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and references therein. This point was first driven home to the author in the context of interactions leading to fractional charges and fractional quantum Hall effect. A point that requires clarification (at least to the present author) is whether atomic Orbitals can ever be used for the description of molecular states when we cross a phase boundary between atomic and bonding states. Because of this, a formal connection between the present model and existing textbook level theories for chemical bonding such as valence band and molecular orbital descriptions, is not attempted. It is in any case seemingly unnecessary besides being beyond the author's present competence. The density functional approach need not suffer from such a philosophical problem
-
See Laughlin, R. B. Rev. Modem Phys. 1999, 71, 863 and references therein. This point was first driven home to the author in the context of interactions leading to fractional charges and fractional quantum Hall effect. A point that requires clarification (at least to the present author) is whether atomic Orbitals can ever be used for the description of molecular states when we cross a phase boundary between atomic and bonding states. Because of this, a formal connection between the present model and existing textbook level theories for chemical bonding such as valence band and molecular orbital descriptions, is not attempted. It is in any case seemingly unnecessary besides being beyond the author's present competence. The density functional approach need not suffer from such a philosophical problem.
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and references therein
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The classical Bohr approach to the H: molecule is to extend the one-nucleus two-electron model for the He atom to the two-nuclei-twoelectron hydrogen molecule and end up with singular, nonintegrable, and multidimensional Hamiltonian) See A. Lopez-Castillo, A. Phys. Rev. Letts. 1996, 77, 4516 and references therein).
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In homonuclear M-M bonds, the charge-transfer states are degenerate with respect to the direction of charge transfer. Because of this there is likely to be a rapid fluctuation between the two possible charged configurations of the atoms constituting the bond. As long as the fluctuation time is fast compared to the measurement time, the measured chargedifference on the two atoms will average out to zero. The length scales in the bonding direction remain unaffected, however. Such an averaging in intermediate valence systems is discussed in terms of the homogeneous mixed valence systems in condensed matter studies (For a review see Lawrence, J. M.; Rizeborough, P. S.; Parks, R. D. Rep. Prog. Phys. 1981, 44, 1.
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note
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This discrepancy is expected if we consider mixing in of higher principal quantum number Bohr states (see ref 12). Such effects may be included by considering the local effective dielectric constant, f H-H, of the bond in the hydrogen molecule, to be greater than unity, and consider only the ground state. In this particular case, we would require the effective dielectric constant, εH-H ≈ 0.74/0.71 ≈ 1.04, at room temperature.
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85037465842
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note
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The constraints for the minimization of energy is here taken in the context of chemical bond and its equilibrium distance, req, such that at this equilibrium separation the density is the correct density, p(eq).
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In the density functional theory (March, N. H. J. Phys. Chem. 1982, 2262.
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note
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univ = 0 condition.
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79
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85037458093
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note
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It has to be noted that in such spin-density functional formalisms (see ref 42) there is a sum rule arising out of charge conservation that requires the exchange correlation hole to correspond to the removal of one electron charge. The expression of the intemuclear distance as a sum of radii associated with two integral charges of opposite sign, is consistent with this picture.
-
-
-
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80
-
-
85037484003
-
-
note
-
It follows from the notes in ref 40 that when V(r) = 0 = μ, the exchange and correlation are balanced out by the kinetic energy term. The conversion of spin to charge by pairing of electrons results in the residual interactions being only electrostatic in nature, with the cancellation of exchange and correlation terms by the kinetic energy term. This cancellation is reminiscent of the early, and trend-setting, theorem (Phillips, J. C.;
-
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82
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0001190944
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involving cancellation of the potential energy terms of core states by the kinetic energy terms
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Cohen, M. H.; Heine, V. Phys. Rev. 1961, 722, 1821) involving cancellation of the potential energy terms of core states by the kinetic energy terms.
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Cohen, M.H.1
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83
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for example, (a) The distinction between spin-pairing and charge separation is similar to the proposal of covalent and zwitterion formation
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See Salem, L.; Rowland, C. Angew. Chem., Int. Ed. Eng. 1972, 77, 92, for example, (a) The distinction between spin-pairing and charge separation is similar to the proposal of covalent and zwitterion formation.
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Salem, L.1
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84
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85037449559
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note
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(b) It is well known that conservation of angular momentum may be violated when there is spin-orbit coupling. Our argument is the reverse of this, since we claim that spin-charge conversion is not favored because strict angular momentum conservation may be violated.
-
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85
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85037447307
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-
A〉, is averaged to zero, within the time scales of the exchange interaction.
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A〉, is averaged to zero, within the time scales of the exchange interaction.
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Magnetism in Solids
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Martin, D.H.1
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0003004585
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See Feynman, R. P. The Feynman Lectures on Physics, Quantum Mechanics, (Indian Edition); Addison-Wesley Publishing Co.: Reading, MA, 1965; Vol. II, pp 35:3;
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See also Batelaan, H.; Gay, T. J.; Schwendiman, J. J. Phys. Ref. Lett. 1997, 79, 4517.
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0003998388
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Weast, R. C., Ed.; CRC Press: Boca Raton
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Interatomic distances were obtained from CRC Handbook of Chemistry and Physics, 61st ed., Weast, R. C., Ed.; CRC Press: Boca Raton, 1980; F-221.
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CRC Handbook of Chemistry and Physics, 61st Ed.
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100
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84957166742
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Although Mott addressed himself to the many-body problem of the insulator-metal transition, the arguments involved the effects of screening of a single Bohr atom.
