The complete symmetrization of quantum operators: new thoughts on an old problem

The complete symmetrization with respect to x, p _x,... of the operators associated with dynamical properties can sometimes lead to results different from those obtained by the conventional quantum formalism based on the rule op (A ²)=(op A)². For example, angular momentum operators M _z ² and M ² are modified by the additive constants ²/2 and 3 ²/2 respectively (M ²0 for electron in the ground state of H atom, rotator never at rest, but spectra unchanged); the average quadratic dispersion of energy is different from zero. These results can be interpreted by assuming that the system is never strictly isolated but communicates with the other systems of the universe by means of electromagnetic interactions. Quantum mechanics would give only average values over a sufficiently long time and would exhibit a quasi-ergodic character. Examples supporting this possibility are given, in particular that of arsines for which quantum forecasts correspond to average values over one year.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

NMR chemical shifts in the low–pH form of a-chymotrypsin. A QM/MM and ONIOM–NMR study

 The relationship between hydrogen bonding and NMR chemical shifts in the catalytic triad of low-pH α-chymotrypsin is investigated by combined use of the effective fragment potential [(2001) J Phys Chem A 105:293] and ONIOM–NMR [(2000) Chem Phys Lett 317:589] methods. Our study shows that while the His57 N^δ1−H bond is stretched by a relatively modest amount (to about 1.060 ?) this lengthening, combined with the polarization due to the molecular environment, is sufficient to explain the experimentally observed chemical shifts of 18.2 ppm. Furthermore, the unusual down-field shift of H^ɛ1 (9.2 ppm) observed experimentally is reproduced and shown to be induced by interactions with the C=O group of Ser214 as previously postulated. The free-energy cost of moving H^δ1 from His57 to Asp102 is predicted to be 5.5 kcal/mol. Received: 26 September 2001 / Accepted: 6 September 2002 / Published online: 21 January 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: J. H. Jensen e-mail: jan-jensen@uiowa.edu Acknowledgements. This work was supported by a Research Innovation Award from the Research Corporation and a type G starter grant from the Petroleum Research Fund. The calculations were performed on IBM RS/6000 workstations obtained through a CRIF grant from the NSF (CHE-9974502) and on supercomputers at the National Center for Supercomputer Applications at Urbana-Champaign. The authors are indebted to Visvaldas Kairys for help with the CHARMM program, and to Daniel Quinn for many helpful discussions.     

MECHANICS AND THE EVOLUTION AND FUNCTIONAL MORPHOLOGY OF CONCHOSTRACAN CARAPACE MECHANICS AND THE EVOLUTION AND FUNCTIONAL MORPHOLOGY OF CONCHOSTRACAN CARAPACE

Conchostracans, with a laterally compressed body enclosed between two symmetric valves, live swimming in fresh or brackish water. The carapace valve has a number of growth bands with various sculptures. The general trend of sculptural evolution is from smooth to punctate-minute polygon-medium reticulation-large reticulation, while these punctate, polygonal and various reticulate patterns may separately develop into various radial ridges. The development of sculpture can be well explained by mechanical principle. Functional morphology of carapace is discussed in the light of mechanics in this paper.     

Crystal structures of phenyl-substituted cyclopropanes. IV. the crystal structure (at 21‡C and −100‡C) and the phenyl ring conformation in 4-cyclopropylacetanilide

The crystal structure of 4-cyclopropylacetanilide was investigated at room temperature (21C) and at –100C in order to determine the orientation of the phenyl ring with respect to the cyclopropane moiety and the effect of this substituent on the stereochemistry of the three-membered ring. The compound was chosen because it is one of the few species containing a simple phenyl ring as the sole cyclopropane ring substituent and whose crystals are suitable for X-ray diffraction at room temperature. The substance crystallizes in space groupP2_l/c at either temperature (no phase transitions) with cell constants: (at 21C)a=9.725(2),b=10.934(3), andc=9.636(2) å,=106.13(1);V=984.21 å³ andd(calc;z=4)=1.182 g cm^–3. The relevant parameters for the –100C structure area=9.557(4),b=10.980(2), andc=9.641(2) å,=106.34(3);V=970.76 å³ and d(calc;z=4)=1.199 g cm^–3. Final values wereR(F)=0.042, R_w=0.035, using unit weights, and its nonhydrogen atoms were used to phase the low-temperature data, whose final discrepancy indices wereR(F)=0.051,R _w =0.061. The phenyl substituent is almost exactly in the bisecting conformation with respect to the C-C-C angle at the point of attachment to cyclopropane and conjugative effects are clearly evident in the lengths of the cyclopropane ring [1.494(3), 1.498(3), and 1.474(4) å, the later being the distal bond]. If one omits the terminal methylene fragments at C10 and C11, the atoms comprising the acetanilide fragment and the substituted carbon of the cyclopropane ring lie in a nearly perfect plane. Molecular mechanics as well as semiempirical (AM1) calculations were carried out in order to determine the structure of the energy-minimized configurations in the two computational environments. The molecular conformations thus obtained are close to that experimentally observed from the X-ray diffraction experiment. In both theoretical models, the lowest energy conformation is that in which the plane of the phenyl ring bisects the cyclopropane C-C-C angle as was experimentally observed. Finally, the shape of the conformational barrier as a function of the orientation of the plane of the phenyl ring was computed, giving a maximum barrier to rotation of 2.2 kcal/mol. Similar calculations were carried out for two other aryl cyclopropanes, whose rings (naphthalene and anthracene) cannot adopt the bisecting position. Comparisons of experimental geometrical parameters as well as of the barriers to rotation are presented.on leave at the University of Houston, 1995–1996.     

