinerant Electron Magnets: Crucial Role of Spin Anharmonicity

AbstractReview: 24 refs.

Communication: Nucleation of water on ice nanograins: Size, charge, and quantum effects.

The sticking cross sections of water molecules on cold size-selected water clusters have been simulated using classical and quantum (path-integral) molecular dynamics trajectories under realistic conditions. The integrated cross sections for charged clusters show significant size effects with comparable trends as in experiments, as well as essentially no sign effect. Vibrational delocalization, although it contributes to enlarging the geometric cross sections, leads to a counter-intuitive decrease in the dynamical cross section obtained from the trajectories. These results are interpreted based on the apparent reduction in the effective interaction between the projectile and the target owing to zero-point effects.

Thermodynamics of water dimer dissociation in the primary hydration shell of the iodide ion with temperature-dependent vibrational predissociation spectroscopy.

The strong temperature dependence of the I(-)·(H2O)2 vibrational predissociation spectrum is traced to the intracluster dissociation of the ion-bound water dimer into independent water monomers that remain tethered to the ion. The thermodynamics of this process is determined using van't Hoff analysis of key features that quantify the relative populations of H-bonded and independent water molecules. The dissociation enthalpy of the isolated water dimer is thus observed to be reduced by roughly a factor of three upon attachment to the ion. The cause of this reduction is explored with electronic structure calculations of the potential energy profile for dissociation of the dimer, which suggest that both reduction of the intrinsic binding energy and vibrational zero-point effects act to weaken the intermolecular interaction between the water molecules in the first hydration shell. Additional insights are obtained by analyzing how classical trajectories of the I(-)·(H2O)2 system sample the extended potential energy surface with increasing temperature.

Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation

The renormalization of electronic eigenenergies due to electron-phonon interactions (temperature dependence and zero-point motion effect) is important in many materials. We address it in the adiabatic harmonic approximation, based on first principles (e.g., density-functional theory), from different points of view: directly from atomic position fluctuations or, alternatively, from Janak's theorem generalized to the case where the Helmholtz free energy, including the vibrational entropy, is used. We prove their equivalence, based on the usual form of Janak's theorem and on the dynamical equation. We then also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a first-principles context. The AHC theory relies on the rigid-ion approximation, and naturally leads to a self-energy (Fan) contribution and a Debye-Waller contribution. Such a splitting can also be done for the complete harmonic adiabatic expression, in which the rigid-ion approximation is not required. A numerical study within the density-functional perturbation theory framework allows us to compare the AHC theory with frozen-phonon calculations, with or without the rigid-ion approximation. For the two different numerical approaches without non-rigid-ion terms, the agreement is better than 7 $\ensuremath{\mu}\mathrm{eV}$ in the case of diamond, which represent an agreement to five significant digits. The magnitude of the non-rigid-ion terms in this case is also presented, distinguishing specific phonon modes contributions to different electronic eigenenergies.

Generalized theory of spin fluctuations in itinerant electron magnets: Crucial role of spin anharmonicity

The paper critically overviews the recent developments of the theory of spatially dispersive spin fluctuations (SF) in itinerant electron magnetism with particular emphasis on spin-fluctuation coupling or spin anharmonicity. It is argued that the conventional self-consistent renormalized (SCR) theory of spin fluctuations is usually used aside of the range of its applicability actually defined by the constraint of weak spin anharmonicity based on the random phase approximation (RPA) arguments. An essential step in understanding SF in itinerant magnets beyond RPA-like arguments was made recently within the soft-mode theory of SF accounting for strong spin anharmonicity caused by zero-point SF. In the present paper we generalize it to apply for a wider range of temperatures and regimes of SF and show it to lead to qualitatively new results caused by zero-point effects.

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.

Large nuclear zero-point motion effect in semiconductor nanoclusters

Large nuclear zero-point motion effect in semiconductor nanoclusters

Phenomenological model of anomalous magnon softening and damping in half-metallic manganites

To describe anomalous zone-boundary softening and damping of magnons in manganites we present a phenomenological two-fluid model containing ferromagnetic Fermi-liquid and non-Fermi-liquid components associated with the itinerant and core electrons of Mn. The observed discontinuous increase of magnon damping is explained by the intersection of magnon dispersions with the electron-hole Stoner continuum arising due to the breakdown of the half-metallic ground state of manganites supported by the experiments and analysis of zero-point effects. Coupling of the Fermi-liquid and non-Fermi-liquid fluids yields conventional long wavelength magnons damped due to their interaction with longitudinal spin fluctuations.

