Comments on the approximate calculation of lattice potential

The potential of a charge distribution due to a lattice of point charges may be evaluated by the classical multipole expansion method. The leading terms in the resultant expressions are just those used in some of our previous calculations [1–3]. In addition, for cases where the leading terms vanish because of the effect of orthogonality of the basis functions upon the Mulliken expansion (this being especially serious in the case of a one-centre charge distribution), we have derived the first nonvanishing term, involving |r|. In other cases it may be necessary to proceed to still higher multipole terms before a non-zero contribution is obtained. The entire procedure is formulated in such a way that it can be easily applied to LCAO-MO calculations for polyatomic ions in ionic lattices.     

Presentations for groups acting on simply-connected complexes

New expansions for global semigroup theory are developed. Many expansions have a left and a right version, each with specific (dual) properties; e.g., the Rhodes expansions ?^$\text{L}$, resp. ?^$\text{R}$, have unambiguous $\text{L}$-resp. $\text{R}$-order. In applications one sometimes needs expansions having both properties simultaneously; these can be constructed by alternately applying the left and the right expansion (possibly infinitely often) while keeping the same set of generators. Thus one obtains an expansion which is invariant under application of the old two expansions and thus has the properties of both (e.g., one obtains -+ with

, and so -+ has unambiguous $\text{L}$-and $\text{R}$-order). It is proved that, in the case of the Rhodes expansion, the new expansion is ‘close’ to the original semigroup; in particular (and this is the main result of the paper), ?⁺_A is finite (resp. finite $\text{J}$-above) if S is finite (resp. finite$\text{J}$-above).     

The absorption spectrum of the Ag2 molecule

The high dispersion absorption spectrum of the Ag₂ molecule has been photographed in the ～5300–1500-Å region. Observations include the previously reported A ← X, B ← X, C ← X, D ← X, and E ← X transitions and a new H ← X transition which occurs in the vacuum ultraviolet. Extensive spectral blending precluded detailed rotational analyses, but the band structures are consistent with $\text{ΔΩ}\text{= 0}$ and $\text{ΔΩ}\text{≥1}$ for D-X and C-X, respectively. The H state is perturbed and probably predissociated. The following molecular constants (in cm^?1) were obtained from fitting bandhead data to the usual expressions:

     

34.

Synthesis of 2-amino-4-hydroxy-1,3,5-triazanaphthalenes     

J. I. DeGraw  V. H. Brown 《Journal of heterocyclic chemistry》1976,13(3):439-441

The synthesis of 2-amino-4-hydroxy-6-amyl-1,3,5-triazanaphthalene (8) is described as a model sequence pertinent to preparation of 8-deazafolic acid and its analogs. Condensation of 2-acet-amido-4-hydroxy-6-pyrimidinealdehyde (3) with dimethyl 2-oxoheptylphosphonate afforded 1-(2′-acetamido-4′-hydroxy-6′-pyrimidinyl)-1-octene-3-one (4) as a key intermediate. Conversion of 4 to 1-(2′-amino-4′-hydroxy-5′ -phenylazo-6′ pyrimidinyl)-3-octanone (7) followed by reductive cyclization yielded 8 or its tetrahydro derivative (9) .     

35.

Heteroligated Rh(I) tweezer complexes     

Brown AM  Ovchinnikov MV  Mirkin CA 《Angewandte Chemie (International ed. in English)》2005,44(27):4207-4209

     

36.

FORMS OF CHLOROPHYLL a     

J. S. Brown 《Photochemistry and photobiology》1963,2(2):159-173

     

37.

Approximate molecular orbital theory for inorganic molecules     

R. D. Brown  K. R. Roby 《Theoretical chemistry accounts》1970,16(3):175-193

As a first stage in the development of a suitable molecular orbital method for treating inorganic systems, we consider the possible integral approximations that may be made to reduce the complexity of the computation. The significance of invariance of the approximations to different transformations is discussed and the effect of various levels of neglect of differential overlap is analysed by the S-expansion technique. A method — the many-centre ZDO method — that is computationally feasible but contains more information than the widely used CNDO approximation is given particular consideration.

