A modified conjugate gradient algorithm for geometry optimization is outlined for use with ab initioMO methods. Since the computation time for analytical energy gradients is approximately the same as for the energy, the optimization algorithm evaluates and utilizes the gradients each time the energy is computed. The second derivative matrix, rather than its inverse, is updated employing the gradients. At each step, a one-dimensional minimization using a quartic polynomial is carried out, followed by an n-dimensional search using the second derivative matrix. By suitably controlling the number of negative eigenvalues of the second derivative matrix, the algorithm can also be used to locate transition structures. Representative timing data for optimizations of equilibrium geometries and transition structures are reported for ab initioSCF–MO calculations.

Optimization of equilibrium geometries and transition structures

A redundant internal coordinate system for optimizing molecular geometries is constructed from all bonds, all valence angles between bonded atoms, and all dihedral angles between bonded atoms. Redundancies are removed by using the generalized inverse of the G matrix; constraints can be added by using an appropriate projector. For minimizations, redundant internal coordinates provide substantial improvements in optimization efficiency over Cartesian and nonredundant internal coordinates, especially for flexible and polycyclic systems. Transition structure searches are also improved when redundant coordinates are used and when the initial steps are guided by the quadratic synchronous transit approach. © 1996 by John Wiley & Sons, Inc.

Using redundant internal coordinates to optimize equilibrium geometries and transition states

A linear synchronous transit or quadratic synchronous transit approach is used to get closer to the quadratic region of the transition state and then quasi-newton or eigenvector following methods are used to complete the optimization. With an empirical estimate of the hessian, these methods converge efficiently for a variety of transition states from a range of starting structures.

Combining Synchronous Transit and Quasi-Newton Methods to Find Transition States

An algorithm for locating transition states designed for use in the ab initio program package GAUSSIAN 82 is presented. It is capable of locating transition states even if started in the wrong region of the energy surface, and, by incorporating the ideas on hessian mode following due to Cerjan and Miller, can locate transition states for alternative rearrangement/dissociation reactions from the same initial starting point. It can also be used to locate minima.

An algorithm for the location of transition states

https://isiarticles.com/bundles/Article/pre/pdf/22294.pdf

A generalized synchronous transit method for transition state location

The microwave spectra of two isotopic species of trimethylphosphine, (CD 3 ) 2 (CH 3 )P and (CD 3 ) 3 P, have been recorded in the spectral region 20–39 GHz. Only c-type transitions were observed and R -branch assignments have been made for the (CD 3 ) 2 (CH 3 )P molecule and two transitions were observed for the symmetric top molecule, (CD 3 ) 3 P. From these rotational constants along with those reported for five other isotopic species of trimethylphosphine, the complete r 0 structural parameters have been determined and they are: r (PC = 1.845±0.001A, r(CH) = 1.096±0.001 A, ∠CPC = 98.95 ± 0.20°, ∠HCH = 109.02±0.16° with an angle of tilt of the methyl groups of 1.67±0.17°. The Raman spectra (3500-100 cm −1 of (CD 3 )(CH 3 ) 2 P and (CD 3 ) 2 (CH 3 )P in the liquid state have been obtained. From these data, along with the vibrational data for the d 0 - and d 9 -molecules, a complete vibrational assignment is proposed. The fundamental vibrational frequencies, barriers to internal rotation and structural parameters which have been obtained experimentally, are compared to those obtained from ab initio Hartree-Fock calculations employing the 3-21G basis set. Additionally, structural parameters have been calculated utilizing 3-21G * ,6-31G ** and DZ basis sets. All to these results are compared to the corresponding quantities for some similar molecules.

Microwave Spectrum, r0 Structure, and ab initio Calculations for Trimethylphosphine.

Reactions involving fluoride ion part 9, syntheses involving octafluoroisobutene

The far infrared spectrum of 1-butyne (ethyl acetylene) has been recorded in the gas phase from 370 to 40 cm −1 with a resolution of 0.1 cm −1 . The skeletal bending fundamental transitions ν 23 ( a ″) and ν 15 ( a ′) give strong bands at 343.6 and 196.5 cm −1 , respectively, showing detailed rotational structure. Transitions of the torsional mode, ν 24 ( a ″), are assigned to prominent Q spikes superimposed on the ν 15 band at 212.8 and 201.5 cm −1 . From these data the coefficients of the periodic potential function are calculated to be 1060 and −30 cm −1 for the V 3 and V 6 terms, respectively.

Torsional Transitions and Barrier to Internal Rotation of 1-Butyne

The geometrical structure of HCCNO has been calculated using ab initio SCF and GVB methods. Since it has not yet been prepared, attempts are made to predict spectroscopic constants related to its microwave, infrared and visible absorption spectra.

The structure of nitrosoacetylene by ab initio methods

Simple organocopper reagents are shown to undergo anti-stereoselective 1,4-addition to menthyloxy-substituted lactone 1 in the presence of BF3·OEt2; the Lewis acid causes partial epimerisation of the acetal centre after conjugate addition. Enolate alkylation of the adducts leads to di- and trisubstituted lactones that are converted, in favourable cases, into di- and trisubstituted cyclopentenones.

Stephen Bell

Papers

Microwave Spectrum, r0 Structure, and ab initio Calculations for Trimethylphosphine.

Reactions involving fluoride ion part 9, syntheses involving octafluoroisobutene

Torsional Transitions and Barrier to Internal Rotation of 1-Butyne

The structure of nitrosoacetylene by ab initio methods

Conjugate Addition of Organocopper Reagents to γ-Alkoxybutenolides and Application to the Synthesis of Non-racemic Alkyl Cyclopentenones.