Jack Simons

Passing the one-billion limit in full configuration-interaction (FCI) calculations

Abstract Full configuration-interaction calculations have been carried out using more than one-billion determinants. Such large eigenvalue calculations are possible because of advances in the direct CI technology and in the iterative technique used to solve the eigenvalue equations. The CPU time per direct CI iteration varies approximately linearly with the dimension of the matrix from one million to more than one billion. One direct CI iteration is found to take about 1.2-1.4 min per million determinants on an IBM 3090/VF.

Getting into shape : Conformational and supramolecular landscapes in small biomolecules and their hydrated clusters

The last few years have seen a very rapid growth in understanding the influence of non-bonded, particularly hydrogen-bonded interactions, on the shapes and conformations of flexible molecules, including those of pharmacological or biological importance, and of the supramolecular structures of their hydrated clusters. This has come about through the combination of a wide range of newly developed spectroscopic strategies, many of which are laser-based, coupled with powerful and widely available ab initio codes for structural computation. The consequent rapid growth of a new link between the worlds of chemistry and biophysics is surveyed in a review which introduces the range of present strategies, their origins, and their application to studies of neutrotransmitters, amides and peptides, amino acids and nucleic acid bases. It concludes with a prospectus for the future.

First experimental photoelectron spectra of superhalogens and their theoretical interpretations

Photoelectron spectra of the MX2− (M=Li, Na; X=Cl, Br, I) superhalogen anions have been obtained for the first time. The first vertical detachment energies (VDEs) were measured to be 5.92±0.04 (LiCl2−), 5.86±0.06 (NaCl2−), 5.42±0.03 (LiBr2−), 5.36±0.06 (NaBr2−), 4.88±0.03 (LiI2−), and 4.84±0.06 eV (NaI2−), which are all well above the 3.61 eV electron detachment energy of Cl−, the highest among atomic anions. Experimental photoelectron spectra have been assigned on the basis of ab initio outer valence Green function (OVGF) calculations. The corresponding theoretical first VDEs were found to be 5.90 (LiCl2−), 5.81 (NaCl2−), 5.48 (LiBr2−), 5.43 (NaBr2−), 4.57 (LiI2−), and 4.50 eV (NaI2−), in excellent agreement with the experimental values. Photodetachment from the top four valence molecular orbitals (2σg22σu21πu41πg4) of MX2− was observed. Analysis of the polestrength showed that all electron detachment channels in this study can be described as primarily one-electron processes.

Comparison of the convergence characteristics of some iterative wave function optimization methods

The convergence properties of several iterative methods for the optimization of orbitals and configuration mixing coefficients in multiconfigurational electronic wave functions are compared. All of the iterative methods considered here are derived from corresponding approximate energy expressions. These energy expressions are discussed within the context of their suitability for the calculation of noninfinitesimal wave function corrections. A method based on the partitioned orbital Hessian matrix and which uses an approximate super‐CI secular equation for the wave function corrections is shown to posses second‐order convergence and to have the largest radius of convergence of the methods analyzed in detail in this work for several molecular examples. Particular attention is given to convergence properties for excited states, where the differences between these methods are most significant.

Ab initio analytical molecular gradients and Hessians

Molecular gradients and Hessians have been derived for MCSCF, CI, coupled cluster, and Mo/ller–Plesset wave functions. In deriving the gradients and Hessians, atomic orbital basis set effects have been incorporated into the finite basis Hamiltonian, and unitary exponential operators have been used to determine the wave function’s configuration and orbital responses. The gradients and Hessians are expressed in terms of products of configuration and orbital responses and matrices of the same form as the gradient and Hessian matrices appearing in energy and wave function optimizations. The molecular gradients and Hessians have also been cast into forms that are computationally very tractable.

Relative stabilities of fullerene, cumulene, and polyacetylene structures for Cn:n=18-60

The relative stabilities of closed fullerene, cumulene, and polyacetylene carbon structures, as well as the cohesive energies for clusters of size n=18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 50, and 60 have been examined using ab initio self‐consistent‐field and second‐order Mo/ller–Plesset perturbation theory and analytical derivative geometry optimization methods. These geometries and relative stabilities constitute the primary findings of this work. All calculations were carried out using the disco program with atomic basis sets derived from van Duijneveldt’s carbon (6s,3p) primitive orbital basis set, contracted to [3s2p]. For n≥32, the fullerenes are predicted to be the most stable, and their cohesive energies are predicted to increase monotonically as n varies from 24 to 60. The optimized geometries obtained here are very near those obtained earlier by others for the few species where such data exist. Based on earlier work employing larger atomic orbital bases, the relative energies of the fullerene s...

