frequencies and rotational constants, is specified in an array. A property type that represents a quantity that is a matrix such as a Hessian, is specified to be matrix. For property types that have associated units, (e.g., vibrational frequencies, rotational constants, and zero point energy (ZPE)) the units are specified as an attribute of array or scalar. Unitless quantities such as spin multiplicity, symmetry number, or frequency scale factor, are specified to be scalar. Table 1 gives the values of dictRef (i.e., property attributes) currently recognized by MESMER, specifies whether they are scalar or array, and specifies the units presently available in MESMER. Another property that requires further information is the me:hessian property. This property allows a Hessian to be read which can be analysed to determine the vibrational frequencies instead of entering them using me:vibFreqs or when the elimination of frequencies due to internal rotational is required (see section 11.2.3). A typical specification might be: <matrix matrixType="squareSymmetricLT" rows="42" units="kJ/mol/Ang2"> The keyword matrixType specifies the matric type and how it is stored. In the case of a Hessian it must be symmetric, but can be specified by either by the triangular elements (squareSymmetricLT) or the upper triangular elements (squareSymmetricUT), in both cases including the diagonal. The me:ZPE property, and the related properties, me:Hf0, me:Hf298, specify the location of potential energy surface features. Discussion of these important keywords is deferred to section 7.3.1.1. dictRef scalar or array Available input units me:ZPE Scalar kJ/mol or kJ per mol cm-1 or wavenumber kcal/mol or kcal per mol Hartree or au me:Hf0 Scalar as above Scalar as above Me:Hf298 Scalar as above me:rotConsts Array cm-1 or amuA^2 me:symmetryNumber Scalar unitless, no units specification me:frequenciesScaleFactor Scalar unitless, no units specification me:vibFreqs Array cm-1 me:MW Scalar Amu
me:HfAT0, me:Hf298, in which case the reference energy is defined. The choice of arbitrary vs defined reference state is encapsulated by the notion of an energy convention. The location of PES features must be entered with either one or other of these conventions for the whole input file, otherwise the different reference states will lead to inconsistencies, so MESMER checks if the same convention is being used and will stop if a mixed specification is detected. Figure 3: Schematic PES illustrating the definitions of ΔH used in MESMER reactionList reactionList is composed of each individual reaction that may occur in a ME system. Effectively, the reactionList specifies which molecules are connected via which transition state. A reaction may be one of a number of types listed in Table3. The reaction type assigned for a given reaction is determined by the number of species and their species types (more detail below) involved in the reaction, and these are also listed in Table 3. If MESMER cannot assign a reaction to one these types it will stop. Each reaction may include the following: An id attribute, is used to identify the reaction; An active attribute. If this is the reaction is ignored by MESMER. This feature makes it possible to do calculations on only part of a complex reaction system. A molecule can also have this attribute, but this does not affect the calculation. Inactive reactions and molecules are shown either greyed or omitted (at the users choice) when the XML file is viewed in Firefox. Reactant 1 Reactant 2 Product 1 Product 2 Reaction type modelled Absent modelled Absent Isomerization deficientReactant excessReactant modelled Absent Association
<me:molecule ref="cyclopropene" me:population="1.0" /> </me:InitialPopulation> me:modelParameters The tree structure for me:modelParameters includes the following elements: me:grainSize includes a specification of the grain size to be used in partitioning the system phase space. It has an associated value and associated units. The units available are identical to those given in Table 2 for specification of ZPE. For a convergent solution of the ME utilizing the exponential down model, the grain size should be smaller than the, the average energy transferred in a deactivating collision, values of any of the modelled molecules. me:energyAboveTheTopHill specifies the energy range to be spanned by the grains, where the units are kT. The value of this parameter sets up a model wherein the energy grains span a region possessing x kT of energy in excess of the highest energy stationary point. In general, the maximum grain energy in the ME should be at least 20 kT above the highest energy molecular configuration, including reactants. However, if the maximum grain energy is too large, then numerical errors may result given that the probability for activating collisions is so small as to exceed machine precision. The me:energyAboveTheTopHill value can be set automatically using the me:automaticallySetMaxEne keyword which is described in section 7.3.5. me:maxTemperature applies if more than one me:PTpair has been specified in me:conditions. If me:maxTemperature is not specified, then each ME run at a particular me:PTpair will use the me:energyAboveTheTopHill value to determine the maximum grain energy – i.e., the maximum grain energy will be different at different temperatures. Using me:maxTemperature makes the maximum grain energy at each me:PTpair identical, choosing the maximum grain energy to be x kT above the highest energy stationary point, where T is equal to the value set in me:maxTemperature regardless of the temperature specified in the me:PTpair.
(13.29) it follows that: (13.30) Further progress can be made by applying the convolution theorem: (13.31) where Q and q, and G and g are transform pairs, and denotes convolution. Solution of 13.30 is possible by recognizing that (13.32) And (13.33) where if E < Ea and is unity otherwise, is the Heavyside step function. Convolving the ILTs in Eq. 13.32 and 13.33 gives: (13.34) The units should be input follows: in states per cm-1 in molecules cm-3 s-1 where kB is in units of cm-1 K-1, and T0 in units of K. The association ILT A similar expression can be obtained for the case where the Arrhenius expression is for the high pressure association rate coefficient. Under high pressure conditions the forward and the reverse rate coefficients are related by the equilibrium constant as indicated by Eq. 13.13: (13.35) If has a modified Arrhenius form then the equivalent expression to Eq. 13.30 is,