A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

Cobalt-catalyzed regioselective carbocyclization reaction of o-iodophenyl ketones and aldehydes with alkynes, acrylates, and acrylonitrile: a facile route to indenols and indenes

An efficient cobalt-catalyzed carbocylization for the synthesis of indenols and indenes and a new method for reductive decyanation are described. 2-Iodophenyl ketones and aldehydes 1a-g undergo carbocyclization with various disubstituted alkynes 2a-k in the presence of Co(dppe)I(2) and zinc powder in acetonitrile at 80 degrees C for 3 h to afford the corresponding indenol derivatives 3a-s and4a-m in good to excellent yields. For some unsymmetrical alkynes, the carbocyclization was remarkably regioselective, affording a single regioisomer. The cobalt-catalyzed carbocyclization reaction was successfully extended to the synthesis of indene derivatives. Thus, the reaction of 2-iodophenyl ketones and aldehydes (1) with acrylates H(2)C=CHCO(2)R (7a-d) and acrylonitrile H(2)C=CHCN (7e) proceeds smoothly in the presence of Co(dppe)Cl(2)/dppe and zinc powder in acetonitrile at 80 degrees C for 24 h to afford the corresponding indenes 8a-k and 9a-c in moderate to good yields. Interestingly, when 7e was employed for the carbocylization, reductive decyanation also occurred to give an indene derivative without the cyano functionality. A possible mechanism for this cobalt-catalyzed carbocyclization reaction is also proposed.     

Synthesis of phthalide derivatives using nickel-catalyzed cyclization of o-haloesters with aldehydes

The reaction of o-bromobenzoate (1 b) with benzaldehyde (2 a) in the presence of [NiBr(2)(dppe)] (dppe=1,2-bis(diphenylphosphino)ethane) and zinc powder in THF (24 hours, reflux temperature), afforded 3-phenyl-3H-isobenzofuran-1-one (3 a) in an 86 % yield. Similarly, o-iodobenzoate reacts with 2 a to give 3 a, but in a lower yield (50 %). A series of substituted aromatic and aliphatic aldehydes (2 b, 4-MeC(6)H(4)CHO; 2 c, 4-MeOC(6)H(4)CHO; 2 d, 3-MeOC(6)H(4)CHO; 2 e, 2-MeOC(6)H(4)CHO; 2 f, 4-CNC(6)H(4)CHO; 2 g, 4-(Me)(3)CC(6)H(4)CHO; 2 h, 4-C(6)H(5)C(6)H(4)CHO; 2 i, 4-ClC(6)H(4)CHO; 2 j, 4-CF(3)C(6)H(4)CHO; 2 k, CH(3)(CH(2))(5)CHO; 2 l, CH(3)(CH(2))(2)CHO) also underwent cyclization with o-bromobenzoate (1 b) producing the corresponding phthalide derivatives in moderate to excellent yields and with high chemoselectivity. Like 1 b, methyl 2-bromo-4,5-dimethoxybenzoate (1 c) reacts with tolualdehyde (2 b) to give the corresponding substituted phthalide 3 m in a 71 % yield. The methodology can be further applied to the synthesis of six-membered lactones. The reaction of methyl 2-(2-bromophenyl)acetate (1 d) with benzaldehyde under similar reaction conditions afforded six-membered lactone 3 o in a 68 % yield. A possible catalytic mechanism for this cyclization is also proposed.     

Regioselective synthesis of indenols via nickel-catalyzed carbocyclization reaction

