David M. Silver

Many‐body perturbation theory applied to electron pair correlation energies. I. Closed‐shell first‐row diatomic hydrides

Diagrammatic many‐body perturbation theory is formulated through third order and applied to LiH, BH, and HF with various sizes of two‐center Slater orbital basis sets. The most extensive calculations use 46 orbitals to recover 94, 95, and 97% of the experimental correlation energy for the three molecules, respectively, when the perturbation expansion is carried through third order with pair restrictions and including selections of higher‐order diagrams via denominator shifts. A detailed analysis of the ’’pair’’ correlation energies relative to SCF occupied orbitals is given, including both inter‐ and intrapair contributions for the different spin cases.

Blood flow in the human eye

It is widely appreciated that impaired vascular circulation in the eye plays a significant role in the pathology of the retina, the optic nerve and the choroid. Capillary closure, microaneurysm formation, shunts, neovascularization and breakdown of the blood retinal barrier are non-specific responses to ischemia, congestion and thrombosis. Examples include diabetic retinopathy, where the microaneurysms and neovascularization reflect an underlying focal hypoxia and impaired ocular blood flow (Ashton 1953,1969; Davis 1968; Kohner et al. 1969; Gamer & Ashton 1972). Unfortunately, the identification of patients with impaired ocular blood flow, and the assessment of treatments aimed at improving the ocular circulation have been precluded by the absence of a suitable routine measurement of ocular blood flow. This situation is now changing with the recent development of non-invasive procedures for the assessment of ocular blood flow in the retina and ciliary choroidal networks. The non-invasive procedure of laser doppler velocimetry was developed for the measurement of retinal blood flow (Riva & Feke 1981; Riva et al. 1981, 1985). In this procedure the retinal blood flow is derived from the velocity (V) of red cells and the cross sectional area (A) of a given artery or vein; blood flow equals VA (mm3 min-1) for an individual vessel, and the total blood flow is the sum of flows in all the retinal arteries or veins. The mean velocity of blood was measured using a bidirectional laser doppler system and the vessel diameter assessed from monochromatic fundus photographs. In 8 healthy human eyes the average total volumetric flow in the retina was 34 p1 min-1 with a range of 18-44 pl min-I. The values of the retinal blood flow in man are similar to those determined in primate eyes by the radioactive labelled microsphere entrapment procedure, namely 25 If: 9 ~l min-l (Alm & Bill 1973). The non-invasive quantitative assessment of the ciliary choroidal blood flow is based on the analysis of the intraocular pressure (IOP) pulse. The flow of blood into the eye is pulsatile and causes a rhythmic fluctuation of the steady-state IOP. It is the magnitude and the form of the IOP pulse that is used to assess the pulsatile component of ocular blood flow. The high fidelity recording of the IOP that is essential for the evaluation of the pulsatile blood flow (PBF) is obtained with a pneumatic tonometric probe (Langham 1987). In order to quantitate, automate and rapidly analyze the IOP pulsations, the electronic signal from the probe is digitalized and fed into a modified IBM PS2/30 computer. Representative recordings of the IOP in eyes of 4 normal subjects are shown in Fig.1. Each IOP measurement is completed within 10 microseconds and the measurement repeated at intervals of 30 milliseconds, giving a total of 30 IOP readings during each cycle of the IOP. The average of all the individual IOP measurements is the steady state value, Goldmann (1954) recognized the problem of

Iris cross-sectional area decreases with pupil dilation and its dynamic behavior is a risk factor in angle closure.

PurposeTo estimate the change in iris cross-sectional (CS) area with pupil dilation using anterior segment optical coherence tomography comparing eyes with angle closure (AC) to open angle glaucoma (OAG). MethodsSixty-five patients from the Wilmer Glaucoma service, 36 with definite or suspected OAG and 29 with definite or suspected AC, underwent anterior segment optical coherence tomography imaging under 3 conditions (pupil constriction to light, physiologic dilation in the dark, and after pharmacologic dilation). The nasal and temporal iris CS areas were measured with custom software, 3 times in each of 4 meridians. The principal outcome variables were iris CS area and change in iris CS area/mm pupil diameter change. The relation of these parameters to potential variables that would influence iris area was estimated by multivariate regression. ResultsCS area was smaller in eyes with larger pupil diameter, those that had undergone trabeculectomy, and those of European-derived persons (P<0.05 for all in a univariate analysis). In a multivariate model with CS area as the dependent variable, larger pupil diameter (with a 0.19 mm2 decrease in CS area for each 1 mm of pupil enlargement, P=0.0002), and trabeculectomy remained significant factors. In a second multivariate model, AC irides had less change in CS area/mm pupil enlargement than OAG or OAG suspects (P=0.01). Change in iris CS area was essentially complete in 5 seconds (n=10 eyes). ConclusionsThe iris loses nearly half its volume from a pupil diameter of 3 to 7 mm, probably by eliminating extracellular fluid. Smaller iris CS area change with physiologic pupil dilation is a potential risk factor for AC. Dynamic iris CS area change deserves testing as a prospective indicator of AC.

Pressure-volume relation for the living human eye.

