Dispersion Correction Derived from First Principles for Density Functional Theory and Hartree−Fock Theory

The modeling of dispersion interactions in density functional theory (DFT) is commonly performed using an energy correction that involves empirically fitted parameters for all atom pairs of the system investigated. In this study, the first-principles-derived dispersion energy from the effective fragment potential (EFP) method is implemented for the density functional theory (DFT-D(EFP)) and Hartree–Fock (HF-D(EFP)) energies. Overall, DFT-D(EFP) performs similarly to the semiempirical DFT-D corrections for the test cases investigated in this work. HF-D(EFP) tends to underestimate binding energies and overestimate intermolecular equilibrium distances, relative to coupled cluster theory, most likely due to incomplete accounting for electron correlation. Overall, this first-principles dispersion correction yields results that are in good agreement with coupled-cluster calculations at a low computational cost

Derivation and Implementation of the Gradient of the R–7 Dispersion Interaction in the Effective Fragment Potential Method

The dispersion interaction energy may be expressed as a sum over R–n terms, with n ≥ 6. Most implementations of the dispersion interaction in model potentials are terminated at n = 6. Those implementations that do include higher order contributions commonly only include even power terms, despite the fact that odd power terms can be important. Because the effective fragment potential (EFP) method contains no empirically fitted parameters, the EFP method provides a useful vehicle for examining the importance of the leading R–7 odd power term in the dispersion expansion. To fully evaluate the importance of the R–7 contribution to the dispersion energy, it is important to have analytic energy first derivatives for all terms. In the present work, the gradients of the term E7 ∼ R–7 are derived analytically, implemented in the GAMESS software package, and evaluated relative to other terms in the dispersion expansion and relative to the total EFP interaction energy. Periodic boundary conditions in the minimum image convention are also implemented. A more accurate dispersion energy contribution can now be obtained during molecular dynamics simulations

Quantum coherent plasmon in silver nanowires: a real-time TDDFT study

A plasmon-like phenomenon, arising from coinciding resonant excitations of different electronic characteristics in 1D silver nanowires, has been proposed based on theoretical linear absorption spectra. Such a molecular plasmon holds the potential for anisotropic nanoplasmonic applications. However, its dynamical nature remains unexplored. In this work, quantum dynamics of longitudinal and transverse excitations in 1D silver nanowires are carried out within the real-time time-dependent density functional theory framework. The anisotropic electron dynamics confirm that the transverse transitions of different electronic characteristics are collective in nature and oscillate in-phase with respect to each other. Analysis of the time evolutions of participating one-electron wave functions suggests that the transverse transitions form a coherent wave packet that gives rise to a strong plasmon resonance at the molecular level

Recent Developments in the General Atomic and Molecular Electronic Structure System

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized

Quantum mechanical origin of the plasmonic properties of noble metal nanoparticles

Doctor of PhilosophyDepartment of ChemistryChristine M. AikensSmall silver and gold clusters (less than 2 nm) display a discrete absorption spectrum characteristic of molecular systems whereas larger particles display a strong, broad absorption band in the visible. The latter feature is due to the surface plasmon resonance, which is commonly explained by the collective dipolar motion of free electrons across the particle, creating charged surface states. The evolution between molecular properties and plasmon is investigated. Time-dependent density functional theory (TDDFT) calculations are performed to study the absorption spectrum of cluster-size silver and gold nanorods. The absorption spectrum of these silver nanorods exhibits high-intensity longitudinal and transverse modes (along the long and short axis of the nanorod respectively), similar to the plasmons observed experimentally for larger nanoparticles. These plasmon modes result from a constructive addition of the dipole moments of nearly degenerate single-particle excitations. The number of single-particle transitions involved increases with increasing system size, due to the growing density of states available. Gold nanorods exhibit a broader absorption spectrum than their silver counterpart due to enhanced relativistic effects, affecting the onset of the longitudinal plasmon mode. The high-energy, high-intensity beta-peak of acenes also results from a constructive addition of single-particle transitions and I show that it can be assigned to a plasmon. I also show that the plasmon modes of both acenes and metallic nanoparticles can be described with a simple configuration interaction (CI) interpretation. The evolution between molecular absorption spectrum and plasmon is also investigated by computing the density of states of spherical thiolate-protected gold clusters using a charge-perturbed particle-in-a-sphere model. The electronic structure obtained with this model gives good qualitative agreement with DFT calculations at a fraction of the cost. The progressive increase of the density of states with particle size observed is in accordance with the appearance of a plasmon peak. The optical properties of nanoparticles can be tuned by varying their composition. Therefore, the optical behavior of the bimetallic Au[subscript](25-n)Ag[subscript]n(SH)[subscript]18[superscript]- cluster for different values of n using TDDFT is analyzed. A large blue shift of the HOMO-LUMO absorption peak is observed with increasing silver content, in accordance with experimental results

Dispersion Correction Derived from First Principles for Density Functional Theory and Hartree−Fock Theory

