No abstract

No abstract

We present a procedure for obtaining optimized trial wave functions for use in quantum Monte Carlo calculations that have both smaller statistical errors and improved expectation values, compared to commonly used functions. Results are presented for several two-electron atoms and ions (including some excited states) and for the Be atom.PACS numbers: 31.20.Di, 71.10,+x Monte Carlo (MC) calculations have been shown to provide energies of small atoms and molecules that are comparable to the best configuration-interaction (CI) calculations. 1 ' 2 The most commonly used trial or guiding wave functions that are used in the calculation consist of a Hartree-Fock determinant multiplied by a Jastrow correlation factor (HF-J) or a multiconfiguration self-consistent-field function (consisting of a small linear combination of determinants) multiplied by a Jastrow function (MCSCF-J). Using these wave functions, variational MC calculations typically recover about 15%-80% of the correlation energy and diffusion MC and Green's-function MC calculations recover about [80 -100(±2)]% of the correlation energy. 3 In this Letter we present a procedure for the determination of wave functions that even in a variational MC calculation recover more than 99.99% of the correlation energy for the ground and excited states of two-electron ions, and 99% of the correlation energy for the Be atom.Past attempts at finding improved trial wave functions have mostly consisted of adjustment of the parameters of the wave function to minimize the expectation value of the energy E. With this method it has been possible to optimize__at most a few parameters since a single calculation of E takes a significant amount of computer time, and this must be repeated several times before an optimal set of parameters is found. Instead, we have developed a procedure wherein we minimize the variance of the local energy. 4 More specifically we find the parameters in y/ that minimize Z/.*iwG)where w(i) = \ y/(i)/y/o(i) | 2 , E g is a guess for the energy of the state we are interested in, and the sum is over a fixed set of configurations of the electrons samples from | yro I 2 . yo is taken to be the best wave function available before we start the optimization procedure, usually HF-J. The chief advantage of this procedure is that 500 to 2000 configurations are found to be sufficient-a remarkably small number considering that some of the functional forms tried had as many as 100 free parameters. There are two reasons for this. First, the configurations over which the optimization is performed are fixed, and so we are using correlated sampling to arrive at an optimal set of parameters. Hence the difference in the Copt's for two sets of values of the parameters being optimized, is much more accurately determined than the values of the obpt's themselves. Second, we are performing a fit, not an integral. So, if the true wave function were representable by an nparameter trial wave function, then only n configurations would be necessary to determine the n parameters exactly....

No abstract

 Users may download and print one copy of any publication from the public portal for the purpose of private study or research.  You may not further distribute the material or use it for any profit-making activity or commercial gain  You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.