PURPOSE The pressure-volume relation for an eye is the mathematical equation that relates changes in intraocular pressure to changes in intraocular volume. This relation is useful for calculating outflow facility from tonography and pulsatile ocular blood flow from intraocular pressure pulsations. The present work develops a new relation by culling together all the published direct manometric rigidity measurements on living human eyes. METHODS A total of 182 data items taken from 21 eyes are available in the 1958-62 literature of Ytteborg, Prijot, Eisenlohr, Langham and Maumenee. The approach was (i) to perform an error analysis based on the various experimental conditions, (ii) to assume general mathematical forms for the relation, (iii) to use least-squares analysis and statistical measures to find the optimal data representation, and (iv) to introduce the total volume of the eye into the formulation. RESULTS A new formula for the pressure-volume relation for the living human eye is derived relating DeltaV, the change in volume, to P, the corresponding intraocular pressure: DeltaV = V (C + C(0) x ln P + C( 1) x P), where V is the volume of the eye, C, C(0) and C(1) are numerical parameters. This equation gives the most statistically significant fit to the experimental data. CONCLUSION The new equation for the pressure-volume relation derived from all the currently available ocular rigidity data on the living human eye gives a larger volume increment for a given increment of pressure than Friedenwalds equation based on measurements performed on cadaver eyes.

Universal atomic basis sets

Abstract A single Slater-orbital basis set, consisting of nine 1s and six 2p functions, is used to calculate matrix Hartree—Fock ground state energies for several light atoms. The resulting energies are compared with the most accurate calculations of these energies obtained using different basis sets individually optimized for each atom.

Reaction paths on the H4 potential energy surface

Portions of the electronic potential energy surface corresponding to various nuclear geometries of the H4 molecular system have been studied. The variational calculations employed double‐zeta basis sets (1s and 1s′ Slater‐type orbitals on each center) to form configuration interaction wavefunctions. At selected points on the surface, the effects of exponent optimization and increased basis set size (1s, 1s′, and 2p orbitals per center) were assessed. A low energy reaction path allowing a bimolecular mechanism for exchange, requiring less energy than a single H2 dissociation, was not found. However, a path leading from trapezoidal to linear structures (and vice versa) was found to offer the possibility of exchange with less than 6 kcal/mole of energy above this dissociation limit.

Diagrammatic perturbation theory: Many‐body effects in the X1Σ+ states of first‐row and second‐row diatomic hydrides

Diagrammatic many‐body perturbation theory is employed in a study of the X1Σ+ states oif first‐ and second‐row diatomic hydrides at their respective equilibrium nuclear separations. All two‐, three‐, and four‐body terms are determined through third‐order in the energy within the algebraic approximation (i.e., parameterization of state functions by expansion in a finite basis). Pade approximants to the energy are constructed. From the first‐order wavefunction rigorous upper bounds to the expectation value of the electronic energy are obtained from the Rayleigh quotient. Two different zero‐order Hamiltonians are used, and the convergence properties of the resulting perturbation expansions are compared. In both schemes three‐ and four‐body terms are significant, having a magnitude that is as much as 24% of the sum of the second‐ and third‐order terms.

Special invariance properties of the [N+1/N] Padé approximants in Rayleigh-Schrödinger perturbation theory

Padé approximants to the electronic energy of atoms and molecules are investigated by using the expansion parameter of Rayleigh-Schrödinger perturbation theory as a formal variable. These problems are characterized by the fact that the exact Hamiltonian is known and, although the Hamiltonian is split into a zero order and a perturbing part, the exact Hamiltonian is recovered when the expansion parameter equals unity. The present study shows that for these problems the sequence of [N+1/N] Padé approximants is special in that, when the expansion parameter is set equal to unity, the numerical value of each of these approximants is invariant to two modifications in the zero-order Hamiltonian; namely, a change of scale and a shift of origin in the zero-order energy spectrum. This suggests that it is the essence of the exact Hamiltonian which produces the final energy result, rather than the arbitrary scaling of the unperturbed Hamiltonian. This formalism is particularly appropriate for ab initio perturbative calculations, where the variational principle cannot be used to determine optimal values for the scale and shift parameters.

Aqueous flow through the iris-lens channel: estimates of differential pressure between the anterior and posterior chambers.

Purpose:To explore the hypothesis that differential pressure between the anterior and posterior chambers arises from the dynamics of aqueous flow across the iris-lens channel. Methods:Navier-Stokes equations of fluid dynamics were derived and evaluated numerically for a viscous homogeneous isotropic fluid (aqueous) passing through the iris-lens channel, which is a spherical disc-shaped region conforming to the lens curvature while maintaining a separation distance (channel height) over a certain disc width (channel length). The effect of iridotomy was assessed using Poiseuille flow dynamics. Results:In the absence of measured values, ranges of anatomic and physiological variables were used for calculations. The magnitude of the posterior to anterior pressure difference was greater with increases in channel length or aqueous flow and with decreases in channel height or pupil diameter. With a nominal channel length of 0.5 mm, aqueous outflow of 2.2 μl/min, and pupil diameter of 1 mm, the pressure difference increased from 0.9 to 10 mm Hg when the channel height decreased from 7 to 3 μm. A channel height of 10 μm or greater reduced the pressure difference below 1 mm Hg for the full range of other channel parameters considered. A 50-μm iridotomy reduced the pressure difference below 1 mm Hg. Conclusions:The flow of aqueous through the iris-lens channel is driven by the pressure differential between the posterior and anterior chambers. Viscous forces within the aqueous govern the magnitudes of the flow resistance and the pressure differential. The geometry and dimensions of a specific iris-lens channel will determine whether the pressure differential is of clinical significance.

Universal basis sets for electronic structure calculations

The concept of a ’’universal’’ basis set for electronic structure calculations is explored by presenting energy results obtained when basis sets are transferred from one atom to another. The calculations are performed using the diagrammatic techniques of many‐body perturbation theory. A single universal basis set is shown to give uniformly accurate descriptions of the matrix Hartree–Fock and correlation energies of the He, Be, and Ne atoms.