We present an efficient implementation of the coupled-cluster Green’s function (CCGF) method for simulating photoemission spectra of periodic systems. We formulate the periodic CCGF approach with Brillouin zone sampling in the Gaussian basis at the coupled-cluster singles and doubles (CCSD) level. To enable CCGF calculations of realistic solids, we propose an active-space self-energy correction scheme by combining CCGF with the cheaper many-body perturbation theory ( GW ) and implement the model order reduction (MOR) frequency interpolation technique. We find that the active-space self-energy correction and MOR techniques significantly reduce the computational cost of CCGF while maintaining the high accuracy. We apply the developed CCGF approaches to compute spectral properties and band structure of silicon (Si) and zinc oxide (ZnO) crystals using triple-ζ Gaussian basis sets and medium-size k -point sampling and find good agreement with experimental measurements.
We present an efficient implementation of the coupled-cluster Green’s function (CCGF) method for simulating photoemission spectra of periodic systems. We formulate the periodic CCGF approach with Brillouin zone sampling in the Gaussian basis at the coupled-cluster singles and doubles (CCSD) level. To enable CCGF calculations of realistic solids, we propose an active-space self-energy correction scheme by combining CCGF with the cheaper many-body perturbation theory ( GW ) and implement the model order reduction (MOR) frequency interpolation technique. We find that the active-space self-energy correction and MOR techniques significantly reduce the computational cost of CCGF while maintaining the high accuracy. We apply the developed CCGF approaches to compute spectral properties and band structure of silicon (Si) and zinc oxide (ZnO) crystals using triple-ζ Gaussian basis sets and medium-size k -point sampling and find good agreement with experimental measurements.
A systematically converging series of ab initio, postdensity functional, size-consistent, electron-correlated approximations is desired for predictive computing of electronic band structures of insulating, semiconducting, and metallic solids. A series that meets all of these desiderata (except the applicability to metals) is ab initio many-body Green’s function theory based on Gaussian-type orbital (GTO) basis sets. Here, its leading-order approximation, the second-order Green’s function (GF2) method in the diagonal and frequency-independent approximations with the aug-cc-pVDZ basis set, is applied to the fundamental band gaps of three semiconductors (diamond, silicon, and silicon carbide in the zincblende structure) using cluster models. Corrections are made to the basis set incompleteness errors by the explicit correlation (F12) ansatz (GF2-F12) for the valence band edges. The crystals are modeled as surface-passivated clusters of increasing sizes, whose wave functions are expanded by up to 2709 GTO basis functions. Immense computational costs of these calculations are overcome by the highly scalable stochastic algorithm of the Monte Carlo GF2-F12 method, whose operation cost per state increases only as a cubic power of system size, which has a tiny memory footprint and easily achieves near-perfect parallel efficiency on thousands of CPUs or on hundreds of GPUs. The correlated, F12-corrected highest-occupied and lowest-unoccupied molecular orbital energy (HOMO–LUMO) gap is 5.78 ± 0.07 eV for C 87 H 76 as compared with the experimental value of the fundamental (indirect) band gap of bulk diamond at 5.48 eV. The correlated, F12-corrected HOMO–LUMO gaps for Si 75 H 76 and Si 32 C 43 H 76 are 2.56 ± 0.15 and 3.50 ± 0.12 eV, respectively, which are expected to decrease further with increasing cluster sizes. The experimental fundamental (indirect) band gaps of bulk silicon and silicon carbide are 1.17 and 2.42 eV, respectively.
We demonstrate that the coupled-cluster singles-and-doubles Green's function (GFCCSD) method is a powerful and prominent tool drawing the electronic band structures and the total energies, which many theoretical techniques struggle to reproduce. We have calculated single-electron energy spectra via the GFCCSD method for various kinds of systems, ranging from ionic to covalent and van der Waals, for the first time: the one-dimensional LiH chain, one-dimensional C chain, and one-dimensional Be chain. We have found that the bandgap becomes narrower than in HF due to the correlation effect. We also show that the band structures obtained from the GFCCSD method include both quasiparticle and satellite peaks successfully. Besides, taking one-dimensional LiH as an example, we discuss the validity of restricting the active space to suppress the computational cost of the GFCCSD method. We show that the calculated results without bands that do not contribute to the chemical bonds are in good agreement with full-band calculations. With the GFCCSD method, we can calculate the total energies and spectral functions for periodic systems in an explicitly correlated manner.
Periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD) has shown promise for quantitative calculations of band structures in solids. However, its steep computational scaling has limited calculations to relatively coarse k-point meshes, leading to sizable finite-size errors and discrepant estimates of thermodynamic-limit band gaps in recent benchmarks. In this work, we revisit EOM-CCSD band gaps for ten semiconductors and insulators using interacting-bath dynamical embedding theory (ibDET), a systematically improvable Green's function embedding framework that enables dense Brillouin-zone sampling at modest computational cost. By pushing the k-point sampling up to 10 × 10 × 10, well beyond the system sizes accessible in canonical periodic EOM-CCSD calculations, we significantly reduce finite-size errors and obtain stable thermodynamic-limit extrapolations. We further compare G0W0@PBE, G0W0@HF, and EOM-CCSD on an equal footing using the same numerical settings in PySCF. We find that EOM-CCSD yields a mean absolute error of 0.32 eV relative to experimental band gaps for a test set of ten semiconductors and insulators, which is lower than that of G0W0@PBE. For ZnO, EOM-CCSD also accurately describes the Zn 3d-band binding energy, despite overestimating the band gap. These results demonstrate that ibDET offers a practical route to high-accuracy many-body electronic structure calculations in periodic systems.
