We present an approach for ab initio many-body calculations of excited states in solids. Using auxiliary-field quantum Monte Carlo, we introduce an orthogonalization constraint to prevent collapse of the stochastic Slater determinants in the imaginary-time propagation. Trial wave functions from density-functional calculations are used for the constraints. Detailed band structures calculated for standard semiconductors are in good agreement with GW and experimental results. For the challenging ZnO wurtzite structure, we obtain a fundamental band gap of 3.26(16) eV, consistent with experiments.
Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multi-determinant trial wave functions employed in both approaches are generated using the configuration interaction using a perturbative selection made iteratively (CIPSI) technique. Complete basis set full configuration interaction (CBS-FCI) energies estimated with CIPSI are used as a reference in this compara…
The role of charged centers in radiation-induced phenomena occurring in solid nitrogen irradiated with an electron beam was studied. The experiments were performed employing luminescence method and activation spectroscopy techniques - spectrally resolved thermally stimulated luminescence TSL and thermally stimulated exoelectron emission. To discriminate radiation-induced processes in the bulk and at the surface the samples were probed in depth by varying electron energy. Desorption of excited N2* (C3Πu) molecule was detected for the first time. The mechanism of this phenomenon based on recombi…
We present accurate many-body results of the electronic densities in several solid materials, including Si, NaCl, and Cu. These results are obtained using the ab initio auxiliary-field quantum Monte Carlo (AFQMC) method working in a plane-wave basis with norm-conserving, multiple-projector pseudopotentials. AFQMC has been shown to be an excellent many-body total energy method. Computation of observables and correlation functions other than the ground-state energy requires back-propagation, whose adaption and implementation in the plane-wave basis AFQMC framework are discussed in the present pa…
Open-shell systems such as magnetic molecules or defects with a triplet ground state are challenging to describe in electronic structure methods, but are of great interest for quantum information applications. We demonstrate a spin-flip approach within the Bethe-Salpeter equation to calculate ground and excited states of open-shell molecules and defected solids. The approach works in periodic boundary conditions without any need for embedding or selection of a subspace. Our benchmark results for the torsion potential-energy surface of ethylene and the optical excitations of the diamond NV$^{-}…
The auxiliary-field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time-independent Schroedinger equation in atoms, molecules, solids, and a variety of model systems by stochastic sampling. We introduce the theory and formalism behind this framework, briefly discuss the key technical steps that turn it into an effective and practical computational method, present several illustrative results, and conclude with comments on the prospects of ab initio computation by this framework.
We present a systematic downfolding many-body approach for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to dial, in principle, between the simplest model and the original Hamiltonian. As a by-product, pseudopotential errors are essentially eliminated using a frozen-core treatment. The computational cost of the many-body calculation is dramatically reduced without sacrificing accuracy. We use the auxiliary-field quantum Monte Carlo (AFQMC) method to solve the down…
We investigate the use of optimized correlation consistent gaussian basis sets for the study of insulating solids with auxiliary-field quantum Monte Carlo (AFQMC). The exponents of the basis set are optimized through the minimization of the second order Møller--Plesset perturbation theory (MP2) energy in a small unit cell of the solid. We compare against other alternative basis sets proposed in the literature, namely calculations in the Kohn--Sham basis and in the natural orbitals of an MP2 calculation. We find that our optimized basis sets accelerate the convergence of the AFQMC correlation e…
Time and angular resolved photoelectron spectroscopy is a powerful technique to measure electron dynamics in solids. Recent advances in this technique have facilitated band and energy resolved observations of the effect that excited phonons, have on the electronic structure. Here, we show with the help of \textit{ab initio} simulations that the Fourier analysis of time-resolved measurements of solids with excited phonon modes leads, in fact, to an observation of the band- and mode-resolved electron-phonon coupling directly from the experimental data and without need for theoretical computation…
Transient X-ray spectroscopies have become ubiquitous in studying photoexcited dynamics in solar energy materials due to their sensitivity to carrier occupations and local chemical or structural dynamics. The interpretation of solid-state photoexcited dynamics, however, is complicated by the core-hole perturbation and the resulting many-body dynamics. Here, an ab initio, Bethe-Salpeter equation (BSE) approach is developed that can incorporate photoexcited state effects for solid-state materials. The extreme ultraviolet (XUV) absorption spectra for the ground, photoexcited, and thermally expand…
