An interior point method for general large-scale quadratic programming problems

In this paper, we present an interior point algorithm for solving both convex and nonconvex quadratic programs. The method, which is an extension of our interior point work on linear programming problems efficiently solves a wide class of largescale problems and forms the basis for a sequential quadratic programming (SQP) solver for general large scale nonlinear programs. The key to the algorithm is a three-dimensional cost improvement subproblem, which is solved at every interation. We have developed an approximate recentering procedure and a novel, adaptive big-M Phase I procedure that are essential to the sucess of the algorithm. We describe the basic method along with the recentering and big-M Phase I procedures. Details of the implementation and computational results are also presented.Contribution of the National Institute of Standards and Tedchnology and not subject to copyright in the United States. This research was supported in part by ONR Contract N-0014-87-F0053.     

Theoretical study on low-lying electronic states of NiH2

The low-lying electronic states of the NiH2 molecule were investigated by using the MCQDPT2 method. In order to accurately describe the strong correlation derived from the nickel 3d9 super-configuration, a set of diffuse secondary 3d' orbitals were included in the active space, yielding a large active space of 12 electrons in 13 orbitals. It is shown that the absolute minimum energy configuration of NiH2 is bent, in agreement with the experimental observation. The global ground state is 1A1 (or A1 in the spin-orbit coupling case), whereas the lowest linear state is 3Deltag (or 3g). Some other cheaper single-configurational and multi-configurational methods were also used to study both states, and their shortcomings are discussed. Our theoretical results suggest that the arrangement of the experimental frequencies of NiH2 and NiD2 may be incorrect.     

Rotational Spectrum of Vinylarsine

The rotational spectrum of vinylarsine in the ground state has been studied in the range 7–320 GHz. The spectra of asynconformer and agaucheconformer have been unambiguously assigned on the basis of the existence of ab-type or ac-type spectrum. Rotational constants, quartic, and some sextic centrifugal distortion constants were derived. For thesynform, measurements of lowJ^aR_0,1transitions in a pulsed-nozzle Fourier transform microwave spectrometer (FTMWS) enabled the determination of the diagonal elements of the quadrupole tensor, as well as two spin–rotation constants.Ab initiocalculations performed at the MP2 level using the 6-311++G(3df, 3pd) basis set reproduced experimental rotational constants within 0.2%.     

Refinement of the molecular structure of Aureomycin

The data for Aureomycin have been refined by full-matrix least-squares, including anisotropic thermal parameters for the heavy atoms and isotropic parameters for the hydrogen atoms. The positional parameters are generally similar to those published previously. The amide group remains anomalous. All hydrogen atoms except the crucial one in the amide group were located in a difference map. The final value ofR for the set of visual data is 10.6%.     

Experimental and Ab Initio Equilibrium Structures of cis-Thionylimide,HNSO: Estimation of the Laurie Correction

The equilibrium structure of cis-thionylimide, HNSO has been determined using high-level ab initio calculations and various experimental procedures. The Laurie correction to the N-H bond length is discussed and it is shown that it can be estimated by ab initio methods. The results are found to be in good agreement and the best equilibrium structure is (in Å for the bond lengths): r(N–H) = 1.020(1), r(N–S) = 1.510(2), r(S–O) = 1.448(1), (HNS) = 115.94(39)°, and (NSO) = 120.44(10)°.     

Structures of some fluorinated benzenes determined by ab initio computation

The structures of fluorobenzene, 1,3-difluorobenzene, 1,3,5-trifluorobenzene, 1,2,3-trifluorobenzene, pentafluorobenzene, and hexafluorobenzene have been determined by the ab initio gradient method with a 4-21 basis set. Approximate corrections have been developed to yield r_e and r₀ structures so that comparison can be made with the available experimental information. The C? F bond distance decreases in a uniform manner with increasing fluorination of the ring, either on adjacent or on meta sites. The ring structure also shows systematic deformation, with a decrease of about 0.01 Å in the C? C bond length adjacent to the point of substitution and an increase of about 2.5? in the ring angle at the substitution site in those cases where the requirement of ring closure permits.     

Nonempirical quantum chemical calculation for nitramide,its chloro- and methyl-substituted derivatives. I. Structure of equilibrium forms

We have carried out quantum chemical calculations for a series of N-nitramines (H₂NNO₂, MeNHNO₂, CINHNO₂, MeNClNO₂, Me₂NNO₂) using the GAUSSIAN-90 program by the restricted Hartree—Fock method, taking into account electron correlation according to Møller—Plesset second-order perturbation theory in a standard 6–31G^* basis. In this paper, we present the geometric parameters of the equilibrium forms of the molecules obtained as a result of full optimization. The calculation allowed us to establish that with an increase in electronegativity of the substituents on the amine nitrogen atom, we observe coordinated lengthening of the NN bond, shortening of the N=O bond, and increase in the pyramidal character of the configuration of the bonds of the amine nitrogen atoms. We observed a close to linear relationship between the length of the NN bond and the magnitude of the angle of deviation of this bond from the plane of the ONO atoms. The greatest difference in NN bond lengths (0.06 Å) occurs between the Me₂NNO₂ and ClNHNO₂ molecules.Moscow State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 1, pp. 4–11, January–February, 1993.     

Efficiency of post-Hartree-Fock force field for the interpretation of vibrational spectra ofN,N-dimethylnitramine

Harmonic force fields for the molecule ofN,N-dimethylnitramine were calculated in the RHF/6-31G^* and MP2/6-31G^** approximations. Scaling of the force fields obtained made it possible to reliably interpret the vibrational spectra of light and perdeuterated compounds reported in the literature. The assignment is confirmed by good reproducibility of experimental isotope shifts upon¹⁵N-amino- and¹⁵N-nitrosubstitution. The frequencies of intramolecular vibrations in far IR and Raman spectra as well as in neutron inelastic scattering spectra for the light and perdeuterated samples of solidN,N-dimethylnitramine were identified using the force field calculated with the inclusion of electron correlation (MP2). Although general structures of the force fields calculated in the RHF and MP2 approximations are similar, considerable differences in the force constants of the NO and NN stretching vibrations and especially in the constants of the NO_str/NO_str and NO_str/NN_str interactions remain even after scaling the force fields.