We propose two schemes for interpolation of the one-particle Green's function (GF) calculated within a coupled-cluster singles and doubles (CCSD) method for a periodic system. These schemes use Wannier orbitals for circumventing huge cost for a large number of sampled k points. One of the schemes is the direct interpolation, which obtains the GF straightforwardly by using Fourier transformation. The other is the self-energy-mediated interpolation, which obtains the GF via the Dyson equation. We apply the schemes to a LiH chain and trans-polyacetylene and examine their validity in detail. It is demonstrated that the direct-interpolated GFs suffer from numerical artifacts stemming from slow convergence of CCSD GFs in real space, while the self-energy-mediated interpolation provides more physically appropriate GFs due to the localized nature of CCSD self-energies. Our schemes are also applicable to other correlated methods capable of providing GFs.
Understanding emergent many-body phenomena in correlated materials remains one of the grandest challenges in solid-state quantum chemistry calculations. The individuality of electrons diminishes as correlation increases, which leads to the emergence of new features in the system. Seeking to address such problems accurately requires the aid of non-perturbative many-body techniques as well as the corresponding high-quality basis sets. In periodic systems, a given element may be present in different spatial arrangements displaying vastly different physical and chemical properties, and an elemental basis set independent of the physical properties of materials may lead to significant simulation inaccuracies. In fact, with the rapid progress of quantum chemistry methods in condensed-phase simulations, the need for a library of reliable Gaussian basis sets explicitly designed for periodic calculations has become urgent. In the meantime, the development of parameter-free, systematic and reliable quantum chemistry methods for simultaneously treating weak and strong correlations in periodic systems has never stopped. Their ability to treat realistic solid materials needs to be tested, and the obtained results can serve as benchmarks for empirical parameter-guided solid-state calculations. In this thesis, we present numerical studies of various solid-state systems, emphasizing the design and optimization of Gaussian basis sets and assessing the band structure properties of the periodic solid systems. The work begins by introducing the theoretical framework of the electronic structure theory and presenting the fundamentals of a fully self-consistent GW approximation and the self-energy embedding theory (SEET) in Chapters 2 and 3. It continues with a description of the Gaussian basis set optimization scheme we devised for solid-state quantum chemistry calculations. The scheme we present is designed to avoid a lack of material specificity within a given basis set by simultaneously minimizing the total energy of the system and optimizing the band energies when compared to the reference plane wave calculation while accounting for the overlap matrix condition number. We compare the quality of the Gaussian basis sets generated via our method against the existing basis sets. And the optimization scheme is tested to yield improved results. We finally present a quantitative study of electronic properties of realistic materials with the treatment of Green's function based weakly correlated self-consistent GW approximation and the strongly correlated self-energy embedding theory. In the transition metal oxide BiVO3, we found the inaccurate illustration of orbitals including t_{2g} in transition metal Vanadium by DFT. Our calculation shows a systematic trend of DFT failure in illustrating both insulating and metallic solutions, demonstrating the dangers of using DFT when the experimental data is scarce.
The Green's function coupled cluster (GFCC) method, originally proposed in the early 1990s, is a powerful many-body tool for computing and analyzing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, in order for the GFCC to become a method that may be routinely used in the electronic structure calculations, robust numerical techniques and approximations must be employed to reduce its extremely high computational overhead. In our recent studies, it has been demonstrated that the GFCC equations can be solved directly in the frequency domain using iterative linear solvers, which can be easily distributed in a massively parallel environment. In the present work, we demonstrate a successful application of model-order-reduction (MOR) techniques in the GFCC framework. Briefly speaking, for a frequency regime of interest that requires high-resolution descriptions of spectral function, instead of solving the GFCC linear equation of full dimension for every single frequency point of interest, an efficiently solvable linear system model of a reduced dimension may be built upon projecting the original GFCC linear system onto a subspace. From this reduced order model is obtained a reasonable approximation to the full dimensional GFCC linear equations in both interpolative and extrapolative spectral regions. Here, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some selected frequencies within the spectral region of interest. During the iterations, the quality of the subspace, as well as the linear system model, can be systematically improved. The method is tested in this work in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems such as carbon monoxide, 1,3-butadiene, benzene, and adenine. To reach the same level of accuracy as that of the original GFCC method, the application of MOR in the GFCC method is able to significantly lower the original computational cost for the aforementioned molecules in designated frequency regimes. As a byproduct, the reduced order model obtained by this method is found to provide a high-quality initial guess, which improves the convergence rate for the existing iterative linear solver.