Long-range Correlation Energy Research Articles

Second quantization of many-body dispersion interactions for chemical and biological systems

The many-body dispersion (MBD) framework is a successful approach for modeling the long-range electronic correlation energy and optical response of systems with thousands of atoms. Inspired by field theory, here we develop a second-quantized MBD formalism (SQ-MBD) that recasts a system of atomic quantum Drude oscillators in a Fock-space representation. SQ-MBD provides: (i) tools for projecting observables (interaction energy, transition multipoles, polarizability tensors) on coarse-grained representations of the atomistic system ranging from single atoms to large structural motifs, (ii) a quantum-information framework to analyze correlations and (non)separability among fragments in a given molecular complex, and (iii) a path toward the applicability of the MBD framework to molecular complexes with even larger number of atoms. The SQ-MBD approach offers conceptual insights into quantum fluctuations in molecular systems and enables direct coupling of collective plasmon-like MBD degrees of freedom with arbitrary environments, providing a tractable computational framework to treat dispersion interactions and polarization response in intricate systems.

Gyrokinetic simulations of zonal flows and ion temperature gradient turbulence in HL-2A ITB plasmas

The characteristics of zonal flows (ZFs) in ion temperature gradient (ITG) turbulence during the formation of internal transport barrier (ITB) have been investigated by nonlinear gyrokinetic simulations for the HL-2A tokamak experiment. The turbulent ion heat transport and zonal flow dynamics are investigated in the local turbulence limit for a neutral beam heated L-mode plasma. Linear stability analyses have shown that the maximum growth rate, γmax, is decreased across the whole confinement region during the formation of ITB although the critical parameter, ηi, is increased, which is identified to be due to the stabilizing of ITG with an increased ion-to-electron temperature ratio τ. The entropy generated by ion heat flux is significantly decreased together with the enhanced ZF amplitude and reduced ion heat transport when ITB has been fully developed, especially the modes with intermediate radial wavenumbers, implying that the long and medium radial scale turbulences are strongly suppressed by the ZF shear. Meanwhile, the long-range correlation and relative energy of the self-generated ZF are increased while the turbulent energy is decreased when ITB is triggered, indicating that the ZF gains more energy from background turbulence. It is found that the ratio between τ and ηi is a key parameter in determining the ZF shearing rate ωE×BZF and γmax. The value of ωE×BZF>γmax occurs around τ/ηi > 1.4, which is suggested to be responsible for the reduction of ion heat transport and hence the ITB formation.

Surface science using coupled cluster theory via local Wannier functions and in-RPA-embedding: The case of water on graphitic carbon nitride.

A first-principles study of the adsorption of a single water molecule on a layer of graphitic carbon nitride is reported employing an embedding approach for many-electron correlation methods. To this end, a plane-wave based implementation to obtain intrinsic atomic orbitals and Wannier functions for arbitrary localization potentials is presented. In our embedding scheme, the localized occupied orbitals allow for a separate treatment of short-range and long-range correlation contributions to the adsorption energy by a fragmentation of the simulation cell. In combination with unoccupied natural orbitals, the coupled cluster ansatz with single, double, and perturbative triple particle-hole excitation operators is used to capture the correlation in local fragments centered around the adsorption process. For the long-range correlation, a seamless embedding into the random phase approximation yields rapidly convergent adsorption energies with respect to the local fragment size. Convergence of computed binding energies with respect to the virtual orbital basis set is achieved employing a number of recently developed techniques. Moreover, we discuss fragment size convergence for a range of approximate many-electron perturbation theories. The obtained benchmark results are compared to a number of density functional calculations.

Random phase approximation in projected oscillator orbitals

The projected oscillator orbitals (pOOs) are localized virtual orbitals constructed by multiplying localized occupied orbitals by harmonics. Following a recent paper by Mussard and \'Angy\'an (Theor Chem Acc 134:1, 2015), further developments of projected oscillator orbitals are shown, notably the equations for pOOs of general order as well as their overlaps are derived. The performance of these localized virtual orbitals is demonstrated up to third order. It is found that a good fraction of the aug-cc-pVQZ RPA correlation energy is recovered by use of a smaller number of pOOs. This is especially true where considering only the long-range correlation energy, which is important for the description of London dispersion forces.

