Excitons, trions, biexcitons, and exciton-trion complexes in two-dimensional transition metal dichalcogenide sheets of MoS2, MoSe2, MoTe2, WS2 and WSe2 are studied by means of density functional theory and path integral Monte Carlo method in order to accurately account for the particle-particle correlations. In addition, the effect of dielectric environment on the properties of these exciton complexes is studied by modifying the effective interaction potential between particles. Calculated exciton and trion binding energies are consistent with previous experimental and computational studies, and larger systems such as biexciton and exciton-trion complex are found highly stable. Binding energies of biexcitons are similar or higher than those of trions, but the binding energy of the trion depends significantly stronger on the dielectric environment than that of biexciton. Therefore, as a function of an increasing dielectric constant of the environment the exciton-trion complex "dissociates" to a biexciton rather than to an exciton and a trion.Layered transition metal dichalcogenides (TMD) are chemically, thermally, and mechanically stable even in the monolayer form, and thus, provide an ideal platform for studying condensed matter physics in two dimensions. The semiconducting TMDs present many unusual optical properties such as strong excitonic effects 1 , valley-dependent circular dichroism 2 , and second-harmonic generation 3 , whose magnitude depends sensitively on the number of layers. For instance, the prototypical MoS 2 material is a semiconductor with 1.1 eV indirect band gap in bulk, but 1.9 eV direct band gap in the monolayer 1 . Importantly, the reduced dimensionality is manifested in a large exciton binding energy of 0.5-1 eV, but also of significant binding energy in the case of charged excitons, or trions, consisting of three charge carriers. This suggests that even larger complexes might be stable. Indeed, first experimental reports assigned to biexciton formation have very recently appeared in the literature [4][5][6] . Theoretical studies are invaluable in predicting the stability of these complexes and in interpreting the experimental results. Excitons can be calculated reliably from firstprinciples by solving the Bethe-Salpeter equation (BSE) on top of quasi-particle band structure. Binding energies have also been calculated using simple variational or tight-binding models based on an effective 2D interaction potential and the effective mass approach 6-13 , yielding fairly good agreement with experiments and with the BSE results in the case of excitons. This has also raised interest to apply similar approaches to study larger exciton complexes 6,14 , in comparison to the theoretical estimates based on quantum well systems 4,15,16 . Difficulties in constructing reasonable wave function ansatz in the case of the larger complexes hinders straightforward extension of the simple variational models. Within the effective mass approach, quantum Monte Carlo (QMC) methods, such as diffusion Monte Carlo and...

QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.

We review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility. The auxiliary field QMC (AFQMC) implementation has been greatly expanded to include k-point symmetries, tensor-hypercontraction, and accelerated graphical processing unit (GPU) support. These scaling and memory reductions greatly increase the number of orbitals that can practically be included in AFQMC calculations, increasing the accuracy. Advances in real space methods include techniques for accurate computation of bandgaps and for systematically improving the nodal surface of ground state wavefunctions. Results of these calculations can be used to validate application of more approximate electronic structure methods, including GW and density functional based techniques. To provide an improved foundation for these calculations, we utilize a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets; these can also be applied in quantum-chemical and other many-body applications, not only QMC. These advances increase the efficiency, accuracy, and range of properties that can be studied in both molecules and materials with QMC and QMCPACK.

In this work we develop tools that enable the study of non-adiabatic effects with variational and diffusion Monte Carlo methods. We introduce a highly accurate wave function ansatz for electronion systems that can involve a combination of both fixed and quantum ions. We explicitly calculate the ground state energies of H2, LiH, H2O and FHF − using fixed-node quantum Monte Carlo with wave function nodes that explicitly depend on the ion positions. The obtained energies implicitly include the effects arising from quantum nuclei and electron-nucleus coupling. We compare our results to the best theoretical and experimental results available and find excellent agreement.