Temperature dependence on the structure of Zundel cation and its isotopomers

Temperature dependence on the structural fluctuations of Zundel cation, H5O2(+), and its isotopomers, D5O2(+) and T5O2(+), have been studied using path integral molecular dynamics simulations in which nuclear quantum effect is fully taken into account. It has been found that the fluctuations of hydrogen-oxygen and oxygen-oxygen distances, which are relevant to the hydrogen bonded structure, grow drastically as the temperature increases within the range of investigation between 100 K and 900 K. The fluctuation with respect to the position of non-bonded hydrogen also increases substantially as the temperature increases. The temperature dependence on the fluctuation is greater for D5O2(+) or T5O2(+) than that of H5O2(+), since the zero-point effect of the former is less than the latter.

Simulation of quantum zero-point effects in water using a frequency-dependent thermostat

Molecules like water have vibrational modes with a zero-point energy well above room temperature. As a consequence, classical molecular dynamics simulations of their liquids largely underestimate the energy of modes with a higher zero-point temperature, which translates into an underestimation of covalent interatomic distances due to anharmonic effects. Zero-point effects can be recovered using path integral molecular dynamics simulations, but these are computationally expensive, making their combination with ab initio molecular dynamics simulations a challenge. As an alternative to path integral methods, from a computationally simple perspective, one would envision the design of a thermostat capable of equilibrating and maintaining the different vibrational modes at their corresponding zero-point temperatures. Recently, Ceriotti et al. [Phys. Rev. Lett. 102, 020601 (2009)] introduced a framework to use a custom-tailored Langevin equation with correlated noise that can be used to include quantum fluctuations in classical molecular dynamics simulations. Here we show that it is possible to use the generalized Langevin equation with suppressed noise in combination with Nose-Hoover thermostats to efficiently impose a zero-point temperature on independent modes in liquid water. Using our simple and inexpensive method, we achieve excellent agreement for all atomic pair correlation functions compared to the path integral molecular dynamics simulation.

Quantum Chemistry as a Tool in Asymmetric Biocatalysis: Limonene Epoxide Hydrolase Test Case

Cluster model: Large active-site models (see figure) are used to investigate the selectivity of limonene epoxide hydrolase, both the wild type and mutants optimized through directed evolution. Good agreement is found between theory and the experimental data, thus demonstrating that the quantum chemical cluster approach can be a powerful tool in the field of asymmetric biocatalysis.

Quantum effects in the abstraction reaction by H atoms of primary and secondary hydrogens in n-C4H10: a test of a new potential energy surface construction method

Recently, von Horsten et al. suggested an efficient method to construct two dimensional potential energy surfaces (PESs) for use in quantum scattering simulations, in which they utilised the minimum energy path (MEP) and assumed harmonic behaviour of the PES near the MEP. In the same paper, the authors applied this method to various H-abstraction reactions from C1-C3 alkane molecules. In this work we demonstrate an alternative PES construction method, and apply it to the more challenging H-abstraction from n-C(4)H(10) reactions. The geometry optimizations and frequency calculations are done at the MP2/cc-pVTZ level of theory, while the energies are calculated with the CCSD(T) method with the same basis set. The calculations give adiabatic energy barrier heights of 45.9 kJ mol(-1) and 34.4 kJ mol(-1) for the primary and secondary hydrogens in n-C(4)H(10). When compared to purely classical transition state theory, quantum scattering calculations show that quantum tunnelling and zero-point effects have large contributions at low temperatures, typically below 500 K. The branching ratio study suggests that the abstraction of secondary hydrogen in n-C(4)H(10) dominates the overall reaction rate at low temperatures. The rate constants for the two abstraction channels become more comparable as the temperature increases.

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.

A benchmark for non-covalent interactions in solids

A benchmark for non-covalent interactions in solids (C21) based on the experimental sublimation enthalpies and geometries of 21 molecular crystals is presented. Thermal and zero-point effects are carefully accounted for and reference lattice energies and thermal pressures are provided, which allow dispersion-corrected density functionals to be assessed in a straightforward way. Other thermal corrections to the sublimation enthalpy (the 2RT term) are reexamined. We compare the recently implemented exchange-hole dipole moment (XDM) model with other approaches in the literature to find that XDM roughly doubles the accuracy of DFT-D2 and non-local functionals in computed lattice energies (4.8 kJ/mol mean absolute error) while, at the same time, predicting cell geometries within less than 2% of the experimental result on average. The XDM model of dispersion interactions is confirmed as a very promising approach in solid-state applications.

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.