Λ-、△-[Rh（bpy）2chrysi]^3＋对含C：T错配的DNA序列识别作用的分子模拟研究

通过分子模拟方法研究了手性金属配合物[Rh（bpy）2Chrysi]^3＋（bpy=2，2’-bipyridineChrysi=5，6-chrysenequinonediimine）对包含C：T错配碱基对的B-DNA序列的识别作用．结合类似的针对含G：A错配的和正常的B-DNA序列的识别作用研究，发现配合物I-Rh（bpy）zChrysi]^3＋可以对错配B-DNA序列进行序列特异性的识别．能量对比计算结果表明，该经典插入识别作用倾向于在错配碱基对附近进行，其中△-[Rh（bpy）2chrysi]^3＋比其手性异构体更占优势．这同Barton教授工作组的实验结果是一致的．另外插入作用倾向于在错配序列中的正常双碱基对C3A4／G3T4（错配碱基对附近）中从小沟进行．与该配合物对含G：A错配的和正常的B-DNA序列的识别作用不同的是，对包含C：T错配碱基对的B-DNA序列的识别作用倾向于从小沟进行．这一点可能源于C：T碱基对结构的不同．     

Extraction of kinetic information from single-molecule experiments.

We discuss two possible approaches for extracting kinetic information from single-molecule experiments. The first approach is based on computing correlation functions from measured fluorescence signals, and the second on studying the statistics of on and off times of the same fluorescence signal. We show that in both cases it is possible to extract kinetic information about the nature of intramolecular fluctuations of the single molecule. We show that for single-molecule kinetics the intramolecular fluctuations produce stochastic memory effects which lead to new dynamic features that do not exist in traditional chemical kinetics. In particular, we investigate a new type of chemical oscillations in correlation functions observed experimentally by Edman and Rigler (Proc. Natl. Acad. Sci. USA 2000, 97, 8266).     

Wave chaos in quantum systems with point interaction

We study perturbations of the quantized version ₀ of integrable Hamiltonian systems by point interactions. We relate the eigenvalues of to the zeros of a certain meromorphic function . Assuming the eigenvalues of ₀ are Poisson distributed, we get detailed information on the joint distribution of the zeros of and give bounds on the probability density for the spacings of eigenvalues of . Our results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory.SFB 237 Essen-Bochum-Düsseldorf     

Classical physics and Penrose's thesis

We expose and discussPenrose's thesis: Nature produces harnessable noncomputable processes, but none at the classical level. We then suggest a partial counterexample to it, based on aGedanken experiment about an undecidable family of integrable Hamiltonian systems that could lead to a sort of idealized solution to the Halting problem for Turing machines.1. Partially supported by a Fulbright/CNP_q-Brazil grant. Permanent address after November 5, 1990: Center for the Study of Mathematical Theories of Communication, IDEA/School of Communications, Federal University of Rio de Janeiro, Av. Pasteur 250, 22290 Rio de Janeiro, RJ Brazil.     

Mobility and non-separability

A mobility phenomenon is typical for a large class of non-linear evolutions. It is shown that the mobility can be responsible for a malignant form of quantum mechanical non separability of two correlated systems. An explicit example based on Weinberg's non linear quantum mechanics is considered. We show that in such a theory a transfer of information without a transfer of energy is possible and discuss physical roots of this phenomenon. In Polchinski's approach this effect is not present.1 Permanent address: Laboratory of Dielectrics and Organic Semiconductors, Technical University of Gdask, Gdask, Poland.     

Alcohols,ethers, carbohydrates,and related compounds. II. The anomeric effect

The anomeric effect has been studied for a variety of compounds using the MM4 force field, and also using MP2/6-311++G(2d,2p) ab initio calculations and experimental data for reference purposes. Geometries and energies, including conformational, rotational barriers, and heats of formation were examined. Overall, the agreement of MM4 with the experimental and ab initio data is good, and significantly better than the agreement obtained with the MM3 force field. The anomeric effect is represented in MM4 by various explicit terms in the force constant matrix. The bond length changes are accounted for with torsion-stretch elements. The angle changes are accounted for with torsion-bend elements. The energies are taken into account with a number of torsional terms in the usual way. A torsion-torsion interaction is also of some importance. With all of these elements included in the calculation, the MM4 results now appear to be adequately accurate. The heats of formation were examined for a total of 12 anomeric compounds, and the experimental values were fit by MM4 with an RMS error of 0.42 kcal/mol.