Butane molecular mechanics calculation

The relationships of the components used to calculate strain energy from steric energy may be made clearer by considering an example. A final portion of the output of the molecular mechanics calculation for the anti conformation of butane is shown here. 

As indicated, the heat of formation (HFO) is taken as the sum of three terms. The first is the steric energy (E). The second is the bond enthalpy (BE), which is calculated from normal bond increments. The third is a partition function increment (PFC), which is itself the sum of three terms a conformational population increment (POP), a torsional contribution term (TOR), and a translation / rotation term (T / R). Since the molecular mechanics calculation has considered only one conformation, the POP and TOR terms are defined to be zero for this calculation (but see below). The T/R term is a molecular translational and rotational term that is always taken to be 2.4kcal/mol at room temperature, since even an anfi-butane molecule that is not rotating about the C2-C3 bond will still be undergoing translation and rotation of the entire molecule as a unit. Therefore, HFO is the total of the bond increment contributions (BE = —35.08) plus the steric energy (E = 2.17) plus the partition function increment (PFC = 2.4). The sum, -30.51 kcal/mol, is slightly lower than the literature value of -30.15 kcal/mol. ... 

A variant on this procedure produces a first approximation to the molecular mechanics (MM) heat paiameters (Chapters 4 and 5) for C—C and C—H. Instead of atomization energies, the enthalpies of formation of propane and butane (—25.02 and —30.02 kcal mol ) are put directly into the b vector. The results (2.51 kcal mol and —3.76 kcal mol ) are not very good approximations to the heat parameters actually used (2.45 kcal mol and —4.59 kcal mol ) because of other factors to be taken up later, but the calculation illustrates the method and there is rough agreement. 

In 1968 Bartell published an article on the use of molecular models in the curriculum. In this paper the qualitative valence shell electron pair repulsion (VSEPR) model and the relative role of bonded and nonbonded interaaion in directed valence is discussed. The author correctly predicted the increasing importance of model force fields for geometry prediction. An early discussion of the use of molecular mechanics in teaching can be found in a paper by Cox. 07 A cursory description of the methodology of force field calculations is presented, along with computational results on the relative energy of the rotamers of butane and the conformers of cyclohexane. 

Unlike conformational analysis, in which relative energies are compared by assigning fixed amounts of strain to specific interactions (such as butane gauche interactions), molecular mechanics determines the energy of a conformation by computing the value of a mathematical function. An equation such as equation 3.3 can be used to calculate the total steric energy of the molecule as the sum of a number of different kinds of interactions. Most molecular mechanics methods include as a... 

The strain energy at 25° of the substance butane should therefore be taken to be the difference between the strainless heat of formation and the heat of formation value that includes estimates of POP and TOR, and that difference is 0.67 kcal/mol. Notice that this value is not shown on the molecular mechanics output. Again, it must be emphasized that the strain energy shown on the molecular mechanics output above reflects only the inherent strain of the particular conformer calculated, not the strain in the substance represented by the computer model. A value of zero for pop and tor on the output is an indication that appropriate values must be entered if the calculated value of AHf is expected to reproduce an experimental value and if a more accurate value for the strain energy is desired. 

In this section, we will show that although molecular mechanics does not calculate the precise thermodynamic energies for the conformations of butane, it will give strain energies that predict the order of stability correctly. We will also investigate the difference between a local minimum and a global minimum. 

Let us first make a cursory examination of Table 2.1. Take the simple molecule butane and consider the bond length of the terminal carbon-carbon bond, as in the first entry. The MM4 molecular mechanics program has been developed to fit insofar as possible, and as accurately as possible, aU of the experimental and computational data on many small molecules, including those in Table 2.1. The bond lengths shown in the table were aU calculated by MM4 for the sake of consistency. And these numbers all agree well with the various available experiments and theoretical calculations. Note that for the C1-C2 bond for butane (the first entry), has a value of 1.530 A. The other butane r, values are all slightly larger. 

Use a molecular-mechanics program to calculate the barrier to internal rotation in ethane. Use a molecular-mechanics program to find the geometries of the gauche and anti conformations of butane and the energy difference between them. 

Consider the rotation about the C(2)—C(3) bond in butane discussed in Section 3.2 and its potential energy diagram shown in Figure 3.7. As calculated by molecular mechanics, E, n for the anti and gauche conformations of butane are -21.2 and... 

Dynamic Monte Carlo simulations were first used by Verdier and Stockmayer (5) for lattice polymers. An alternative dynamical Monte Carlo method has been developed by Ceperley, Kalos and Lebowitz (6) and applied to the study of single, three dimensional polymers. In addition to the dynamic Monte Carlo studies, molecular dynamics methods have been used. Ryckaert and Bellemans (7) and Weber (8) have studied liquid n-butane. Solvent effects have been probed by Bishop, Kalos and Frisch (9), Rapaport (10), and Rebertus, Berne and Chandler (11). Multichain systems have been simulated by Curro (12), De Vos and Bellemans (13), Wall et al (14), Okamoto (15), Kranbu ehl and Schardt (16), and Mandel (17). Curro s study was the only one without a lattice but no dynamic properties were calculated because the standard Metropolis method was employed. De Vos and Belleman, Okamoto, and Kranbuehl and Schardt studies included dynamics by using the technique of Verdier and Stockmayer. Wall et al and Mandel introduced a novel mechanism for speeding relaxation to equilibrium but no dynamical properties were studied. These investigations indicated that the chain contracted and the chain dynamic processes slowed down in the presence of other polymers. 

In order to explain the isomerization of neopentane to isopentane on platinum films, Anderson and Avery [34) proposed a mechanism involving, as precursor, an a,a,y-triadsorbed species, and, in the transition state, a 71 complex of the Dewar type, attached to the surface by two carbon-metal bonds. By simplified Hiickel molecular orbital (MO) calculations, they showed that hyperconjugative effect and partial charge transfer to the metal could account for the relative isomerization rates of the various molecules studied (neopentane > isobutane > n-butane) (Scheme 19). 

The previous sections indicate the ability of chemically detailed simulations to explain experimental data and the potential for predictions in unknown systems. All-atomic simulation often bridges the gap between indirect structural information obtained from spectroscopic, thermal, and mechanical measurements and molecular level details. The local dynamics of polymer chains [193] agrees with C-H NMR relaxation data on a relative scale [2] however, absolute correlation times in the simulation appear to be 2.5 times the real value. This mismatch could be associated with overestimated torsion barriers in atomistic models, such as an eclipsed barrier of 5-6kcalmol for n-butane (from ab initio calculations) in comparison to the experimental value of 4.0 kcal mol [228] such differences can... 

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