Functional Perturbation Theory Research Articles

Green/WeakCoupling: Implementation of fully self-consistent finite-temperature many-body perturbation theory for molecules and solids

The accurate ab-initio simulation of molecules and periodic solids with diagrammatic perturbation theory is an important task in quantum chemistry, condensed matter physics, and materials science. In this article, we present the WeakCoupling module of the open-source software package Green, which implements fully self-consistent diagrammatic weak coupling simulations, capable of dealing with real materials in the finite-temperature formalism. The code is licensed under the permissive MIT license. We provide self-consistent GW (scGW) and self-consistent second-order Green's function perturbation theory (GF2) solvers, analysis tools, and post-processing methods. This paper summarises the theoretical methods implemented and provides background, tutorials and practical instructions for running simulations. Program summaryProgram Title:Green/WeakCouplingCPC Library link to program files:https://doi.org/10.17632/2ysyhzww6t.1Developer's repository link:https://github.com/Green-Phys/green-mbptProgramming language:C++17, CUDA, PythonLicensing provisions: MIT LicenseExternal routines/libraries:MPI >= 3.0, BLAS, Eigen >= 3.4.0, cmake >= 3.18, cuBLAS.Nature of problem: The simulation of periodic solids and molecules using diagrammatic perturbation theorySolution method: We present an open-source implementation of the fully self-consistent finite-temperature many-body perturbation theory formalism at the GW and second-order perturbation theory level.

Can GW handle multireference systems?

Due to the infinite summation of bubble diagrams, the GW approximation of Green's function perturbation theory has proven particularly effective in the weak correlation regime, where this family of Feynman diagrams is important. However, the performance of GW in multireference molecular systems, characterized by strong electron correlation, remains relatively unexplored. In the present study, we investigate the ability of GW to handle closed-shell multireference systems in their singlet ground state by examining four paradigmatic scenarios. First, we analyze a prototypical example of a chemical reaction involving strong correlation: the potential energy curve of BeH2 during the insertion of a beryllium atom into a hydrogen molecule. Second, we compute the electron detachment and attachment energies of a set of molecules that exhibit a variable degree of multireference character at their respective equilibrium geometries: LiF, BeO, BN, C2, B2, and O3. Third, we consider a H6 cluster with a triangular arrangement, which features a notable degree of spin frustration. Finally, the dissociation curve of the HF molecule is studied as an example of single bond breaking. These investigations highlight a nuanced perspective on the performance of GW for strong correlation depending on the level of self-consistency, the choice of initial guess, and the presence of spin-symmetry breaking at the Hartree-Fock level.

Classical statistical simulation of quantum field theory

We propose a procedure of computing the n-point function in perturbation theory of the quantum field theory as the average over the complex Gaussian noises in a classical theory. The complex Gaussian noises are the sources for the creation and annihilation of particles and the energy of the resultant configuration is the same as the zero point energy of the corresponding quantum field theory.

Nonintegrable threshold singularities of two-point functions in perturbation theory

In perturbation theory, the spectral densities of two-point functions develop non-integrable threshold singularities at higher orders. In QCD, such singularities emerge when calculating the diagrams in terms of the pole quark mass, and they become stronger when one rearranges the perturbative expansion in terms of the running quark mass. In this paper we discuss the proper way to handle such singularities.

Rotational States of Adsorbed H2 on Fe(OH)3 Molecule

Dispersion-corrected density functional (DFT-D3) and Quantum perturbation theories are used to calculate the potential energy surface (PES), rotational states and energy rotational levels of adsorb...

Wave Function Perspective and Efficient Truncation of Renormalized Second-Order Perturbation Theory.