---

Zusammenfassung Als erste Stufe in der Entwicklung einer geeigneten Molekular-orbital-Methode für die Behandlung anorganischer Systeme untersuchen wir mögliche IntegralnÄherungen, die geeignet sind, die Berechnungen zu vereinfachen. Die Bedeutung der Invarianz der NÄherungen unter verschiedenen Transformationen wird diskutiert und der Einflu\ verschiedener Stufen der VernachlÄssigung der differentiellen überlappung wird mit der S-Entwicklungstechnik analysiert. Einer Methode, der Vielzentren-ZDO-Methode, die rechnerisch gut durchführbar ist, aber mehr an Information enthÄlt als die meistens benutzte CNDO-NÄherung, wird besondere Beachtung geschenkt.

---

Résumé Dans une première étape lors du développement d'une méthode d'orbitales moléculaires convenant aux systèmes inorganiques, nous envisageons les approximations possible pour les intégrales. On discute la signification de l'invariance des ces approximations par rapport à différentes transformations et l'on analyse par la technique du développement en S l'effet des différents niveaux d'approximation du recouvrement différentiel nul. On considère en particular une méthode — la méthode ZDO polycentrique-quis'avère réalisable numériquementtout en contenant plus d'information que l'approximation CNDO couramment utilisée.

     

38.

DESTRUCTION OF PHOTOREACTIVATING ENZYME BY 365 nm RADIATION*   总被引：3，自引：0，他引：3  

Robert B.  Webb ‡ Mickey S.  Brown 《Photochemistry and photobiology》1973,18(4):249-254

Abstract— Following the observation that in vivo photoreactivation of 365-nm-induced pyrimidine dimers could not be observed chemically, a study was made of the inactivation of photoreactivating enzyme activity by this near-ultraviolet wavelength. It was observed that: (1) Dimers induced in extracted bacterial DNA by 365 nm radiation are completely photoreactivable and are monomerized as an exponential function of the photoreactivation time. (2) Photoreactivability of 254-nm-induced damage in Escherichia coli B/r Hcr is progressively destroyed in vivo as a function of the dose of 365 nm radiation. (3) The ability of the yeast photoreactivating enzyme to monomerize dimers induced at 365 nm in bacterial DNA is destroyed in vitro as a function of the dose of 365 nm radiation, and at a rate comparable to killing of E. coli. These results are consistent with biological measurements which indicate that photoreactivability of ultraviolet (near and far) lethal damage is reduced by exposure of the bacteria to 365 nm radiation.     

39.

Alloxazines and isoalloxazines. Mass spectrometric analysis of riboflavin and related compounds     

Peter Brown  Cecil L. Hornbeck  John R. Cronin 《Journal of mass spectrometry : JMS》1972,6(12):1383-1399

The positive ion electron-impact mass spectra of a series of alloxazines, iso-alloxazines and some derivatives have been examined. The compounds employed were lumichrome (7,8-dimethylalloxazine), 1,3-dimethyllumichrome, lumiflavin (7,8,10-trimethyl-iso-alloxazine), 3-methyllumiflavin, riboflavin [7,8-dimethyl-10-(D-1′-ribityl)-iso-alloxazine], riboflavin tetraacetate, 3-methylriboflavin tetraacetate and riboflavin tetrapropionate. By using exact mass measurements, metastable ion defocusing and the mass/composition shifts occurring with derivatives, it has been possible to arrive at detailed interpretations of the mass spectra of all compounds. With lumichrome and lumiflavin, fragmentation commences by elimination of HNCO from the pyrimidine ring. With riboflavin and its derivatives the ribityl chain cleaves off first, followed by decomposition of the iso-alloxazine ring. Application of these methods and findings to the structural analysis of chemically interesting modified flavins is predicted to be rewarding.     

40.

Transition to Ohmic conduction in microscopic tunnel junctions at low temperatures     

Brown R  Simánek E 《Physical review. B, Condensed matter》1992,45(11):6069-6073

     

[首页] « 上一页 [1] [2] [3] 4 [5] [6] [7] [8] [9] [10] [11] 下一页 » 末  页»

State	Te	ωc	Xωt
X	0.0	192.0	0.58
B	35 838.6	151.8	0.87
C	37 631.6	171.0	0.84
D	39 014.5	168.2	1.20
E	40 159.9	146.1	1.58
H	58 273.1	165.9	2.46

Synthesis of 2-amino-4-hydroxy-1,3,5-triazanaphthalenes

The synthesis of 2-amino-4-hydroxy-6-amyl-1,3,5-triazanaphthalene (8) is described as a model sequence pertinent to preparation of 8-deazafolic acid and its analogs. Condensation of 2-acet-amido-4-hydroxy-6-pyrimidinealdehyde (3) with dimethyl 2-oxoheptylphosphonate afforded 1-(2′-acetamido-4′-hydroxy-6′-pyrimidinyl)-1-octene-3-one (4) as a key intermediate. Conversion of 4 to 1-(2′-amino-4′-hydroxy-5′ -phenylazo-6′ pyrimidinyl)-3-octanone (7) followed by reductive cyclization yielded 8 or its tetrahydro derivative (9) .     

