An ab initio study of TiC with the diffusion quantum Monte Carlo method

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Abstract

The discovery of metallo-carbohedrenes (Met-Cars) such as the titanium carbon cluster Ti8C12 by Guo et al. [Science 255 (192) 1411] gave rise to many questions about its structure and bonding. In a first step toward the full cluster, the Ti atom and the TiC dimer are investigated using the diffusion quantum Monte Carlo (DQMC) method. The dissociation energy and the energy splittings of low-lying states are calculated.

Introduction

Since the titanium carbon cluster Ti8C12 was found by Guo, Kerns, and Castleman [1], many experimental and theoretical studies of this and similar compounds have followed 2, 3. These clusters which have become known as metallo-carbohedrenes, or `Met-Cars', have an unusual stability. The two proposed structures for the Ti8C12 cluster are a cage-like pentagonal dodecahedron 1, 4 with Th symmetry and a tetracapped tetrahedral cage structure with Td symmetry [2].

While electron structure calculations on Met-Cars are possible with DFT methods, the number of electrons is currently too large for high-level ab initio methods such as coupled cluster with perturbative triple excitation CCSD(T), multireference configuration interaction MRCI, or fixed-node diffusion quantum Monte Carlo FN-DQMC. The diatomic TiC is the simplest compound for studying bonding in Met-Cars and comparing methods as an initial step toward reliable theoretical investigation of Ti8C12 and similar clusters.

The diatomic TiC has recently been investigated with CCSD(T) and MRCI by Hack et al. [5]. Since electronic structure calculations of transition metal compounds are much less standard than such calculations for first and second row elements, an assessment of the accuracy of the different ab initio methods is necessary. Due to the lack of experimental data for TiC itself, the comparison of calculated and experimental excitation energies for the Ti atom is very valuable.

In this study, we apply the DQMC method to the Ti atom and the TiC dimer. The DQMC method has recently demonstrated its ability to calculate electron correlation energies with an accuracy comparable to the CCSD(T) method with large basis sets [6].

Section snippets

Method

The DQMC method has been the subject of several recent review articles 7, 8, 9. It is based on the application of the imaginary time propagator eτH to an arbitrary initial wavefunction. The propagation is performed stochastically leading to a distribution proportional to the ground state wavefunction after sufficiently long propagation time. The energy is obtained as a statistical expectation value. With importance sampling, the efficiency can be greatly improved. It is realized here with a

Results

The experimental ground state is 3d24s23F and the 3d34s15F state is known to be only 0.69 eV, after subtracting relativistic contributions, above the ground state 20, 21. The FN-DQMC result for the 5F3F splitting of the Ti atom is in good agreement with the non-relativistic experimental value as shown in Table 1. The energy difference can be compared to results from other ab initio methods 5, 20, 21. Of the DFT methods, only the hybrid B3LYP gives the correct order of the states. The ROHF

Acknowledgements

The authors wish to thank J.B. Anderson for his support of this work. Financial Support from NSF (Grant No. CHE-9734808 to J.B.A.) and Deutsche Forschungsgemeinschaft (A.L.) is gratefully acknowledged.

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