We present an approach to a renormalized second-order Green's function perturbation theory (GF2), which avoids all dependency on continuous variables, grids, or explicit Green's functions and is instead formulated entirely in terms of static quantities and wave functions. Correlation effects from MP2 diagrams are iteratively incorporated to modify the underlying spectrum of excitations by coupling the physical system to fictitious auxiliary degrees of freedom, allowing for single-particle orbitals to delocalize into this additional space. The overall approach is shown to be rigorously O[N5], after an appropriate compression of this auxiliary space. This is achieved via a novel scheme, which ensures that a desired number of moments of the underlying occupied and virtual spectra are conserved in the compression, allowing a rapid and systematically improvable convergence to the limit of the effective dynamical resolution. The approach is found to then allow for the qualitative description of stronger correlation effects, avoiding the divergences of MP2, as well as its orbital-optimized version. On application to the G1 test set, we find that modification up to only the third spectral moment of the underlying spectrum from which the double excitations are built are required for accurate energetics, even in strongly correlated regimes. This is beyond simple self-consistent changes to the density matrix of the system but far from requiring a description of the full dynamics of the frequency-dependent self-energy.

Marked correlation functions in perturbation theory

We develop perturbation theory approaches to model the marked correlation function constructed to up-weight low density regions of the Universe, which might help distinguish modified gravity models from the standard cosmology model based on general relativity. Working within Convolution Lagrangian Perturbation Theory, we obtain that weighted correlation functions are expressible as double convolution integrals that we approximate using a combination of Eulerian and Lagrangian schemes. We find that different approaches agree within 1% on quasi non-linear scales. Compared with N-body simulations, the perturbation theory is found to provide accurate predictions for the marked correlation function of dark matter fields, dark matter halos as well as Halo Occupation Distribution galaxies down to 30 Mpc/h. These analytic approaches help to understand the degeneracy between the mark and the galaxy bias and find a way to maximize the differences among various cosmological models.

Structural, Electronic, Lattice Dynamic, and Elastic Properties of SnTiO3 and PbTiO3 Using Density Functional Theory

The structural, electronic, and elastic properties of tetragonal phase of SnTiO3 and PbTiO3 are investigated using first principle calculations. The unknown exchange-correlation functional is approximated with generalized gradient approximation (GGA) as implemented in pseudopotential plane wave approach. The convergence test of total energy with respect to energy cutoff and k-point sampling is preformed to ensure the accuracy of the calculations. The structural properties such as equilibrium lattice constant, equilibrium unit cell volume, bulk modulus, and its derivative are in reasonable agreement with the previous experimental and theoretical works. From elastic constants, mechanical parameters such as anisotropy factor A, shear modulus G, bulk modulus B, Young’s modulus E, and Poison’s ratio n are determined by using Voigt–Reuss–Hill average approximation. In addition, Debye temperature and longitudinal and transversal sound velocities are predicted from elastic constants. The electronic band structure and density of states of both compounds are obtained and compared with the available experimental as well as theoretical data. Born effective charge (BEC), phonon dispersion curve, and density of states are computed from functional perturbation theory (DFPT). Lastly, the spontaneous polarization is determined from the modern theory of polarization, and they are in agreement with the previous findings.

A concise introduction to quantum field theory

We review the basic principles of Quantum Field Theory (QFT) in a brief but comprehensive introduction to the foundations of QFT. The principles of QFT are introduced in canonical and covariant formalisms. The problem of ultraviolet (UV) divergences and its renormalization is analyzed in the canonical formalism. As an application, we review the roots of Casimir effect. For simplicity, we focus on the scalar field theory but the generalization for fermion fields is straightforward. However, the quantization of gauge fields require extra techniques which are beyond the scope of this paper. The special cases of free field theories and conformal invariant theories in lower space-time dimensions illustrate the relevance of the foundations of the theory. Finally, a short introduction to functional integrals and perturbation theory in the Euclidean formalism is included in the last section.

Giant contribution of the ligand states to the magnetic properties of the Cr2Ge2Te6 monolayer.