The modeling of dispersion interactions in density functional theory (DFT) is commonly performed using an energy correction that involves empirically fitted parameters for all atom pairs of the system investigated. In this study, the first-principles-derived dispersion energy from the effective fragment potential (EFP) method is implemented for the density functional theory (DFT-D(EFP)) and Hartree–Fock (HF-D(EFP)) energies. Overall, DFT-D(EFP) performs similarly to the semiempirical DFT-D corrections for the test cases investigated in this work. HF-D(EFP) tends to underestimate binding energies and overestimate intermolecular equilibrium distances, relative to coupled cluster theory, most likely due to incomplete accounting for electron correlation. Overall, this first-principles dispersion correction yields results that are in good agreement with coupled-cluster calculations at a low computational cost.Reprinted (adapted) with permission from Journal of Physical Chemistry A 119 (2015): 2161, doi:10.1021/acs.jpca.5b00379. Copyright 2015 American Chemical Society.</p

Derivation and Implementation of the Gradient of the R–7 Dispersion Interaction in the Effective Fragment Potential Method

The dispersion interaction energy may be expressed as a sum over R–n terms, with n ≥ 6. Most implementations of the dispersion interaction in model potentials are terminated at n = 6. Those implementations that do include higher order contributions commonly only include even power terms, despite the fact that odd power terms can be important. Because the effective fragment potential (EFP) method contains no empirically fitted parameters, the EFP method provides a useful vehicle for examining the importance of the leading R–7 odd power term in the dispersion expansion. To fully evaluate the importance of the R–7 contribution to the dispersion energy, it is important to have analytic energy first derivatives for all terms. In the present work, the gradients of the term E7 ∼ R–7 are derived analytically, implemented in the GAMESS software package, and evaluated relative to other terms in the dispersion expansion and relative to the total EFP interaction energy. Periodic boundary conditions in the minimum image convention are also implemented. A more accurate dispersion energy contribution can now be obtained during molecular dynamics simulations.Reprinted (adapted) with permission from The Journal of Physical Chemistry A, 120(4); 639-647. Doi: 10.1021/acs.jpca.5b11042. Copyright 2016 American Chemical Society. </p

Origin and TDDFT Benchmarking of the Plasmon Resonance in Acenes

The origin of plasmon resonance in acenes is described by analyzing the excitation spectrum of naphthalene in terms of configuration interaction. The strong longitudinal β-peak in the UV region of the spectrum results from a constructive interaction of the transition dipole moments of two degenerate configurations <i>V</i>₁ and <i>V</i>₂. <i>V</i>₁ corresponds to the excitation of an electron from the HOMO to the LUMO+1. <i>V</i>₂ corresponds to the excitation of an electron from the HOMO-1 to the LUMO. The weak longitudinal α-peak in the visible results from a destructive interaction of the dipole moments of the same two configurations. Previous time-dependent density functional theory (TDDFT) calculations showed a similar behavior for silver and gold nanoparticles but often with more than two interacting configurations. The plasmon occurs at the frequency where all configurations interact constructively. The β-peak of acenes can therefore be identified as the plasmon peak. The natural transition orbitals involved in the α- and β- peaks of naphthalene have identical shapes, which reflects the fact that the transitions involved in these two peaks are similar, but they may have opposite phases. An analysis of the transition density of the β-peak of naphthalene reveals that the electron density moves from one side of the molecule to the other upon excitation, as expected for a dipolar plasmon. The plasmonic character of the β-peak is compared to the single-particle transition character of the transverse p-band. Several exchange-correlation functionals have been benchmarked. Hybrid functionals give the best description of the β-peak and the α-peak. The couplings between the two interacting configurations at all levels of theory are similar to experimental values. On the other hand, long-range corrected functionals give the most accurate energies for the transverse p-band

Perspective: Ab initio force field methods derived from quantum mechanics

It is often desirable to accurately and efficiently model the behavior of large molecular systems in the condensed phase (thousands to tens of thousands of atoms) over long time scales (from nanoseconds to milliseconds). In these cases, ab initio methods are difficult due to the increasing computational cost with the number of electrons. A more computationally attractive alternative is to perform the simulations at the atomic level using a parameterized function to model the electronic energy. Many empirical force fields have been developed for this purpose. However, the functions that are used to model interatomic and intermolecular interactions contain many fitted parameters obtained from selected model systems, and such classical force fields cannot properly simulate important electronic effects. Furthermore, while such force fields are computationally affordable, they are not reliable when applied to systems that differ significantly from those used in their parameterization. They also cannot provide the information necessary to analyze the interactions that occur in the system, making the systematic improvement of the functional forms that are used difficult. Ab initio force field methods aim to combine the merits of both types of methods. The ideal ab initio force fields are built on first principles and require no fitted parameters. Ab initio force field methods surveyed in this perspective are based on fragmentation approaches and intermolecular perturbation theory. This perspective summarizes their theoretical foundation, key components in their formulation, and discusses key aspects of these methods such as accuracy and formal computational cost. The ab initio force fields considered here were developed for different targets, and this perspective also aims to provide a balanced presentation of their strengths and shortcomings. Finally, this perspective suggests some future directions for this actively developing area.This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Xu, Peng, Emilie B. Guidez, Colleen Bertoni, and Mark S. Gordon. "Perspective: Ab initio force field methods derived from quantum mechanics." The Journal of Chemical Physics 148, no. 9 (2018): 090901, and may be found at DOI: 10.1063/1.5009551. Copyright 2018 Author(s). Posted with permission