Ab initio molecular orbital calculations of the cobalt porphine complex. I. LCAO SCF MO calculation of low-spin,high-spin,and π-ionized states of Co-porphine

Ab initio LCAO SCF MO calculations are carried out on planar Co-porphine with a basis set of roughly double zeta quality for Co and N and of single zeta quality for C and H. The net charge on Co and N and the overlap population between them are 1.78, ?0.57, and 0.06, respectively, in the ²A_1g, state, which is known to be the ground state by experiment. The bonding in this complex is thus largely ionic. The first and second calculated ionization potentials are 6.51 and 6.77 eV, respectively, and are in reasonable agreement with the observed ionization potentials of 6.44 and 6.62 eV for Ni-tetraphenylporphine. CI calculations within the framework of the ligand field theory are also performed. The calculated order of the five lowest states is ⁴B_2g ≈ ⁴E_g, ⁴A_2g, ²A_1g, ⁴E_g from below and is not in agreement with the semiempirical order of ²A_1g ≈ ⁴B_2G, ⁴A_2g, ²E_g, ⁴E_g determined by Lin.     

Reinvestigation of the stereochemistry of kulokekahilide-2

An attempt to carry out a total synthesis of kulokekahilide-2 (1) by macrolactonization of a seco acid prepared from a suitably protected hexapeptide and a dioxy acid moiety unexpectedly resulted in the formation of the 43-epimer (1a) of the cytotoxic depsipeptide, for which structure 1b has previously been proposed. A second attempt involving macrolactamization of the corresponding amino acid gave the target product, 1b, but the spectral data of the product did not match those of natural 1. Furthermore, neither 1a nor 1b showed any cytotoxicity, from which it is concluded that the structure of natural 1 is incorrect and should be re-examined.     

Skeleton transformation of α-pyrone induced by 5-aryl substituent into ring-fused dihydrofuran

A skeleton transformation of 5-aryl-α-pyrones into dihydrofurans was developed. In the course of our study of the skeleton transformation reaction of α-pyrones by using dimethylsulfoxonium methylide, α-pyrones having an aryl group at the 5-position were converted into corresponding dihydrofurans as major products and bicyclo[3.1.0]hexanes as minor products. Selectivity for dihydrofurans was improved by optimizing the reaction conditions and investigating the substituent effect.     

Development of Computational Algorithms for Evaluating Option Prices Associated with Square-Root Volatility Processes

The stochastic volatility model of Heston (Rev Financ Stud 6:327–343, 1993) has been accepted by many practitioners for pricing various financial derivatives, because of its capability to explain the smile curve of the implied volatility. While analytical results are available for pricing plain Vanilla European options based on the Heston model, there hardly exist any closed form solutions for exotic options. The purpose of this paper is to develop computational algorithms for evaluating the prices of such exotic options based on a bivariate birth-death approximation approach. Given the underlying price process S _t , the logarithmic process U _t  = logS _t is first approximated by a birth-death process B^U_tB^U_t via moment matching. A second birth-death process B^V_tB^V_t is then constructed for approximating the stochastic volatility process V _t through infinitesimal generator matching. Efficient numerical procedures are developed for capturing the dynamic behavior of { B^U_t , B^V_t }\{ B^U_t , B^V_t \} . Consequently, the prices of any exotic options based on the Heston model can be computed as long as such prices are expressed in terms of the joint distribution of { S _t ,V _t } and the associated first passage times. As an example, the prices of down-and-out call options are evaluated explicitly, demonstrating speed and fair accuracy of the proposed algorithms.     

Synthesis of isoxazoles en route to semi-aromatized polyketides: dehydrogenation of benzonitrile oxide-para-quinone acetal cycloadducts

A variety of highly functionalized polycyclic isoxazoles are prepared by a two-step protocol: (1) 1,3-dipolar cycloaddition of o,o'-disubstituted benzonitrile oxides to para-quinone mono-acetals, then (2) dehydrogenation. The cycloaddition proceeds in a regioselective manner, favouring the formation of the 4-acyl cycloadducts, which are suitable intermediates for the synthesis of semi-aromatized polycyclic targets derived from polyketide type-II biosynthesis.