Conformational landscapes of aromatic amino acids in the gas phase: Infrared and ultraviolet ion dip spectroscopy of tryptophan

The conformational structures of tryptophan, isolated in the gas phase, have been assigned by combining the results of ultraviolet hole-burning and infrared ion dip spectroscopy with the predictions of ab initio calculations conducted at the MP2/6-311 + G(d,p)//B3LYP/6-31 + G(d) levels of theory. As in phenylalanine, the most strongly populated, and lowest energy conformer presents a folded alanyl side chain that is stabilised by a ‘daisy chain’ of hydrogen-bonded interactions. These link the acidic proton, the amino group and the indole ring. There is a further interaction between the carbonyl oxygen and the neighbouring CH group on the pyrrole ring. A quantitative evaluation of the dipole–dipole interactions between the alanyl side chain and the indole ring in the 1La and 1Lb electronic states does not support the suggestion of electronic state mixing. In particular it casts doubt on the assignment of the fluorescence of the most stable, ‘special’ conformer to emission from the 1La state.

Applications of multiconfigurational coupled‐cluster theory

A coupled‐cluster method which permits the use of multiconfiguration reference states has recently been developed in this laboratory. In the present work, it is applied to several states of H2 (1Σg+), Li(2S), HeH2(1A1), and CH2(3B1,1A1), which include both open and closed shells. These applications are made within an approximation in which the cluster operator (T) is truncated at T2, T≃T1+T2 and the expansion of e−THeT is truncated at the double‐commutator level. For cases where a single configuration function ceases to be a good starting point, it is found that a single configuration based truncated coupled‐cluster procedure may exhibit serious difficulties. In such cases we find it possible to choose a multiconfigurational reference state for which our coupled‐cluster procedure converges reasonably rapidly. This paper contains several illustrations of such convergence characteristics.

A unitary multiconfigurational coupled‐cluster method: Theory and applications

A unitary wave operator exp(G) is used to relate a multiconfigurational reference function Φ to the full, potentially exact, electronic eigenfunction Ψ=exp(G)Φ. If the reference function Φ is of a generalized complete‐active‐space (CAS) form, then the energy, computed as 〈Φ‖exp(−G)H exp(G)‖Φ〉 is size extensive; here H is the full N‐electron Hamiltonian. The Hausdorff expansion of exp(−G)H exp(G) is truncated at second order as part of our development. The parameters which appear in the cluster operator G are determined by making this second‐order energy stationary. Applications to the widely studied H2O (at the double zeta basis level) and lowest and first excited 1A1 states of BeH2 are performed in order to test this method on problems where ‘‘exact’’ results are known.

Sugars in the gas phase. Spectroscopy, conformation, hydration, co-operativity and selectivity

The functional importance of carbohydrates in biological processes, particularly those involving specific molecular recognition, is immense. Characterizing the three-dimensional structures of carbohydrates and glycoconjugates and their interactions with other molecules, particularly the ubiquitous solvent, water, are key starting points on the road towards the understanding of these processes. The review introduces a new strategy, combining electronic and vibrational spectroscopy of mass-selected carbohydrate molecules and their hydrated (and also protonated) complexes, conducted under molecular beam conditions, with ab initio computation. Its early successes have revealed a uniquely powerful means of characterizing carbohydrate conformations and hydrated structures, the hydrogen-bonded networks they support (or which support them) and the specificity of their interactions with other molecules. The new information, obtained in the gas phase, complements that provided by more ‘traditional’ condensed phase methods such as NMR, X-ray diffraction, molecular mechanics and molecular dynamics calculations. The review concludes with a vision of the challenges and opportunities offered by applications of molecular beam spectroscopy and their relevance in a biological context. Contents PAGE 1.  Preamble 490 2. Sweetness and light: Sugars in the gas phase 492 3. Experimental and computational strategies 495 4. The conformational landscapes of some key monosaccharides: glucose, galactose, mannose, fucose and xylose 498 4.1. Notation 498 4.2. Glucose, galactose and mannose 499 4.3. Fucose and xylose 503 5. Probing the glycosidic linkage: lactose and glycan ‘building blocks’ 504 5.1. Notation 506 5.2. Lactose 506 5.3. Mannose disaccharides 508 6. Adding water to sugar: hydrogen-bonding, co-operativity and selectivity 512 6.1. Notation 512 6.2. Mono-hydrated complexes: glucose, galactose and mannose 512 6.3. Co-operativity and conformational selectivity 516 6.4. Mono-hydrated complexes: xylose and fucose 519 6.5. Some concluding remarks 521 7. Using sugars: imino sugars and peptide mimics 522 7.1. Sugar mimics: imino sugars 522 7.2. Mimicking peptide secondary structure: carbopeptoids 524 8. Challenges and opportunities 527 Acknowledgements 529 References 530