The electronic structure Schrödinger equation is solved for the van der Waals complexes spin-polarized H2 and H3, and the closed-shell systems He2 and He3 by Monte Carlo methods. Two types of calculations are performed, variational Monte Carlo, which gives an upper bound to the eigenvalue of the Schrödinger equation, and Green's function Monte Carlo, which can solve the Schrödinger equation exactly within statistical sampling errors. The simulations are carried out on an ETA-10 supercom puter, and already existing computer codes were exten sively modified to ensure highly efficient coding. A major component of the computations was the develop ment of highly optimized many-electron wave functions. The results from the variational Monte Carlo simulations are reported for both the two- and three-body interac tion energies.
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References
1.
Anderson, J.B.1975. A random-walk simulation of the Schrödinger equation: H3+. J. Chem. Phys.63(4):1499-1503 .
2.
Aziz, R.A., McCourt, F.R.W., and Wong, C.C.K.1987. A new determination of the ground state interatomic potential for He2. Molecular Phys.61(6): 1487-1511.
3.
Aziz, R.A., Nain, V.P.S., Carley, J.S., Taylor, W.L., and McConville, G.T.1979. An accurate intermolecular potential for helium. J. Chem. Phys.70(9):4330-4342.
4.
Born, M., and Oppenheimer, J.R.1927. Zur Quantentheorie der Molekeln . Ann. Physik84(20):457-484.
5.
Bulski, M., and Chalasiński, G.1987. On the nonadditivity of the second-order exchange-dispersion energy in the interaction of three helium atoms. J. Chem. Phys.86(2):937-946.
6.
Ceperley, D.M., Chester, G.V., and Kalos, M.H.1977. Monte Carlo simulation of a many-fermion study . Phys. Rev. B 16(7):3081-3099.
7.
Ceperley, D.M., and Kalos, M.H.1979. Quantum many-body problems. In Monte Carlo methods in statistical pliysics, edited by K. Binder.New York: Springer-Verlag , pp. 145-194.
8.
Ceperley, D.M., and Partridge, H.1986. The He2 potential at small distances . J. Chem. Phys.84(2):820-821.
9.
Chalasiński, G., and Gutowski, M.J.1988. Interactions between small systems. Models for studying the nature of intermolecular forces and challenging problems for ab initio calculations. Chem. Rev.88:943-962.
10.
Frye, D., Lie, G.C., and Clementi, E.1989. Gaussian functions in Hylleraas-configuration interaction calculations. II. Potential curves for the b 3Σu+ and the e3Σu+ states of hydrogen. J. Chem. Phys.91(4):2366-2372 .
11.
Kalos, M.H.1970. Energy of a boson fluid with Lennard-Jones potentials . Phys. Rev. A 2(1):250-255.
12.
Kalos, M.H., Lee. M.A., Whitlock, P.A., and Chester, G.V.1981. Modern potentials and the properties of condensed He. Phys. Rev. B 24(1):114-130.
13.
Kolos, W., and Wolniewicz, L.1965. Potential energy curves for the X1Σg+, b3Σu+ and C1IIu states of the hydrogen molecule. J. Chem. Phys.43:2429.
14.
Kolos, W., and Wolniewicz, L.1974. Variational calculation of the long-range interaction between two ground-state hydrogen atoms. Chem. Phys. Lett.24(4):457-460.
15.
Lengsfield, B.H. Iii , McLean, A.D., Yoshimine, M., and Liu, B.1983. The binding energy of the ground state of Be2. J. chem. Phys.79(4):1891-1895.
16.
Lester, W.A., and Hammond, B.L.1990. Quantum Monte Carlo for the electronic structure of atoms and molecules. Ann. Rev. Phys. Chem.41 (1):283-311.
17.
Liu, B., and McLean, A.D.1980. Ab initio potential curve for Be2(1Σ g+) from the interacting correlated fragments method. J. Chem. Phys.72(1):3418-3419.
18.
Liu, B., and McLean, A.D.1989. Interacting correlated fragments model for weak interactions, basis set superposition error, and the helium dimer potential . J. Chem. Phys.91(4):2348-2359.
19.
Lowther, R.E., and Coldwell, R.L.1980. Monte Carlo calculation of the Born-Oppenheimer potential between two helium atoms. Phys. Rev. A 22(1):14-21.
20.
Margenau, H.1931. The role of quadrupole forces in van der Waals attractions . Phys. Rev.38:747.
21.
Meath, W.J., and Aziz, R.A.1984. On the importance and problems in the construction of many-body potentials. Molecular Phys.52(1):225-243.
22.
Mentch, F., and Anderson, J.B.1984. Quantum chemistry by random walk: linear H 3. J. Chem. Phys.80(6):2675-2680.
23.
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E.1953. Equations of state calculations by fast computing machines . J. Chem. Phys.21:1087.
24.
Mohan, V., and Anderson, J.B.1990. Quantum chemistry by random walk: energies of helium dimers and trimers. In Quantum simulation of condensed matter phenomena , edited by J. D. Doll and J. E. Gubernatis.Singapore : World Scientific Publications, pp. 243-249.
25.
Moskowitz, J.W., and Kalos, M.H.1981. A new look at correlations in atomic and molecular systems. I. Application of fermion Monte Carlo variational method. Interrcat. J. Quant. Chem.20:1107-1119.
26.
Nelder, J.A., and Mead, R.1965. Comput. J.7:308.
27.
Rybak, S., Szalewicz, K., Jeziorski, B., and Jaszuński, M.1987. Intraatomic correlation effects for the He-He dispersion and exchange-dispersion energies using explicitly correlated Gaussian geminals. J. Chem. Phys.86(10):5652-5659.
28.
Schmidt, K.E.1987. Variational and Green's function Monte Carlo of few-body systems. Lecture Notes in Phys 273:363-407.
29.
Schmidt, K.E., and Kalos, M.H.1984. Few- and many-fermion problems. In Applications of Monte Carlo method in statistical physics, edited by K. Binder. Vol. 36, Topics in. current physics. New York : Springer-Verlag, pp. 125-143.
30.
Schmidt, K.E., and Moskowitz, J.W.1986. Monte Carlo calculations of atoms and molecules . J. Statist. Phys.43(5/6):1027-1041.
31.
Schmidt, K.E., and Moskowitz, J.W.1990. Correlated Monte Carlo wave functions for the atoms He through Ne. J. Chem. Phys.93:4172.
32.
Schwartz, C.1962. Ground state of the helium atom. Phys. Rev.128:1146.
33.
Slater, J.C., and Kirkwood, J.G.1931. The van der Waals forces in gases. Phys. Rev.37(6):682-697.
34.
Vos, R.J., van Lenthe, J.H., and van Duijneveldt, F.B.1990. Convergence to the configuration-set limit in multireference configuration-interaction calculations on the He dimer . J. Chem. Phys.93(1):643-651.
35.
Wells, B.H., and Wilson, S.1985. van der Waals interaction potentials: many-body effects . Molecular Phys.55(1):199-210.