The magnetic properties of the Cr2Ge2Te6 monolayer - an important two-dimensional (2D) ferromagnetic (FM) material - are systematically investigated on the basis of ab initio electronic structure calculations within density functional theory (DFT). For these purposes we construct a minimal tight-binding model in the basis of maximally localized Wannier functions, which describes the behavior of the magnetic Cr 3d, Ge 4p, and Te 5p electrons. This model allows us to rationalize the results of conventional DFT calculations at the microscopic level. We explore the abilities of different techniques, including the Green's function perturbation theory and constraint calculations with an external magnetic field, for the analysis of magnetic interactions, that allow us to decompose these interactions in terms of partial contributions coming from different atomic sites. We argue that, although the magnetism of Cr2Ge2Te6 originates from the Hund's rule effects in the partially filled Cr 3d shell, the contributions of the ligand - and particularly Te 5p - states are crucially important and have a significant effect on the behavior of isotropic exchange interactions, magnetocrystalline anisotropy energy (MAE), and antisymmetric Dzyaloshinskii-Moriya (DM) interactions induced by an electric field. In particular, the Te 5p states increase dramatically the FM coupling and DM interactions between the Cr spins. They are also largely responsible for the behavior of MAE, manifesting themselves in non-Heisenberg type effects, which go beyond the scopes of the conventional Mermin-Wagner theorem for the analysis of 2D magnetism of Cr2Ge2Te6.

First-Principles Study of Electronic Structure, Optical Properties and LO-TO Splitting of GaP

The electronic structure and optical properties of GaP were calculated using generalized gradients in density functional theory. The Bonn effective charge, optical frequency dielectric constant and the LO-TO splitting value were calculated by density functional theory perturbation method.

Resonance enhanced multiphoton ionization − time of flight (REMPI-TOF) detection of Br ( 2 P j ) atoms in the photodissociation of 4-bromo-2,3,5,6-tetrafluoropyridine at 234 nm: Effect of low-lying πσ* states

Abstract The photodissociation dynamics of 4-bromo-2,3,5,6-tetrafluoropyridine (BTFP) have been studied in a supersonic molecular beam around 234 nm, which prepares the molecule in its ππ* state. The dynamics of the C Br bond dissociation have been investigated using resonance-enhanced multiphoton ionization coupled with time-of-flight mass spectrometer (REMPI-TOFMS) by detecting the nascent spin orbit states of the primary bromine atoms, namely, Br (2P3/2) and Br*(2P1/2). State specific polarization dependent TOF profiles were obtained, from which the translational energy distributions and recoil anisotropy parameters, βi, were extracted using forward convolution method. A strong polarization dependence of TOF profiles suggests anisotropic distributions of the Br and Br* fragments. Two components, namely, the fast and the slow, are observed in the translational energy distribution of Br and Br* atoms, formed from different potential energy surfaces. The average translational energies released into the Br and Br* channels for the fast component are 17.3 ± 2.0 and 11.1 ± 2.0 kcal/mol, respectively. Similarly, for the slow component, the average translational energies imparted into the Br and Br* channels are 2.6 ± 1.0 and 1.5 ± 1.0 kcal/mol, respectively. The relative quantum yields of Br and Br* are 0.87 ± 0.15 and 0.13 ± 0.06. The anisotropy parameters for Br and Br* are characterized by a similar value of 0.60 ± 0.05. The energy partitioning into the translational modes is interpreted with the help of various models. The experimental studies revealing the nature of translational energies distribution for Br and Br* and its average value along with the theoretical calculations employing Time-Dependent Density Functional Theory (TD-DFT) and Multi Configuration Quasi Degenerate second order Perturbation Theory (MCQDPT2) suggest that the initially prepared ππ* state crosses over to a nearby σ* repulsive state along the C Br bond, mainly, πσ* state from where the dissociation takes place. The results also indicate the process of fast internal conversion to ground state from the initially prepared ππ* state, which eventually forms slow Br atoms after C-Br bond dissociation process on the ground state. During the course of experiments, the absorption spectrum was also obtained with its absolute absorption cross section. Non-adiabatic curve crossing plays an important role in the C Br bond dissociation of BTFP.

