Quantum Monte Carlo calculation of the singlet–triplet splitting in methylene

Abstract

The fixed-node quantum Monte Carlo (QMC) method is used to calculate the total energy of CH 2 in the ~1 and 1A1 states. For both states. the best QMC variationally bounded energies lie more than 15 kcal/mole (0.024 h) below the best previous variational calculations. Subtracting these energies to obtain the singlet-triplet splitting yields Ta = 9.4 ± 2.2 kcal/mole. Adjusting for zero-point energies and relativistic effects. we obtain To =8.9±2.2 kcal/mole. This result is in excellent agreement with the recent direct measurements of McKellar et. ai.of To =9.05±0.06 kcal/mole. and of Leopold et. ai. of "'9 kcal/mole. as well as with recent theoretical investigations which indicate an energy gap of 9-11 kCal/mole. We summarize the QMC method. discuss a possible scheme for iteratively correcting the procedure. and note that the present results were obtained using only single determinant functions for both states. in contrast to conventional ab initio approaches which must use at'least two configurations to properly describe the singlet state. '• A preliminary account of this work was presented at the 17th Annual Sanibel SympOSium, March 1983.

Quantum chemistry by quantum monte carlo: Beyond ground‐state energy calculations

“…Work thus far with QMC has been limited to ground-state potential-energy surfaces and lowest energy states of a particular symmetry [1][2][3][4]. This restriction comes from an essential feature of the mapping of the Schrooinger equation into its diffusion, analog--that time in these two equations differs by a factor of i .…”

“…Using QMC, workers have studied molecular correlation energies [1,2] as well as critical points on potentiai-energy surfaces [3]. A calculation of the singlet-triplet splitting in methylene has also been carried out [4]. The two states studied, however, are both lowest-energy states of their respective symmetries.…”

“…In the past few years, quantum mechanical Monte Carlo {QMC) methods have begun to make a contribution to quantum chemistry [1][2][3][4]. The Monte Carlo technique is complementary to traditional ab initio approaches for obtaining molecular properties.…”

Molecular physics and chemistry applications of quantum Monte Carlo

“…The QMC method of obtaining energies of atomic and molecular systems has been descrihed in detail elsewhere (1)(2)(3)(4)(5)(6)(7)(8) .. The key point to note here is that a simubt.ion is performed in which an ensemble of random walks (the coordinates of which, at any given time, represent a configuration of the electrons) evolves to an equilibrium distribution.…”

“…In the past few years, quantum mechanical Monte Carlo (QMC) methods have • begun to be applied in the domain of atomic and molecular physics (1)(2)(3)(4)(5)(6). Long in the realm of condensed-matter physics, and more recently nuclear and particle physics, Monte Carlo methods play an indispensible role in treating multi-dimensional, and hence many-body problems.…”