On finding the rate constants of linear and nonlinear systems

In lowest approximation, a certain chemical reaction is described by a system of first-order linear differential equations with unknown constant coefficients. One can therefore write down an expression for the state of the system at time t, and from this find the endpoint of the reaction in terms of the initial state and the rate constants. The relative values of some rate constants can then be estimated from experimental data. A better approximation in which the differential equations are nonlinear is also considered, and it turns out that because of symmetry in the reaction, the relationship between the final state and the ratios of the rate constants is unchanged. Although the differential equations now appear much less tractable, the problem of relating the rate constants to the endpoint of the reaction can be formulated and solved in terms of probabilities. The results illustrate an important property of reaction schemes in which some of the steps are reversible. More generally, this is a property of differential equations: provided that they continue to satisfy certain linear constraints, the parameters of a linear system of ordinary differential equations can vary without affecting the asymptotic solution.     

An AM1 semiempirical study of host-guest complexation in hemicarcerand complexes

Semiempirical AM1 calculations have been carried out on host-guest complexes of model hemicarcerands 1a and 2a. The justification for the choice of the AM1 Hamiltonian was based on a comparison between reported X-ray data for the smaller tetrabromocavitand 4a and computational results obtained using several different Hamiltonians. The complexation behavior of hemicarcerands 1a and 2a have been compared with experimental results reported by Cram et al. for the related hemicarcerands 1b and 2b. Based on this comparison, a criterion for predicting guest encapsulation was developed, E(complexation), which relies on the calculation of AM1 heats of formation for host, guest, and hemicarceplex. If E(complexation) is lower than 10 kcal/mol, then a guest will be encapsulated, while if it is greater than 30 kcal/mol, a guest will not be encapsulated. The use of constrained-path AM1 optimizations to determine the energy barriers to guest entry and exit from the host was found to be a useful tool for examining suitable host-guest combinations when the E(complexation) criteria does not hold. We have computed the barriers to exit of N, N-dimethylformamide (dmf) and furan from the hemicarcerand 1a, the former has been compared with the experiment and shows excellent agreement. Based on the success of the above computational methods in predicting which host-guest combinations will form stable hemicarceplexes we have synthesized a new target hemicarceplex 1b.furan.     

Synthesis of (2R, 3S, 4R)-2-Hydroxymethyl-3,4-Dihydroxypyrrolidine Hydrochloride from D-Glucose

(2R, 3S, 4R)-2-Hydroxymethyl-3,4-dihydroxypyrrolidine hydrochlo-ride was synthesized from diacetone-D-glucose.     

非平衡态/不可逆过程的热力学理论(Ⅱ)

<正> 7 解的唯一性 如果不考虑非平衡态和不可逆性,则等能密度理论中的基本命题与经典弹性理论中的在形式上完全相同。无论整个系统的动能是大还是小,图6中(sumform)_o上的面力T_i和在(sumform)_c和在的位移u_i将始终在空间坐标系x_i和时刻i下给出。与一般力学中相同,必须知道有关位移u_i及其时间导数的初始条件。它们的影响则可通过(38)和(39)向等能面转化,从而得到     

Energy and photoinduced electron transfer in a wheel-shaped artificial photosynthetic antenna-reaction center complex

Functional mimics of a photosynthetic antenna-reaction center complex comprising five bis(phenylethynyl)anthracene antenna moieties and a porphyrin-fullerene dyad organized by a central hexaphenylbenzene core have been prepared and studied spectroscopically. The molecules successfully integrate singlet-singlet energy transfer and photoinduced electron transfer. Energy transfer from the five antennas to the porphyrin occurs on the picosecond time scale with a quantum yield of 1.0. Comparisons with model compounds and theory suggest that the F?rster mechanism plays a major role in the extremely rapid energy transfer, which occurs at rates comparable to those seen in some photosynthetic antenna systems. A through-bond, electron exchange mechanism also contributes. The porphyrin first excited singlet state donates an electron to the attached fullerene to yield a P(*+)-C(60)(*-) charge-separated state, which has a lifetime of several nanoseconds. The quantum yield of charge separation based on light absorbed by the antenna chromophores is 80% for the free base molecule and 96% for the zinc analogue.