Optical Absorption of Armchair MoS2 Nanoribbons: Enhanced Correlation Effects in the Reduced Dimension

We carry out first-principles calculations of the quasi-particle band structure and optical absorption spectra of H-passivated armchair MoS2 nanoribbons (AMoS2NRs) by employing the approach combining the Green’s function perturbation theory (GW) and the Bethe-Salpeter equation (BSE), i.e., GW+BSE. Optical absorption spectra of AMoS2NRs show the exciton multibands (their binding energies are close to or less than 1 eV) which are much stronger than a single layer of MoS2. However, they are absent in the spectra by the approach of GW and the random phase approximation (RPA), i.e., GW+RPA. This signifies that the excitonic correlation effects are strongly enhanced in the reduced dimensional structure of MoS2. We also calculate the exciton wave functions for the few lowest energy excitons, which are found to have non-Frenkel character.

Effect of proton donors on the intramolecular coordination C=O→Si-F in (acyloxymethyl)trifluorosilanes.Ab initio,DFT and FTIR study, QTAIM analysis

The intramolecular С=OSi coordination in H-complexes of (acetoxymethyl)trifluorosilane and (benzoyloxymethyl)trifluorosilane with proton donors HCl, PhOH, MeOH, and CHCl3 was investigated by density functional theory and second-order Moller-Plesset perturbation theory (MP2) methods. Interrelation and mutual influence of the intramolecular coordination bond С=OSi and intermolecular hydrogen bonds C=O···H and Si–F···H in H-complexes was established using the AIM and NBO analyses. The С=OSi coordination is weakened by the C=O···H hydrogen bonding but enhanced by the Si–Fax···H hydrogen bonding. The structure of H-complexes of (acetoxymethyl)trifluorosilane with proton donors in solution was determined by comparing the ν(C=O) and ν(Si–F) frequencies calculated using the conductor-like polarizable continuum model and their experimental Fourier transform infrared values. Copyright © 2014 John Wiley & Sons, Ltd.

Convergent study of Ru–ligand interactions through QTAIM, ELF, NBO molecular descriptors and TDDFT analysis of organometallic dyes

We report a theoretical study of a series of Ru complexes of interest in dye-sensitised solar cells, in organic light-emitting diodes, and in the war against cancer. Other metal centres, such as Cr, Co, Ni, Rh, Pd, and Pt, have been included for comparison purposes. The metal–ligand trends in organometallic chemistry for those compounds are shown synergistically by using three molecular descriptors: quantum theory of atoms in molecules (QTAIM), electron localisation function (ELF) and second-order perturbation theory analysis of the natural bond orbital (NBO). The metal–ligand bond order is addressed through both delocalisation index (DI) of QTAIM and fluctuation index (λ) of ELF. Correlation between DI and λ for Ru–N bond in those complexes is introduced for the first time. Electron transfer and stability was also assessed by the second-order perturbation theory analysis of the NBO. Electron transfer from the lone pair NBO of the ligands toward the antibonding lone pair NBO of the metal plays a relevant role in stabilising the complexes, providing useful insights into understanding the effect of the ‘expanded ligand’ principle in supramolecular chemistry. Finally, absorption wavelengths associated to the metal-to-ligand charge transfer transitions and the highest occupied molecular orbital (HOMO)--lowest unoccupied molecular orbital (LUMO) characteristics were studied by time-dependent density functional theory.

Strong many-body effects in silicene-based structures

Silicene, which is the silicon equivalent of carbon-based graphene and shares some unique properties with graphene, has been attracting more and more attention since its successful synthesis. Using Green's function perturbation theory, many-body effects in silicene, hydrogenated silicene (silicane), fluorinated silicene (fluorosilicene), as well as armchair silicene nanoribbons (ASiNRs) are studied. Optical resonances in silicene have been aroused by excitonic effects: The $\ensuremath{\pi}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{*}$ excitonic resonance at 1.23 eV is contributed by the characteristic dispersion of Dirac fermions, while the one at 3.75 eV is due to the $\ensuremath{\sigma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{*}$ transition. Hydrogenation or fluorination of silicene removes the conductivity at the Dirac point and causes band-gap opening. In addition to the remarkable self-energy effects, optical absorption properties of silicane, fluorosilicene, and ASiNRs are dominated by strong excitonic effects with formation of bound excitons with considerable binding energies.

