Range of Quantum Mechanics Methods

The quantum mechanics methods in HyperChem differ in how they approximate the Schrodinger equation and how they compute potential energy. The ab initio method expands molecular orbitals into a linear combination of atomic orbitals (LCAO) and does not introduce any further approximation. 

The Extended Hiickel method, for example, does not explicitly consider the effects of electron-electron repulsions but incorporates repulsions into a single-electron potential. This simplifies the solution of the Schrodinger equation and allows HyperChem to compute the potential energy as the sum of the energies for each electron. 

---

The finite field procedure is the most often used procedure because of two main advantages (1) it is very easy to implement, and (2) it can be applied to a wide range of quantum mechanical methods. To calculate the energy in the presence of a uniform electric field of strength F, an F-r term needs to be added to the one-electron Hamiltonian. This interaction term can be constructed from just the dipole moment integrals over the basis set. Any ab initio or semiem-pirical method can then be used to solve the problem, with or without electron correlation. It is the ability to obtain properties from highly correlated methods that makes finite field calculations usually the most accurate available. 

Quantum mechanical methods can now be applied to systems with up to 1000 atoms 87 this capacity is not only from advances in computer technology but also from improvements in algorithms. Recent developments in reactive classical force fields promise to allow the study of significantly larger systems.88 Many approximations can also be made to yield a variety of methods, each of which can address a range of questions based on the inherent accuracy of the method chosen. We now discuss a range of quantum mechanical-based methods that one can use to answer specific questions regarding shock-induced detonation conditions. 

Our first example that attempts to imravel this complexity is entitled Gas-Phase Thermochemistry and Mechanism of Organometallic Tin Oxide CVD Precursors . The authors, M. Allendorf and A.M.B. van Mol, describe the development of quantum chemistry methods that can predict heats of formation for a broad range of tin compounds in the gas phase, which need to be considered when Sn(CH3)4 or (CH3)2SnCl2 and other tin alkyls are used as precursors together with oxygen and water for tin oxide deposition. 

Monte Carlo methods employ random numbers to solve problems. The range of problems that may be treated by Monte Carlo is large. These include simulation of physical (and other) processes, integration of multi-dimensional integrals, and applications in statistical mechanics see, for example [1, 2], The treatment of problems arising in the field of quantum mechanics using Monte Carlo is generally referred to as quantum Monte Carlo (QMC) see, for example [3-5]. 

An alternative to the molecular mechanical approach is the quantum mechanics (QM) framework. Much of work has been devoted in the past decades to establish and improve QM methodologies ranging from simple semiempirical methods to high-level correlated ab initio methods [20,21,29], The substantial advantage of quantum mechanical calculations is the inclusion of all n-body effects, including charge transfer and polarisation. Furthermore, bonds are automatically formed and broken as necessary along the simulation. 

---