Local random phase approximation with projected oscillator orbitals

An approximation to the many-body London dispersion energy in molecular systems is expressed as a functional of the occupied orbitals only. The method is based on the local-RPA theory. The occupied orbitals are localized molecular orbitals and the virtual space is described by projected oscillator orbitals, i.e. functions obtained by multiplying occupied localized orbitals with solid spherical harmonic polynomials having their origin at the orbital centroids. Since we are interested in the long-range part of the correlation energy, responsible for dispersion forces, the electron repulsion is approximated by its multipolar expansion. This procedure leads to a fully non-empirical long-range correlation energy expression. Molecular dispersion coefficients calculated from determinant wave functions obtained by a range-separated hybrid method reproduce experimental values with less than 15% error.

FDE-vdW: A van der Waals inclusive subsystem density-functional theory.

We present a formally exact van der Waals inclusive electronic structure theory, called FDE-vdW, based on the Frozen Density Embedding formulation of subsystem Density-Functional Theory. In subsystem DFT, the energy functional is composed of subsystem additive and non-additive terms. We show that an appropriate definition of the long-range correlation energy is given by the value of the non-additive correlation functional. This functional is evaluated using the fluctuation-dissipation theorem aided by a formally exact decomposition of the response functions into subsystem contributions. FDE-vdW is derived in detail and several approximate schemes are proposed, which lead to practical implementations of the method. We show that FDE-vdW is Casimir-Polder consistent, i.e., it reduces to the generalized Casimir-Polder formula for asymptotic inter-subsystems separations. Pilot calculations of binding energies of 13 weakly bound complexes singled out from the S22 set show a dramatic improvement upon semilocal subsystem DFT, provided that an appropriate exchange functional is employed. The convergence of FDE-vdW with basis set size is discussed, as well as its dependence on the choice of associated density functional approximant.

Long-range correlation energy calculated from coupled atomic response functions.

An accurate determination of the electron correlation energy is an essential prerequisite for describing the structure, stability, and function in a wide variety of systems. Therefore, the development of efficient approaches for the calculation of the correlation energy (and hence the dispersion energy as well) is essential and such methods can be coupled with many density-functional approximations, local methods for the electron correlation energy, and even interatomic force fields. In this work, we build upon the previously developed many-body dispersion (MBD) framework, which is intimately linked to the random-phase approximation for the correlation energy. We separate the correlation energy into short-range contributions that are modeled by semi-local functionals and long-range contributions that are calculated by mapping the complex all-electron problem onto a set of atomic response functions coupled in the dipole approximation. We propose an effective range-separation of the coupling between the atomic response functions that extends the already broad applicability of the MBD method to non-metallic materials with highly anisotropic responses, such as layered nanostructures. Application to a variety of high-quality benchmark datasets illustrates the accuracy and applicability of the improved MBD approach, which offers the prospect of first-principles modeling of large structurally complex systems with an accurate description of the long-range correlation energy.

Quantum dynamics of hydrogen interacting with single-walled carbon nanotubes: Multiple H-atom adsorbates