2-Halophenyl ketones 1a-e (1a, o-IC(6)H(4)COCH(3)) undergo carbocyclization with alkyl propiolates (2a, CH(3)(CH(2))(4)C[triple bond]CCO(2)CH(3); 2b, TMSC[triple bond]CCO(2)Et 2c, CH(3)C[triple bond]CCO(2)CH(3); 2d, CH(3)OCH(2)C[triple bond]CCO(2)CH(3); 2e, CH(3)(CH(2))(3)C[triple bond]CCO(2)CH(3); 2f, PhC[triple bond]CCO(2)CH(3); and 2g, (CH(3))(3)C[triple bond]CCO(2)CH(3)) in the presence of Ni(dppe)Br(2) and zinc powder in acetonitrile at 80 degrees C to afford the corresponding indenol derivatives 3a-m with remarkable regioselectivity in good to excellent yields. The nickel-catalyzed carbocyclization reaction was successfully extended to other simple disubstituted alkynes. Thus, the reaction of 2-halophenyl ketones 1a-e with disubstituted alkynes (2h, PhC[triple bond]CPh; 2i, CH(3)C(6)H(4)C[triple bond]CC(6)H(4)CH(3); 2j, CH(3)CH(2)C[triple bond]CCH(2)CH(3); 2k, PhC[triple bond]CCH(3); 2l, TMSC[triple bond]CCH(3); and 2m, PhC[triple bond]C(CH(2))(3)CH(3)) proceeded smoothly to afford the corresponding indenols 4a-t in good to excellent yields. For unsymmetrical alkynes 2k-m, the carbocyclization gave two regioisomers with regioselectivities ranging from 1:2 to 1:12 depending on the substituents on the alkyne and on the aromatic ring of halophenyl ketone. A possible mechanism for this nickel-catalyzed carbocyclization reaction is also proposed.     

Overtone spectroscopy of some benzaldehyde derivatives

Overtone spectrum of o, m and p-nitrobenzaldehydes and p-chlorobenzaldehyde has been studied in 2000–12000 cm⁻¹ region. Vibrational frequencies and anharmonicity constants for aryl as well as alkyl CH stretch vibrations have been determined. We have also determined the internuclear distances for the aryl CH bond in the different molecules. The small variation observed in these distances is an indication of the substitution effect. It is observed that in the case of p-disubstituted benzens, the shift in aryl CH bond is proportional to sum of the Hammet σ of the substituents. However in the case of o-disubstituted benzenes it is only 80% of the para-substituted shift.     

Multiple ionization of argon in coincidence with projectile ions in 60–120 MeV Si q+-Ar collisions

A projectile ion-recoil ion coincidence technique has been employed to study the multiple ionization and the charge transfer processes in collisions of 60–120 MeV Si ^q+ (q = 4−14) ions with neutral argon atoms. The relative contribution of different ionization channels, namely; direct ionization, electron capture and electron loss leading to the production of slow moving multiply charged argon recoil ions have been investigated. The data reported on the present collision system result from a direct measurement in the considered impact energy for the first time. The total ionization cross-sections for the recoil ions are shown to scale as q ^1.7/E _p ^0.5 , where E _p is the energy in MeV of the projectile and q its charge state. The recoil fractions for the cases of total- and direct ionizations are found to decrease with increasing recoil charge state j. The total ionization fractions of the recoils are seen to depend on q and to show the presence of a ‘shell-effect’ of the target. Further, the fractions are found to vary as 1/j ² upto j = 8+. The average recoil charge state 〈j〉 increases slowly with q and with the number of lost or captured electrons from or into the projectile respectively. The projectile charge changing cross-sections σ _qq′ are found to decrease with increasing q for loss ionization and to increase with q for direct-and capture ionization processes respectively. The physics behind various scaling rules that are found to follow our data for different ionization processes is reviewed and discussed.     

Asymmetric reductive ring-opening of bicyclic olefins catalyzed by palladium and nickel complexes

[reaction: see text] Asymmetric reductive ring opening of oxa- and azabenzonorbornadienes with organic acids and zinc powder under mild conditions catalyzed by Ni(binap)Cl(2) or Pd(binap)I(2) produces the corresponding 1,2-dihydronaphth-1-ols in good to excellent yields with high enantioselectivity.     

Synthesis of seven-membered lactones via nickel- and zinc-catalyzed highly regio- and stereoselective cyclization of 2-iodobenzyl alcohols with propiolates

A new class of substituted seven-membered lactones 3 were conveniently synthesized via cyclization of o-iodobenzyl alcohol 1 (o-IC(6)H(4)CH(2)OH) with various propiolates 2 (RC triple bond CCOOMe) in the presence of Ni(dppe)Br(2) and Zn powder in acetonitrile at 80 degrees C. The catalytic reaction is highly regio- and stereoselective affording seven-membered lactones in moderate to good yields. This methodology can be successfully extended to various substituted o-iodobenzyl alcohols. An intermediate 7 was obtained from the reaction of 1a with methyl 2-octynoate (2a) in the presence of Ni(dppe)Br(2) and Zn at room temperature. A mechanism involving an unusual E/Z isomerization of the carbon-carbon double bond of 7 prior to lactone formation is proposed to account for the catalytic reaction.