Abstract In this paper, a novel exact fixed‐node quantum Monte Carlo (EFNQMC) algorithm was proposed, which is a self‐optimizing and self‐improving procedure. In contrast to the previous EFNQMC method, the importance function of this method is optimized synchronistically in the diffusion procedure, but not before beginning the EFNQMC computation. In order to optimize the importance function, the improved steepest descent technique is used, in which the step size is automatically adjustable. The procedure is quasi‐Newton type and converges super linearly. The present method also uses a novel trial function, which has correct electron‐electron and electron‐nucleus cusp conditions. The novel EFNQMC algorithm and the novel trial function are employed to calculate the energies of 1 1A1 state of CH2, 1A1 state of C8 and the ground‐states of H2, LiH, Li2 and H2O.
Abstract In this paper, a novel exact fixed‐node quantum Monte Carlo (EFNQMC) algorithm was proposed, which is a self‐optimizing and self‐improving procedure. In contrast to the previous EFNQMC method, the importance function of this method is optimized synchronistically in the diffusion procedure, but not before beginning the EFNQMC computation. In order to optimize the importance function, the improved steepest descent technique is used, in which the step size is automatically adjustable. The procedure is quasi‐Newton type and converges super linearly. The present method also uses a novel trial function, which has correct electron‐electron and electron‐nucleus cusp conditions. The novel EFNQMC algorithm and the novel trial function are employed to calculate the energies of 1 1A1 state of CH2, 1A1 state of C8 and the ground‐states of H2, LiH, Li2 and H2O.
In this paper, a novel exact fixed-node quantum Monte Carlo (EFNQMC) algorithm was proposed, which is a self-optimizing and self-improving procedure. In contrast to the previous EFN-QMC method, the importance function of this method is optimized synchronistically in the diffusion procedure, but not be-fore beginning the EFNQMC computation. In order to optimize the importance function, the improved steepest descent tech-nique is used, in which the step size is automatically adjustable.The procedure is quasi-Newton type and converges super linear-ly. The present method also uses a novel trial function, which has correct electron-electron and electron-nucleus cusp condi-tious. The novel EFNQMC algorithm and the novel trial func-tion are employed to calculate the energies of 1 ^1A1 state of CH2, ^1Ag state of Cs and the ground-states of H2, LiH, Li2 and H2O.
In this paper we proposed a novel exact fixed-node quantum Monte Carlo (EFNQMC)algorithm,which is a self-optimizing and self-improving procedure,In contrast to the previous EFNQMC method,the trial function is optimized synchronistically in the diffusion procedure,but not before the beginning of EFNQMC computation.In order to optimize the trial function,the improved steepest descent technique is used,in which the step size is automatically adjustable.The procedure is quasi-Newton and converges super linearly.We also use a novel trial function,which has correct electron-electron and electron-nucleus cusp conditions.The novel EFNQMC algorithm and the novel trial function are employed to calculate the energies of 1^1A1 state of CH2,^1Ag state of C8 and the ground-states of H2,LiH,Li2,H2O,respectively.The test results show that both the novel algorithm and the trial function proposed in the present paper are very excellent.
We propose an algorithm for optimizing quantum Monte Carlo wave functions. An improved steepest-descent technique is used, with step size automatically adjustable to obtain a procedure that converges superlinearly. We also propose a novel trial function, which has both correct electron–electron cusp conditions and correct electron–nucleus cusp conditions. To test the optimization procedure and the optimized trial function, the ground states for CH4 and H2O molecules were investigated using variational Monte Carlo (VMC) and fixed-node quantum Monte Carlo (FNQMC) calculations. For CH4 and H2O, the VMC recovered 73.3% and 57.9% of the correlation energy, respectively, and the FNQMC recovered 99.3% and 92.8%, respectively. The optimization procedure is three to five times faster than conventional usual steepest-descent procedures. The trial functions optimized are more accurate than prior trial functions of similar complexity.
We develop a formalism and present an algorithm for optimization of the trial wave function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground-state probability density. We take advantage of a basic property of the walker configuration distribution generated in a DMC calculation, to (i) project out a multideterminant expansion of the fixed-node ground-state wave function and (ii) to define a cost function that relates the fixed-node ground-state and the noninteracting trial wave functions. We show that (a) locally smoothing out the kink of the fixed-node ground-state wave function at the node generates a new trial wave function with better nodal structure and (b) we argue that the noise in the fixed-node wave function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust toward the ones of the exact many-body ground state in a simulated annealing-like process. Based on these principles, we propose a method to improve both single determinant and multideterminant expansions of the trial wave function. The method can be generalized to other wave-function forms such as pfaffians. We test the method in a model system where benchmark configuration-interaction calculations can be performed and most components of the Hamiltonian are evaluated analytically. Comparing the DMC calculations with the exact solutions, we find that the trial wave function is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wave functions orthogonal to the exact ground state. Similarly, the DMC total energy and density converges to the exact solutions for the model. In the optimization process we find an optimal noninteracting nodal potential of density-functional-like form whose existence was predicted in a previous publication [Phys. Rev. B 77, 245110 (2008)]. Tests of the method are extended to a model system with a conventional Coulomb interaction where we show we can obtain the exact Kohn-Sham effective potential from the DMC data.
Abstract We compare the accuracy and precision of the wave function correction method to that of traditional diffusion quantum Monte Carlo (traditional DQMC) simulations. Direct calculation of corrections to trial wave functions reduces time step error for Be and Ne electronic ground state energies when compared to traditional DQMC results. The fixed‐node method is utilized for these fermionic systems, so error due to incorrect node locations is not addressed. This correction DQMC method achieves more accurate energies at larger time steps, promising decreased computational cost to reach a given accuracy. For an optimized Be trial wave function, the statistical uncertainty per unit of computational effort is also reduced relative to traditional DQMC. Correction DQMC utilizes walker feed integrals and growth factors, as reported previously. We illustrate the method in a simple harmonic oscillator example, and we report high accuracy energies for Be and Ne at several time steps.