Atoms In Different States Research Articles

Precise ab initio calculations of the 3d transition-metal clusters: Sc2

The ground ${}^5\Sigma _u^ -$5Σu− state of Sc2 was studied by the valence multireference configuration interaction method with single and double excitations plus Davidson correction (MRCISD(+Q)) at the complete basis set limit. The calculations were made under C2v symmetry restrictions, which allowed us to obtain at the dissociation limit the Sc atoms in different states (in all previous studies of Sc2 the D2h symmetry group was employed). From the Mulliken population analysis and energy calculations follows that in the ground state Sc2 dissociates in one Sc in the ground state and the other in the second excited quartet state, 4Fu. The corrected parameters of the ground potential curve are the following: Re = 5.2 bohr, De = 50.37 kcal/mol, and ωe = 234.5 cm-1. The dissociation energy in respect to the dissociation on two Sc in the ground states was estimated as De = 9.98 kcal/mol.

Matrix effects on the mobility of oxygen atoms in different states

The trapping site structures for ozone molecules isolated in Xe matrices are simulated by a technique of time-going-backwards, showing that single substitutional sites are the most probable. Based on this understanding, molecular dynamics simulations of ultraviolet photolysis of O3 molecules in Xe matrices are carried out for various trapping sites for temperatures of 10, 20, and 30 K. By examining thousands of trajectories, we found that the photolysis quantum yield in Xe matrices is about ten times higher than that in Ar matrices, and solid Xe can serve as atomic sieve for selecting oxygen atoms in the D1 state. Our theoretical results are essentially in agreement with the available experimental data.

Critical study of photodetachment of H- at energies up to the n=4 threshold.

We apply the close-coupling method in terms of the hyperspherical coordinates to the two-electron system H[sup [minus]]. A two-dimensional matching procedure is used to connect the close-coupling wave function to an independent-electron wave function in the asymptotic region. The latter is described as the wave function of a detached electron moving in a dipole potential field of the neutral hydrogen atom. The total phbotodetachment cross sections and the partial cross sections for the production of the H atoms in different states [ital n] are calculated up to the [ital n]=4 hydrogenic threshold. The results obtained in the length and acceleration forms agree within about three significant figures. The magnitude and shape of the [sup 1][ital P[ital o]] shape resonance just above the [ital n]=2 threshold are found to depend sensitively on the initial-state wave function. This appears to be one of the reasons for a disparity among the cross sections in the literature. The present result improves greatly on the existing computational results. The relative magnitudes of the partial cross sections for the production of H ([ital n]=1,2,3) atoms below the [ital n]=4 threshold are substantially different from the only previous results of the eigenchannel [ital R]-matrix calculations [H. R.more » Sadeghpour, C. H. Greene, and M. Cavagnero, Phys. Rev. A 45, 1587 (1992)]. The present results on both partial and total cross sections are in excellent agreement with experiments.« less

Dispersion coefficients for atoms in different states

A formalism allowing the calculation of dispersion coefficients between atoms in different excited states is presented. The validity of the integral transformation involving dynamical polarizabilities of each atom at imaginary frequencies is discussed and for this case a partition of the second order energy which allows a partial separation into single centre contributions is proposed. With respect to the interaction of ground state atoms a new contribution, the dynamic induction due to the allowed downward transitions, appears. The C 6 coefficients of H1s + H2s , H1s + H2p and H2s + H2s are calculated exactly. Approximate formulae are proposed and discussed. Upper and lower bounds are calculated by the method of Padé approximant for the interaction of excited hydrogen with ground state rare gas atoms.

THE PROCESS OF DECOMPOSITION OF MARTENSITE DURING THE FIRST STAGE OF TEMPERING

The process of decomposition of supersaturated tetragonal martensite during the first stage of tempering is investigated by considering the characteristics of motion of a carbon atom from one interstitial position to another within the martensite matrix. It is evident that not all the carbon atoms take part simultaneously in the process of precipitation, some remain in solution for a longer time, others shorter, some mobile, others stationary. By assuming that each transition from one state of motion to another has a definite probability, which is independant of time and carbon concentration but dependant on temperature and the nature of crystalline matrix, it can be shown that an isothermal decomposition curve can be expressed as a series with exponential terms, the coefficients of which are related to the distribution of carbon atoms in different states of motion. The agreement between this expression and the existing experimental data is satisfactory. The general tendancy of the variation of the coefficients with temperature is just what should be expected.

