The diffusion Monte Carlo (DMC) method is a widely used algorithm for computing both ground and excited states of many-particle systems; for states without nodes the algorithm is numerically exact. In the presence of nodes approximations must be introduced, for example, the fixed-node approximation. Recently we have developed a genetic algorithm (GA) based approach which allows the computation of nodal surfaces on-the-fly [Ramilowski and Farrelly, Phys. Chem. Chem. Phys., 2010, 12, 12450]. Here GA-DMC is applied to the computation of rovibrational states of CO–4HeN complexes with N ≤ 10. These complexes have been the subject of recent high resolution microwave and millimeter-wave studies which traced the onset of microscopic superfluidity in a doped 4He droplet, one atom at a time, up to N = 10 [Surin et al., Phys. Rev. Lett., 2008, 101, 233401; Raston et al., Phys. Chem. Chem. Phys., 2010, 12, 8260]. The frequencies of the a-type (microwave) series, which correlate with end-over-end rotation in the CO–4He dimer, decrease from N = 1 to 3 and then smoothly increase. This signifies the transition from a molecular complex to a quantum solvated system. The frequencies of the b-type (millimeter-wave) series, which evolves from free rotation of the rigid CO molecule, initially increase from N = 0 to N ∼ 6 before starting to decrease with increasing N. An interesting feature of the b-type series, originally observed in the high resolution infra-red (IR) experiments of Tang and McKellar [J. Chem. Phys., 2003, 119, 754] is that, for N = 7, two lines are observed. The GA-DMC algorithm is found to be in good agreement with experimental results and possibly detects the small (∼0.7 cm−1) splitting in the b-series line at N = 7. Advantages and disadvantages of GA-DMC are discussed.

The fixed-node diffusion Monte Carlo (DMC) algorithm is a powerful way of computing excited state energies in a remarkably diverse number of contexts in quantum chemistry and physics. The main difficulty in implementing the procedure lies in obtaining a good estimate of the nodal surface of the excited state in question. Although the nodal surface can sometimes be obtained from symmetry or by making approximations this is not always the case. In any event, nodal surfaces are usually obtained in an ad hoc way. In fact, the search for nodal surfaces can be formulated as an optimization problem within the DMC procedure itself. Here we investigate the use of a genetic algorithm to systematically and automatically compute nodal surfaces. Application is made to the computation of excited states of the HCN–4He complex and to the computation of tunneling splittings in the hydrogen bonded HCl–HCl complex.

The diffusion Monte Carlo (DMC) method is a widely used algorithm for computing both ground and excited states of many-particle systems; for states without nodes the algorithm is numerically exact. In the presence of nodes approximations must be introduced, for example, the fixed-node approximation. Recently we have developed a genetic algorithm (GA) based approach which allows the computation of nodal surfaces on-the-fly [Ramilowski and Farrelly, Phys. Chem. Chem. Phys., 2010, 12, 12450]. Here GA-DMC is applied to the computation of rovibrational states of CO–4HeN complexes with N ≤ 10. These complexes have been the subject of recent high resolution microwave and millimeter-wave studies which traced the onset of microscopic superfluidity in a doped 4He droplet, one atom at a time, up to N = 10 [Surin et al., Phys. Rev. Lett., 2008, 101, 233401; Raston et al., Phys. Chem. Chem. Phys., 2010, 12, 8260]. The frequencies of the a-type (microwave) series, which correlate with end-over-end rotation in the CO–4He dimer, decrease from N = 1 to 3 and then smoothly increase. This signifies the transition from a molecular complex to a quantum solvated system. The frequencies of the b-type (millimeter-wave) series, which evolves from free rotation of the rigid CO molecule, initially increase from N = 0 to N ∼ 6 before starting to decrease with increasing N. An interesting feature of the b-type series, originally observed in the high resolution infra-red (IR) experiments of Tang and McKellar [J. Chem. Phys., 2003, 119, 754] is that, for N = 7, two lines are observed. The GA-DMC algorithm is found to be in good agreement with experimental results and possibly detects the small (∼0.7 cm−1) splitting in the b-series line at N = 7. Advantages and disadvantages of GA-DMC are discussed.

The fixed-node diffusion Monte Carlo (DMC) algorithm is a powerful way of computing excited state energies in a remarkably diverse number of contexts in quantum chemistry and physics. The main difficulty in implementing the procedure lies in obtaining a good estimate of the nodal surface of the excited state in question. Although the nodal surface can sometimes be obtained from symmetry or by making approximations this is not always the case. In any event, nodal surfaces are usually obtained in an ad hoc way. In fact, the search for nodal surfaces can be formulated as an optimization problem within the DMC procedure itself. Here we investigate the use of a genetic algorithm to systematically and automatically compute nodal surfaces. Application is made to the computation of excited states of the HCN–4He complex and to the computation of tunneling splittings in the hydrogen bonded HCl–HCl complex.