In a previous paper [J. L. McAfee and B. Poirier, J. Chem. Phys. 130, 064701 (2009)], using spin-polarized density functional theory (DFT), the authors reported a binding energy of 0.755 eV, for a single hydrogen atom adsorbed on a pristine (unrelaxed) (5,5) single-walled carbon nanotube (SWNT) substrate. A full three-dimensional (3D) potential energy surface (PES) for the SWNT-H system was also developed, and used in a quantum dynamics calculation to compute all rovibrational bound states, and associated equatorial and longitudinal adsorbate migration rates. A highly pronounced preference for the latter migration pathway at ambient temperatures was observed. In this work, we extend the aforementioned study to include multiple H-atom adsorbates. Extensive DFT calculations are performed, in order to ascertain the most relevant dynamical pathways. For two adsorbates, the SWNT-H-H system is found to exhibit highly site-specific binding, as well as long-range correlation and pronounced binding energy enhancement. The latter effect is even more pronounced in the full-hydrogenation limit, increasing the per-adsorbate binding energy to 2.6 eV. To study migration dynamics, a single-hole model is developed, for which the binding energy drops to 2.11 eV. A global 3D PES is developed for the hole migration model, using 40 radial × 18 cylindrical ab initio geometries, fit to a Fourier basis with radially dependent expansion coefficients (rms error 4.9 meV). As compared with the single-adsorbate case, the hole migration PES does not exhibit separate chemisorption and physisorption wells. The barrier to longitudinal migration is also found to be much lower. Quantum dynamics calculations for all rovibrational states are then performed (using a mixed spectral basis/phase-space optimized discrete variable representation), and used to compute longitudinal migration rates. Ramifications for the use of SWNTs as potential hydrogen storage materials are discussed.

Long-range correlation energies calculations for excited states of [formula omitted] electronic systems

A general formula of long-range electron correlation energy in excited states of π electron systems is presented for the first time. Effect of excited states upon the long-range electron correlations, which are related to problems of exciton and polaron, is discussed. It is found that because charge density distributions are different for removal (addition) of an electron from (into) π electron system, the correlation energies of electron-type polaron and hole-type polaron are not the same even when the system tends to infinity.

Long-Range Correlation Energies, Off-diagonal Interactions and Correlation Hamiltonian for π Electronic Systems

A general formula of the long-range correlation energy E c for the π electron systems is given, which includes diagonal interactions and off-diagonal interactions and we put forward to a correlation Hamiltonian at the first time. It is found that the effects of the off-diagonal interactions W and X on the correlation energies are opposite. The effect of W is to increase the correlation energies, but the effect of X is being counteracted by the integral term J due to |X|∼|J|. The long-range correlation energies decrease with increasing the screening effect. At normal screening, the influence of W on the correlation energies can be neglected.

Theoretical investigation of excited states of molecules. An application on the nitrogen molecule

Diverse existing lines for the calculation of excited states are exposed, with an emphasis on those methods that consider both types of correlation energy: the dynamic and the non-dynamic one. We analyze the possibility of to calculate the dynamic correlation energy using a correlation energy density functional applied to a multi-determinantal wavefunction, which would include the non-dynamic correlation energy, versus the use of mono-determinantal wavefunctions, which are not able to include the long-range correlation energy, and versus the use of variational or perturbative calculations from multi-determinantal wavefunctions, with their excessive computational cost. The results obtained with several methods are compared.

Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence

The combination of density functional theory with other approaches to the many-electron problem through the separation of the electron-electron interaction into a short-range and a long-range contribution is a promising method, which is raising more and more interest in recent years. In this work some properties of the corresponding correlation energy functionals are derived by studying the electron-electron coalescence condition for a modified (long-range-only) interaction. A general relation for the on-top (zero electron-electron distance) pair density is derived, and its usefulness is discussed with some examples. For the special case of the uniform electron gas, a simple parameterization of the on-top pair density for a long-range only interaction is presented and supported by calculations within the ``extended Overhauser model''. The results of this work can be used to build self-interaction corrected short-range correlation energy functionals.

Van der Waals electron correlation energy in silicon

An estimate is made, using a bond polarisability model, of the long-range Van der Waals correlation energy in silicon. A value of -0.41+or-0.04 eV/bond is found, which compares reasonably well with a semi-empirical estimate of Harrison and Ciraci (1974). A Drude model approximation to the polarisability is discussed which simplifies the calculation considerably but gives good agreement with an estimate based on the experimental dielectric function. The estimated long-range correlation energy indicates that this contribution to total binding energy should not be ignored.