Aspects of hybridization

It has been shown that the pairing theory of orbital hybridization accounts satisfactorily for the variations which are observed in the properties of C-H bonds. Since heteropolar effects are in the opposite directions to the effects described, it is concluded that hybridization influences the properties of predominantly covalent bonds to a greater extent than do differences in electronegativity. The extent of second-order hybridization in the molecules CH, NH and OH has been dealt with in the light of this analysis. The consequences of the electronegativity concept have been examined on the basis of a generalized atomic orbital approximation. In particular, variations of the electronegativity of the carbon, nitrogen and oxygen atoms in different states of hybridization have been analyzed. The idea of 'lone' electrons has been formalized and the results of this definition have been discussed. Finally, the effects of orbital hybridization on the dipole moments and nuclear quadrupole coupling constants of molecules have been considered.

Activation Energies for Reactions of Atoms in Different States

A slight modification of Eyring's method enables the activation energy for the reaction of iodine monochloride with normal or with excited chlorine atoms to be calculated. The calculations indicate that normal chlorine atoms are much more reactive with respect to iodine chloride than are chlorine atoms excited to the 2P½ state. Experimental evidence supporting these calculations is obtained from the results of Rollefson and Lindquist with mixtures of hydrogen, chlorine and iodine monochloride. In the modified method, the atomic interactions—which give rise to the activation energy—are obtained from the potential energies of those molecular states which may be adiabatically formed from atoms in the particular electronic states to be considered.

Some Relations between the Optical Spectra of Different Atoms of the same Electronic Structure. II. Aluminium-like and Copper-like Atoms

The relevant results from the writer's previous paper on the relation between spectra of atoms of different atomic structure are summarised.For non-penetrating orbits no new theoretical results are obtained, and there are few known spectra (other than those of lithium-like or sodium-like atoms already treated in the first paper) on which to test the relations previously obtained. Values of the polarisability for the A1+ and Si++ ions are calculated from terms of Al I and Si II respectively corresponding to non-penetrating orbits, and are shown to be very much greater than the values of the polarisability of the neon-like ions Al+++ and Si++++.The main new results are those for penetrating orbits. Assuming a central field of force, it is shown that the quantum defect q for such an orbit can be expressed as the sum of contributions from the electrons in groups of core orbits of different principal quantum number n, and further that if for a given atom in different states of ionisation corresponding orbits of the series electron are compared, the contribution to q from a set of core orbits of given n is very nearly independent of the degree of ionisation so long as the number of electrons in core orbits in the group remains the same. It follows that, if q is the quantum defect for a term of the spectrum of an atom core charge C, the core of which contains SM orbits of principal quantum number M and none of higher quantum number, and q″ is the quantum defect for the corresponding term in the spectrum of the atom of the same element with core charge C + sM, which differs from the atom of core charge C only in lacking the core orbits of principal quantum number M, then q −; q″ is approximately the contribution from the core orbits of principal quantum number M to the quantum defect for the term of the atom core charge C.Further, it is shown that if corresponding terms of different atoms of the same electronic structure are compared, then for large values of C the contribution to q from any group of core orbits should tend asymptotically to be proportional to the average time mean radius of these orbits, and its reciprocal should tend asymptotically to be linear in C.Somewhat similar relations are obtained for the quantity Q = dq/d (ν/R) which measures the variation of quantum defect within a sequence.These theoretical results, and in particular the result that l/(q − q″) should tend asymptotically to be proportional to C, are compared with the values of q deduced from the terms of such observed spectra of aluminium-like and copper-like atoms as are available, and it is found that though the theoretical relations are only established as asymptotically true for large C, there is a considerable measure of agreement with spectra for small values of C, which are the only ones which can be observed.