Many-body effects in silicene, silicane, germanene and germanane

Silicene, which is the silicon equivalent of carbon-based graphene and shares some of the unique properties with graphene, has been attracting more and more attention since its synthesis and represents a breakthrough in current silicon-based technology. In this work, many-body effects in silicene, silicane, germanene and germanane have been demonstrated based on the Green's function perturbation theory, i.e., GW + Bethe-Salpeter equation. Due to confinement, many-body effects play a pivotal role in quasi-particle excitations and optical absorption spectra, which leads to excitonic resonance (π→π* excitation) in silicene and germanene, and strongly bound excitons in silicane and germanane with considerable binding energies.

Theoretical modeling of the electronic structure and exchange interactions in Cu(II)Pc

We calculate the electronic structure and exchange interactions in a copper(II)phthalocyanine (Cu(II)Pc) crystal as a one-dimensional molecular chain using hybrid exchange density functional theory (DFT). In addition, the intermolecular exchange interactions are also calculated in a molecular dimer using Green's function perturbation theory (GFPT) to illustrate the underlying physics. We find that the exchange interactions depend strongly on the stacking angle, but weakly on the sliding angle (defined in the text). The hybrid DFT calculations also provide an insight into the electronic structure of the Cu(II)Pc molecular chain and demonstrate that on-site electron correlations have a significant effect on the nature of the ground state, the band gap and magnetic excitations. The exchange interactions predicted by our DFT calculations and GFPT calculations agree qualitatively with the recent experimental results on newly found η-Cu(II)Pc and the previous results for the α- and β-phases. This work provides a reliable theoretical basis for the further application of Cu(II)Pc to molecular spintronics and organic-based quantum information processing.

The thermal decomposition of 4-bromobutyric acid in the gas phase: A quantum chemical theory calculation

The gas-phase elimination kinetic of 4-bromobutyric acid to give butyrolactone, and hydrogen bromide was studied using Density Functional Theory DFT and Moller-Plesset Perturbation Theory of Second Order MP2 to investigate the more reasonable reaction mechanism. Good agreement of calculated activation parameters with the experimental values was obtained when using PBEPBE/6-31++Gd,p level of theory. Analysis of the calculated thermodynamic and kinetic parameters suggested the reaction mechanism is unimolecular, with involvement of the hydroxyl oxygen of the carboxylic moiety of the substrate assisting the exit of bromide in nucleophilic substitution. The alternate mechanism with the participation of the carbonyl oxygen in a slow step to give an intimate ion-pair intermediate was disregarded due to the high energy of activation. Bond order analysis shows the process is dominated by the breaking of the C-Br bond. The reaction can be described as unimolecular and moderately non-synchronous process.

Spin‐component‐scaled electron correlation methods

AbstractSpin‐component‐scaled (SCS) electron correlation methods for electronic structure theory are reviewed. The methods can be derived theoretically by applying special conditions to the underlying wave functions in perturbation theory. They are based on the insight that low‐order wave function expansions treat the correlation effects of electron pairs with opposite spin (OS) and same spin (SS) differently because of their different treatment at the underlying Hartree–Fock level. Physically, this is related to the different average inter‐electronic distances in the SS and OS electron pairs. The overview starts with the original SCS‐MP2 method and discusses its strengths and weaknesses and various ways to parameterize the scaling factors. Extensions to coupled‐cluster and excited state methods as well the connection to virtual‐orbital dependent density functional approaches are highlighted. The performance of various SCS methods in large thermochemical benchmarks and for excitation energies is discussed in comparison with other common electronic structure methods.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods