Jastrow-Slater wave function

The QMC method is thought to be promising for the treatment of dynamical and static eiectron correiation effects with the compact functional form of wave functions. One standard form of the wave function is the Jastrow-Slater wave function. The Jastrow-Slater wave function is defined by... 

Let us consider the cusp correction scheme for the Jastrow-Slater wave function. This type of wave function allows us to use a MO correction scheme. The s type component of the Is MO inside a given radius is replaced with the correction function,... 

Wave function Single or Multi-determinant Jastrow-Slater wave function and their linear combinations are available. Jastrow factors of Schmidt-Moskowitz type are available. 

The QMC calculations are done with Jastrow-Slater wave functions using a single determinant (JSD), or a state-average (SA) or state-specific (SS) complete-active-space multideterminant expansion (JCAS). The lists of parameters optimized by energy minimization in VMC are indicated within square brackets Jastrow (J), CSF coefficients (c), and orbitals (o). For comparison, the DMC results of Ref. [13] obtained with state-average CAS(6,5) wave functions and a Gaussian basis set are also shown... 

If the r-space wave function is a linear combination of Slater determinants constructed from a set of spin-orbitals 0/, then its p-space counterpart is the same linear combination of Slater determinants constructed from the spin-momentals j obtained as Fourier transforms, Eq. (9), of the spin-orbitals. The overwhelming majority of contemporary r-space wave functions can be expressed as a linear combination of Slater determinants, and in these cases only three-dimensional Eourier transforms, Eq. (9), of the spin-orbitals are necessary to obtain the corresponding A -electron wave function in p space. Use of the full Eq. (5) becomes necessary only for wave functions, such as Hylleraas- or Jastrow-type wave functions, that are not built from a one-electron basis set. Examples of transformations to momentum space of such wave functions for He and H, can be found elsewhere [20-22]. 

Fig. 2. Ne = Np = 16, Vs = 1.31. Dependence of total energy, variance and energy difference for a pair of proton configurations S, S ) on the RQMC projection time. The study is performed for Te = 0.02Dotted lines represent the variational estimates with their error bars. In panel b) and c) the lines are exponential fits to data and in panel d) the continnons line is a linear fit in the region < 0.005. Black circles (3BF-A) are resnlts obtained with the analitical three-body and backflow trial wave functions discnssed earlier, the red triangle is a variational resnlt with a Slater-Jastrow trial function with simple plane wave orbitals and the blue squares are results from a trial function with LDA orbitals and an optmized two-body Jastrow...

Typically QMC calculations are carried out in the FNA using a Slater-Jastrow wave function which is written as a product of an antisymmetric function, and an exponentiated Jastrow function, F Wsj =. The antisymmetric function... 

Although the product form of a SJ wave function has typically been used with a single global Jastrow factor, recently [111] the benefit of separate Jastrow terms for each molecular orbital of the antisymmetric function was demonstrated. The latter approach improves treatment of local electron correlation by facilitating adjustment to the local molecular environment. Also, the nodal structure of the trial wave function can better reflect the parameters of multiple Jastrow functions than the single global Slater-Jastrow wave function. This modification notably improves the nodal structure of trial wave functions and FN-DMC energies. 

The nodal surface is independent of the Jastrow correlation factor which therefore determines only the efficiency of the calculation, not the accuracy. High accuracy is already obtained for many systems with one Slater determinant, often built from Kohn-Sham orbitals. For many years, multideterminant wave functions have been employed which are necessary for high accuracy in systems with non-dynamical correlation. Recent examples are papers by Caffarel and coworkers where large complete active spaces have been used." " These authors emphasize the importance of systematic cancellation of the node location error which can be achieved with CASSCF-type wave functions. While full CASSCF wave... 

One branch of quantum Monte Carlo research aims at providing a quantitative first-principle description of atoms, molecules, and solids beyond the accuracy of density functional theory." " If the basic physics and chemistry of the material in question is well understood at least qualitatively, as is the case for many bulk semiconductors, for example, good trial wave functions such as the Jastrow-Slater type can be constructed. These functions can... 

The Cu (001) surface is exposed. This truncation of the bulk lattice, as well as adsorption, leads to drastic changes in electronic correlation. They are not adequately taken into account by density-functional theory (DFT). A method is required that gives almost all the electronic correlation. The ideal choice is the quantum Monte Carlo (QMC) approach. In variational quantum Monte Carlo (VMC) correlation is taken into account by using a trial many-electron wave function that is an explicit function of inter-particle distances. Free parameters in the trial wave function are optimised by minimising the energy expectation value in accordanee with the variational principle. The trial wave functions that used in this work are of Slater-Jastrow form, consisting of Slater determinants of orbitals taken from Hartree-Fock or DFT codes, multiplied by a so-called Jastrow factor that includes electron pair and three-body (two-electron and nucleus) terms. 

In these calculations, our trial wave function will be of Slater-Jastrow form. The Slater determinants will contain orbitals taken from density functional theory (DFT) calculations. The Jastrow factor is an explicit function of electron-electron distance, enabling a highly accurate and compact description of electron correlation. The Jastrow factor consists of polynomial expansions in electron-electron separation, electron-nucleus separation, in which the polynomial expansion coefficients are optimisable parameters [21]. These parameters were determined by minimising the VMC energy. 

Table 19.1 Ground-state energy Eq, first excited-state energy E, and vertical excitation energy E — Eo for the singlet n —f n transition in the acrolein molecule at the experimental geometry calculated in DMC with different time steps % using the VBl Slater basis set and a state-specific Jastrow-Slater CAS(6,5) wave function with Jastrow, CSF and orbital parameters optimized by energy minimization in VMC...

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