Approximate molecular orbital theory for inorganic molecules

As a first stage in the development of a suitable molecular orbital method for treating inorganic systems, we consider the possible integral approximations that may be made to reduce the complexity of the computation. The significance of invariance of the approximations to different transformations is discussed and the effect of various levels of neglect of differential overlap is analysed by the S-expansion technique. A method — the many-centre ZDO method — that is computationally feasible but contains more information than the widely used CNDO approximation is given particular consideration.

---

Zusammenfassung Als erste Stufe in der Entwicklung einer geeigneten Molekular-orbital-Methode für die Behandlung anorganischer Systeme untersuchen wir mögliche IntegralnÄherungen, die geeignet sind, die Berechnungen zu vereinfachen. Die Bedeutung der Invarianz der NÄherungen unter verschiedenen Transformationen wird diskutiert und der Einflu\ verschiedener Stufen der VernachlÄssigung der differentiellen überlappung wird mit der S-Entwicklungstechnik analysiert. Einer Methode, der Vielzentren-ZDO-Methode, die rechnerisch gut durchführbar ist, aber mehr an Information enthÄlt als die meistens benutzte CNDO-NÄherung, wird besondere Beachtung geschenkt.

---

Résumé Dans une première étape lors du développement d'une méthode d'orbitales moléculaires convenant aux systèmes inorganiques, nous envisageons les approximations possible pour les intégrales. On discute la signification de l'invariance des ces approximations par rapport à différentes transformations et l'on analyse par la technique du développement en S l'effet des différents niveaux d'approximation du recouvrement différentiel nul. On considère en particular une méthode — la méthode ZDO polycentrique-quis'avère réalisable numériquementtout en contenant plus d'information que l'approximation CNDO couramment utilisée.

     

DESTRUCTION OF PHOTOREACTIVATING ENZYME BY 365 nm RADIATION*

Abstract— Following the observation that in vivo photoreactivation of 365-nm-induced pyrimidine dimers could not be observed chemically, a study was made of the inactivation of photoreactivating enzyme activity by this near-ultraviolet wavelength. It was observed that: (1) Dimers induced in extracted bacterial DNA by 365 nm radiation are completely photoreactivable and are monomerized as an exponential function of the photoreactivation time. (2) Photoreactivability of 254-nm-induced damage in Escherichia coli B/r Hcr is progressively destroyed in vivo as a function of the dose of 365 nm radiation. (3) The ability of the yeast photoreactivating enzyme to monomerize dimers induced at 365 nm in bacterial DNA is destroyed in vitro as a function of the dose of 365 nm radiation, and at a rate comparable to killing of E. coli. These results are consistent with biological measurements which indicate that photoreactivability of ultraviolet (near and far) lethal damage is reduced by exposure of the bacteria to 365 nm radiation.     

Alloxazines and isoalloxazines. Mass spectrometric analysis of riboflavin and related compounds

The positive ion electron-impact mass spectra of a series of alloxazines, iso-alloxazines and some derivatives have been examined. The compounds employed were lumichrome (7,8-dimethylalloxazine), 1,3-dimethyllumichrome, lumiflavin (7,8,10-trimethyl-iso-alloxazine), 3-methyllumiflavin, riboflavin [7,8-dimethyl-10-(D-1′-ribityl)-iso-alloxazine], riboflavin tetraacetate, 3-methylriboflavin tetraacetate and riboflavin tetrapropionate. By using exact mass measurements, metastable ion defocusing and the mass/composition shifts occurring with derivatives, it has been possible to arrive at detailed interpretations of the mass spectra of all compounds. With lumichrome and lumiflavin, fragmentation commences by elimination of HNCO from the pyrimidine ring. With riboflavin and its derivatives the ribityl chain cleaves off first, followed by decomposition of the iso-alloxazine ring. Application of these methods and findings to the structural analysis of chemically interesting modified flavins is predicted to be rewarding.