Remarks on the use of approximate wavefunctions for the second-order perturbation energy.
Approximate ground state wave functions used in calculation of interaction energies by second- order perturbation theory
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Approximate ground state wave functions used in calculation of interaction energies by second- order perturbation theory
Spin-spin interaction energy for large separations of two ground state hydrogen atoms
Signs of phosphorus-fluorine nuclear resonance spin-spin coupling constants
Spin-spin coupling constants from perturbation- variation and first order perturbed trial function assumptions
Si and S ion oscillator strengths for resonance lines in solar spectrum, discussing spin-spin and spin-other orbit interactions
NMR spin-spin coupling constants between vinyl protons in cyclopentadiene, 1,3-cyclohexadiene and 1-3-cyclooctadiene from spectrum analysis
The hfs of five rotational transitions of furan (C4H4O) has been resolved with a beam maser spectrometer with a resolution of about 500 Hz. All significant details of the observed structure are accounted for by the spin-spin and spin-rotation interactions of the four protons, and the coupling constants for these interactions have been determined to high precision. In particular, the diagonal elements of the spin-rotation tensors have been determined to about 10 Hz.
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The FP-INDO (finite perturbation-intermediate neglect of differential overlap) method is used to calculate the H-H, C-H, and C-C coupling constants in hertz for molecules of six different benzenoid hydrocarbons: benzene, naphthalene, biphenyl, anthracene, phenanthrene, and pyrene. The calculations are based on both the actual and the average molecular geometries. It is found that only the actual molecular geometries can always yield the correct relative order of values for the H-H coupling constants. For the calculated C-C coupling constants, as for the calculated C-H coupling constants, the signs are positive (negative) for an odd (even) number of bonds connecting the two nuclei. Agreements between the calculated and experimental values of the coupling constants for all six molecules are comparable to those reported previously for other molecules.
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A constructive scheme has been devised to enable mapping of any quantum computation into a spintronic circuit in which the computation is encoded in a basis that is, in principle, immune to quantum decoherence. The scheme is implemented by an algorithm that utilizes multiple physical spins to encode each logical bit in such a way that collective errors affecting all the physical spins do not disturb the logical bit. The scheme is expected to be of use to experimenters working on spintronic implementations of quantum logic. Spintronic computing devices use quantum-mechanical spins (typically, electron spins) to encode logical bits. Bits thus encoded (denoted qubits) are potentially susceptible to errors caused by noise and decoherence. The traditional model of quantum computation is based partly on the assumption that each qubit is implemented by use of a single two-state quantum system, such as an electron or other spin-1.2 particle. It can be surprisingly difficult to achieve certain gate operations . most notably, those of arbitrary 1-qubit gates . in spintronic hardware according to this model. However, ironically, certain 2-qubit interactions (in particular, spin-spin exchange interactions) can be achieved relatively easily in spintronic hardware. Therefore, it would be fortunate if it were possible to implement any 1-qubit gate by use of a spin-spin exchange interaction. While such a direct representation is not possible, it is possible to achieve an arbitrary 1-qubit gate indirectly by means of a sequence of four spin-spin exchange interactions, which could be implemented by use of four exchange gates. Accordingly, the present scheme provides for mapping any 1-qubit gate in the logical basis into an equivalent sequence of at most four spin-spin exchange interactions in the physical (encoded) basis. The complexity of the mathematical derivation of the scheme from basic quantum principles precludes a description within this article; it must suffice to report that the derivation provides explicit constructions for finding the exchange couplings in the physical basis needed to implement any arbitrary 1-qubit gate. These constructions lead to spintronic encodings of quantum logic that are more efficient than those of a previously published scheme that utilizes a universal but fixed set of gates.