![]() ![]() A smooth transition between active and virtual orbitals in active space methods can potentially be beneficial. Active space removes abruptly all configurations outside of it, but even though the contribution of individual configurations outside of the active space can be small, their total contribution can be significant. Introducing an active space of a few most important orbitals and few active electrons is the main method of treating this problem. Even with sensible approximations and truncation, accurately describing the electronic structure of a system requires a large number of Slater determinants and with that comes computational cost. However, in a system with many electrons and many orbitals, the number of possible Slater determinants increases rapidly. Each Slater determinant represents a specific configuration-how the available electrons are distributed across spin orbitals. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory ( Dover Publications, New York, 1989). The wavefunction of a multi-electron system is usually accurately described by a linear combination of Slater determinants. The proposed algorithm of imaginary time propagation on biased random grids of Zombie states may present an alternative to the existing quantum Monte Carlo methods. We also show how low-lying excited states can be calculated efficiently using a Gram–Schmidt orthogonalization procedure. We also present a biasing method, for setting up a basis set of random Zombie states, that allows much smaller basis sizes to be used while still accurately describing the electronic structure Hamiltonian and its ground state and describe a technique of wave function “cleaning” that removes the contributions of configurations with the wrong number of electrons, improving the accuracy further. We also show how imaginary time propagation can be used to find the ground state of a system. In this work, we extend and build on this formalism by developing efficient algorithms for evaluating the Hamiltonian and other operators between Zombie states and address their normalization. Previously, it has been shown that Zombie states with fractional occupations of spin orbitals obeyed the correct fermionic creation and annihilation algebra and presented results for real-time evolution. Zombie states are a recently introduced formalism to describe coupled coherent fermionic states that address the fermionic sign problem in a computationally tractable manner. ![]()
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