Tunneling, multidimensional

Needless to say, tunneling is one of the most famous quantum mechanical effects. Theory of multidimensional tunneling, however, has not yet been completed. As is well known, in chemical dynamics there are the following three kinds of problems (1) energy splitting due to tunneling in symmetric double-well potential, (2) predissociation of metastable state through... 

The theory developed for tunneling splitting can be easily extended to the decay of the metastable state through multidimensional tunneling, namely, tunneling predissociation of polyatomic molecules. In the case of predissociation, however, the instanton trajectory cannot be fixed at both ends, but one end should be free (see Fig. 17). The boundary conditions are... 

The rate of hydrogen transfer can be calculated using the direct dynamics approach of Truhlar and co-workers which combines canonical variational transition state theory (CVT) [82, 83] with semi-classical multidimensional tunnelling corrections [84], The rate constant is calculated using [83] ... 

Allison TC, Trahlar DG (1998) Testing the accuracy of practical semiclassical methods variational transition state theory with optimized multidimensional tunnelling. In Thompson DL (ed) Modern Methods for Multidimensional Dynamics Computations in Chemistry. World Scientific, Singapore, p 618... 

Fernandez-Ramos A, Ellingson BA, Garrett BC, Trahlar DG (2007) Variational transition state theory with multidimensional tunneling. In Lipkowitz KB, Cundari TR, Boyd DB (eds) Reviews in Computational Chemistry, Vol 23. Wiley-VCH, New York, p 125... 

Antonio Fernandez-Ramos, Benjamin A. Ellingson, Bruce C. Garrett, and Donald G. Truhlar, Variational Transition State Theory with Multidimensional Tunneling. 

Before discussing tunneling in VTST where the discussion will focus on multidimensional tunneling, it is appropriate to consider the potential energy surface for a simple three center reaction with a linear transition state in more detail. The reaction considered is that of Equation 6.3. The collinear geometry considered here is shown in Fig. 6.1a it is in fact true that for many three center reactions the transition state can be shown to be linear. The considerations which follow apply to a onedimensional world where the three atoms (or rather the three nuclei) are fixed to a line. We now consider this one-dimensional world in more detail. The Born-Oppenheimer approximation applies as in Chapter 2 so that the electronic energy of... 

Table 6.2 Tests of Variational Transition State Theory by Comparing with Exact Quantum Calculations (Extracted from Allison, T. C. and Truhlar, D. G. Testing the accuracy of practical semiclassical methods variational transition state theory with optimized multidimensional tunneling, in Thompson, D. L., Ed. Modem methods for multidimensional dynamics computations in chemistry, World Scientific, Singapore 1998. pp 618-712. This reference quotes results on many more reactions and BO surfaces over broad temperature ranges.)The numbers in the table are ratios of the results of the approximate calculation to the quantum calculation, all at 300 K...

TST = conventional Transition State Theory, ICVT = Improved Canonical Variational Transition state theory, ICVT/SCT = ICVT/Small Curvature Tunneling, ICVT/p,OMT = ICVT/Microcanonical Optimized Multidimensional Tunneling. 

Truhlar, D. G. Variational transition state theory and multidimensional tunneling for simple and complex reactions in the gas phase, solids, liquids, and enzymes, in Kohen, A. and Limbach, H. H., Eds. Isotope Effects in Chemistry and Biology. CRC Press/Taylor Francis, Boca Raton, FL (2006), pp. 579-619. 

This chapter is devoted to tunneling effects observed in vibration-rotation spectra of isolated molecules and dimers. The relative simplicity of these systems permits one to treat them in terms of multidimensional PES s and even to construct these PES s by using the spectroscopic data. Modern experimental techniques permit the study of these simple systems at superlow temperatures where tunneling prevails over thermal activation. The presence of large-amplitude anharmonic motions in these systems, associated with weak (e.g., van der Waals) forces, requires the full power of quantitative multidimensional tunneling theory. 

The rate factors rr interrelate just two wells, the well 1 and the well r. For just one barrier separating the two wells, the classical path under the barrier does not split into branches. The classical path in the restricted area is approximately separable (see Section 5 later). Therefore, in JT systems, after the weight factors mr(r) are established, the multidimensional tunneling problem reduces to a one-dimensional consideration. 

In ESP theory [30-32] we treat the system by the same methods that we would use in the gas phase except that in the nontunneling part of the calculation we replace V(R) by TT(R), and in the tunneling part we approximate V(R) by TT(R) or a function of TT(R). Next we review what that entails. In particular we will review the application of variational transition state theory [21-25] with optimized multidimensional tunneling [33,34] to liquid-phase reactions for the case [31,32] in which TT(R) is calculated from V(R) by... 

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