A general procedure is presented for generating one-electron integrals over any arbitrary potential operator that is a function of radial distance only. The procedure outlines that for a nucleus centered at point C integrals over Cartesian Gaussians can be written as linear combinations of 1-D integrals. These Cartesian Gaussian functions are expressed in a compact form involving easily computed auxiliary functions. It is well known that integrals over the Coulomb operator can be expressed in terms of F,(T) integrals, where INTRODUCTION Methods of evaluation of one-electron integrals overCartesian Gaussian functions x : ya Z y exp( -aAri) and the Coulomb potential operator V(r) a r -l are known in the quantum chemistry Formu& for other one-electron integrals over various operators have also appeared in the literature. In addition to these integrals and operators, the nuclear attraction one-electron integrals over the inversesquare distance and Yukawa potential operator^^-'^ V(r) a (r-z) and (exp( -r/u))/(r/a), respectively, are of interest to us here at CRDEC and other laboratories. Kahn et a1. ' and McMurchie and Davidson2 (MD) effectively used the inverse-square distance potential operator in obtaining ub initio effective core potentials. The Yukawa operator is a good descriptor of the radial part of the weak interaction. Computer codes to generate the integrals over the inverse-square distance and Yukawa potential operators are not readily available. Therefore, we set *Author to whom all correspondence should be addressed.out to obtain their explicit formulae solutions and develop the necessary software for numerical computation. A general procedure is presented here for generating one-electron integrals over any arbitrary potential operator that is a function of only the orbital electron-nucleus distance. The next section is a discussion of the necessary background information including the methodology developed by MD. MD proposed to use the Hermite Gaussian functions as the intermediaries for molecular integrals over Cartesian Gaussian functions. The differential relation of the Hermite Gaussian functions led to simple expressions for molecular integrals over the Hermite Gaussian functions. These integrals can be expressed in compact form involving easily computed auxiliary functions and recursion relations. Further, integrals over higher angular momentum functions are written as derivatives of integrals over S-functions with respect to small displacements of the nuclei. The procedure outlined in this work can be considered an extension of that proposed by MD. The third section contains the results of the proposed procedure applied to the evaluation of an arbitrary operator V(r) over S-type
Artificial neural network systems were built for detecting amino acids, sugars, and other solid organic matter by pattern recognition of their polarized light scattering signatures in the form of a Mueller matrix. Backward-error propagation and adaptive gradient descent methods perform network training. The product of the training is a weight matrix that, when applied as a filter, discerns the presence of the analytes on the basis of their cued susceptive Mueller matrix difference elements. This filter function can be implemented as a software or a hardware module to a future differential absorption Mueller matrix spectrometer.
We treat infrared patterns of absorption or emission by nerve and blister agent compounds (and simulants of this chemical group) as features for the training of neural networks to detect the compounds' liquid layers on the ground or their vapor plumes during evaporation by external heating. Training of a four-layer network architecture is composed of a backward-error-propagation algorithm and a gradient-descent paradigm. We conduct testing by feed-forwarding preprocessed spectra through the network in a scaled format consistent with the structure of the training-data-set representation. The bestperformance weight matrix (spectral filter) evolved from final network training and testing with software simulation trials is electronically transferred to a set of eight artificial intelligence integrated circuits (ICs') in specific modular form (splitting of weight matrices). This form makes full use of all input-output IC nodes. This neural network computer serves an important real-time detection function when it is integrated into pre- and postprocessing data-handling units of a tactical prototype thermoluminescence sensor now under development at the Edgewood Research, Development, and Engineering Center.
An active spectrophotopolarimeter sensor and support system were developed for a military/civilian defense feasibility study concerning the identification and standoff detection of biological aerosols. Plumes of warfare agent surrogates gamma-irradiated Bacillus subtilis and chicken egg white albumen (analytes), Arizona road dust (terrestrial interferent), water mist (atmospheric interferent), and talcum powders (experiment controls) were dispersed inside windowless chambers and interrogated by multiple CO(2) laser beams spanning 9.1-12.0 microm wavelengths (lambda). Molecular vibration and vibration-rotation activities by the subject analyte are fundamentally strong within this "fingerprint" middle infrared spectral region. Distinct polarization-modulations of incident irradiance and backscatter radiance of tuned beams generate the Mueller matrix (M) of subject aerosol. Strings of all 15 normalized elements {M(ij)(lambda)/M(11)(lambda)}, which completely describe physical and geometric attributes of the aerosol particles, are input fields for training hybrid Kohonen self-organizing map feed-forward artificial neural networks (ANNs). The properly trained and validated ANN model performs pattern recognition and type-classification tasks via internal mappings. A typical ANN that mathematically clusters analyte, interferent, and control aerosols with nil overlap of species is illustrated, including sensitivity analysis of performance.
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