We review the use of continuum quantum Monte Carlo (QMC) methods for the calculation of energy gaps from first principles, and present a broad set of excited-state calculations carried out with the variational and fixed-node diffusion QMC methods on atoms, molecules, and solids. We propose a finite-size-error correction scheme for bulk energy gaps calculated in finite cells subject to periodic boundary conditions. We show that finite-size effects are qualitatively different in two-dimensional materials, demonstrating the effect in a QMC calculation of the band gap and exciton binding energy of…
Accurate and efficient calculations of absorption spectra of molecules and materials are essential for the understanding and rational design of broad classes of systems. Solving the Bethe-Salpeter equation (BSE) for electron-hole pairs usually yields accurate predictions of absorption spectra, but it is computationally expensive, especially if thermal averages of spectra computed for multiple configurations are required. We present a method based on machine learning to evaluate a key quantity entering the definition of absorption spectra: the dielectric screening. We show that our approach yie…
We present the results of Gaussian-based ground-state and excited-state equation-of-motion coupled-cluster theory with single and double excitations for three-dimensional solids. We focus on diamond and silicon, which are paradigmatic covalent semiconductors. In addition to ground-state properties (the lattice constant, bulk modulus, and cohesive energy), we compute the quasiparticle band structure and band gap. We sample the Brillouin zone with up to 64 k-points using norm-conserving pseudopotentials and polarized double- and triple-zeta basis sets, leading to canonical coupled-cluster calcul…
We explore the extended Koopmans' theorem (EKT) within the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method. The EKT allows for the direct calculation of electron addition and removal spectral functions using reduced density matrices of the $N$-particle system, and avoids the need for analytic continuation. The lowest level of EKT with AFQMC, called EKT1-AFQMC, is benchmarked using small molecules, 14-electron and 54-electron uniform electron gas supercells, and diamond at the $Γ$-point. Via comparison with numerically exact results (when possible) and coupled-cluster methods, we f…
Femtosecond X-ray irradiation of solids excites energetic photoelectrons that thermalize on a timescale of a few hundred femtoseconds. The thermalized electrons exchange energy with the lattice and heat it up. Experiments with X-ray free-electron lasers have unveiled so far the details of the electronic thermalization. In this work we show that the data on transient optical reflectivity measured in GaAs irradiated with femtosecond X-ray pulses can be used to follow electron-lattice relaxation up to a few tens of picoseconds. With a dedicated theoretical framework, we explain the so far unexpla…
Strong optical nonlinearities play a central role in realizing quantum photonic technologies. In solid state systems, exciton-polaritons, which result from the hybridization of material excitations and cavity photons, are an attractive candidate to realize such nonlinearities. Here, the interaction between excitons forms the basis of the polaritonic nonlinearity. While the interaction between ground state excitons generates a notable optical nonlinearity, the strength of such ground state interactions is generally not sufficient to reach the regime of quantum nonlinear optics and strong single…
The dynamics of photo-generated electron-hole pairs in solids are dictated by many-body interactions such as electron-electron and electron-phonon scattering. Hence, understanding and controlling these scattering channels is crucial for many optoelectronic applications, ranging from light harvesting to optical amplification. Here we measure the formation and relaxation of the photo-generated non-thermal carrier distribution in monolayer graphene with time- and angle-resolved photoemission spectroscopy. Using sub 10fs pulses we identify impact ionization as the primary scattering channel, which…
We present the first implementation and applications of non-Dyson algebraic diagrammatic construction theory for charged excitations in three-dimensional periodic solids (EA/IP-ADC). The EA/IP-ADC approach has a computational cost similar to the ground-state Møller-Plesset perturbation theory, enabling efficient calculations of a variety of crystalline excited-state properties (e.g., band structure, band gap, density of states) sampled in the Brillouin zone. We use EA/IP-ADC to compute the quasiparticle band structures and band gaps of several materials (from large-gap atomic and ionic solids …
We present ab initio absorption spectra of six three-dimensional semiconductors and insulators calculated using Gaussian-based periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). The spectra are calculated efficiently by solving a system of linear equations at each frequency, giving access to an energy range of tens of eV without explicit enumeration of excited states. We assess the impact of Brillouin zone sampling, for which it is hard to achieve convergence due to the cost of EOM-CCSD. Although our most converged spectra exhibit lineshapes that …
Analytical Forces from the Bethe-Salpeter Equation for Large-Scale Excited-State Relaxation
Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；Initiative for Computational Catalysis, Flatiron Institute（平顿研究所计算催化倡议）；Materials Science Division, Argonne National Laboratory（阿贡国家实验室材料科学部）；Department of Physics, Computer Science, and Mathematics, University of Modena and Reggio Emilia（摩德纳和雷焦艾米利亚大学物理、计算机和数学系）；Department of Chemistry, University of Chicago（芝加哥大学化学系）
