We report fixed-node diffusion Monte Carlo (FN-DMC) calculations of the singlet n-->pi( *) (CO) vertical transition of acrolein. The impact of the fixed-node approximation on the excitation energy is investigated. To do that, trial wave functions corresponding to various nodal patterns are used. They are constructed by using either a minimal complete-active-space self-consistent field (CASSCF) calculation involving an oxygen lone pair n and the pi( *) (CO) molecular orbitals or a more complete set involving all the molecular orbitals expected to play a significant role in the excitation process. Calculations of both states have been performed with molecular orbitals optimized separately for each state via standard "state specific" CASSCF calculations or by using a common set of optimized orbitals ["state averaged" CASSCF calculations] whose effect is to introduce some important correlation between the nodal patterns of the two electronic states. To investigate the role of the basis set three different basis of increasing size have been employed. The comparative study based on the use of all possible combinations of basis sets, active spaces, and type of optimized molecular orbitals shows that the nodal error on the difference of energies is small when chemically relevant active space and state-averaged-type CASSCF wave functions are used, although the fixed-node error on the individual total energies involved can vary substantially. This remarkable result obtained for the acrolein suggests that FN-DMC calculations based on a simple strategy (use of standard ab initio wave functions and no Monte Carlo optimization of molecular orbital parameters) could be a working computational tool for computing electronic transition energies for more general systems.

A new type of electronic trial wavefunction suitable for quantum Monte Carlo calculations of molecular systems is presented. In contrast with the standard Jastrow-Slater form built with a unique global Jastrow term, it is proposed to introduce individual Jastrow factors attached to molecular orbitals. Such a form is expected to be more physical since it allows to describe differently the local electronic correlations associated with various molecular environments (1s-core orbitals, 3d-magnetic orbitals, localized two-center sigma-orbitals, delocalized pi-orbitals, atomic lone pairs, etc.). In contrast with the standard form, introducing different Jastrow terms allows us to change the nodal structure of the wavefunction, a point which is important in the context of building better nodes for more accurate fixed-node diffusion Monte Carlo (FN-DMC) calculations. Another important aspect resulting from the use of local Jastrow terms is the possibility of defining and preoptimizing local and transferable correlated units for building complex trial wavefunctions from simple parts. The practical aspects associated with the computation of the intricate derivatives of the multi-Jastrow trial function are presented in detail. Some first illustrative applications for atoms of increasing size (O, S, and Cu) and for the potential energy curve and spectroscopic constants of the FH molecule are presented. In the case of the copper atom, the use of the multi-Jastrow form at the variational Monte Carlo level has allowed us to improve significantly the value of the total ground-state energy (about 75% of the correlation energy with only one determinant and three atomic orbital Jastrow factors). In the case of the FH molecule (fluorine hydride), it has been found that the multi-Jastrow nodes lead to an almost exact FN-DMC value of the dissociation energy [D(0)=-140.7(4) kcal/mol instead of the estimated nonrelativistic Born-Oppenheimer exact value of -141.1], which is not the case with standard nodes, D(0)=-138.3(4) kcal/mol.