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Mott, N. F. Proc. Cambr. Philos. Soc. 1936, 32, 281. Although Mott addressed himself to the many-body problem of the insulator-metal transition, the arguments involved the effects of screening of a single Bohr atom.
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Mott, N.F.1
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108
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85037487196
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note
-
The use of a close-packed volume fraction is important as it emphasizes the points of closest contact between two lines. The largest number of such lines, for a given size of the Bohr-like atom, is obtained from a close-packing model.
-
-
-
-
109
-
-
85037463584
-
-
note
-
There is no requirement that the bound electron pair is localized in a particular region in space or is even real. The only requirement is that the expression for the distance is obtained from a description equivalent to a screened metallic core and a bound electron pair, the length scales of the bound pair being described by a Bohr-like model (Section II).
-
-
-
-
112
-
-
0000125122
-
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who first stressed the necessity of analyzing the pair density as the simplest theoretical quantity describing the behavior of an electron pair in microscopic systems.
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Bader, R. F. W.; Stephens, M. E. Chem. Phys. Lett. 1974, 26, 445) who first stressed the necessity of analyzing the pair density as the simplest theoretical quantity describing the behavior of an electron pair in microscopic systems.
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Bader, R.F.W.1
Stephens, M.E.2
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114
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85037446424
-
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note
-
± to increase with increasing polarizability or increasing local dielectric constant, CH-H, of the bonding pair of electrons. A similar increase in the dielectric constant could reduce the magnitude of the attractive terms of the core, so that the orbital radius may actually increase with pressure.
-
-
-
-
116
-
-
0000084778
-
-
references therein for a discussion on physical hardness
-
The principle of maximum mechanical hardness, which requires simply that mechanical hardness be related to equilibrium interatomic distances and that the hardness, is related to the extent of shortening of this distance for a given external field. This problem is consistent with the expectation that the stabilization energy will be inversely related to the ssinteratomic separation. See also Pearson, R. G. J. Chem. Ed. 1999, 76,267 and references therein for a discussion on physical hardness.
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Pearson, R.G.1
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0002544706
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It is also consistent with the philosophy of Pearson's hard-soft-acid-base principle, which, of course, forms a cornerstone of some of the modem approaches in chemistry. There has been some debate (Sebastian, K. L. Chem. Phys. Lett. 1994, 231, 40.
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Chattaraj, P. K.; Liu, G. H.; Parr, R. G. Chem. Phys. Lett. 1995, 237, 171)
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3342943865
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on the validity of the proof of the principle given by Parr and Chattaraj (Parr, R. G.; Chattaraj, P. K. J. Am. Chem. Soc. 1991, 113, 1854.
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85037469056
-
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note
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univ = 0, in Section II, satisfies the conditions assumed by Parr and Chattaraj.
-
-
-
-
129
-
-
85037479781
-
-
note
-
Pauling's definition (see ref 14) of electronegativity is based on the observation of an extraionic energy term, A, which contributes to an additional bond energy of heteronuclear bonds. A is given by the difference between the actual bond energy D(M-X) of the heteronuclear bond and the arithmetic mean of the bond energies D(M-M) and D(X-X) of the corresponding homonuclear bonds Δ = O(M-X) - 0.5{D(M-M) + D(X-X). In such a definition, Δ is in the exothermic direction.
-
-
-
-
131
-
-
85037474652
-
-
note
-
univ, = 0 state. A quantitative relation between length scales describing ground-state properties and heat of formation is not anticipated.
-
-
-
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134
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0022801296
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Cohen, M. L. Science 1986, 234, 549.
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Science
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Cohen, M.L.1
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138
-
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85037490491
-
-
to be published. These relationships are applicable to binary compounds of multivalent metals when one considers the heat of formation per atom of the more electronegative element X. These equations, in their present form, are obviously not applicable to compounds of hydrogen.
-
Ganguly, P., to be published. These relationships are applicable to binary compounds of multivalent metals when one considers the heat of formation per atom of the more electronegative element X. These equations, in their present form, are obviously not applicable to compounds of hydrogen.
-
-
-
Ganguly, P.1
-
139
-
-
33645906046
-
-
Dean, J. A., Ed.; McGraw-Hill: New York; Chapter 9
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X, have been taken mainly from; Lange's Handbook of Chemistry, 13th ed.; Dean, J. A., Ed.; McGraw-Hill: New York; 1985; Chapter 9.
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Lange's Handbook of Chemistry, 13th Ed.
-
-
-
144
-
-
85037458475
-
-
note
-
G = 0.32 au) which seemingly contradicts the results of Pauling's electronegativity scales. Similarly, the PMMH principle (see ref 17) requires H to be the more electronegative atom in all M-H bonds. This aspect requires further clarification and will be discussed in a separate communication. Equations 33 and 34 are meant for illustrative purposes at the moment.
-
-
-
-
145
-
-
85037455771
-
-
note
-
X.
-
-
-
-
146
-
-
85037483616
-
-
note
-
s(X). For these large differences, the repulsive interactions between the M atoms may become important. At the same time, the distance between the metal atoms becomes comparable to that in the elements themselves. This could lead to direct M-M interactions, which eventually leads to a reduction in the value of the heat of formation which is referenced to the standard elemental state.
-
-
-
-
147
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0004264260
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Academic Press: New York
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See, for example, Lowe, J. P. Quantum Chemistry, 2nd ed.; Academic Press: New York, 1993; p 376.
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Lowe, J.P.1
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85037473556
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th ed.; John Wiley & Sons: New York, when ε= 1.
-
th ed.; John Wiley & Sons: New York, 1971; pp 612) when ε= 1.
-
(1971)
, pp. 612
-
-
-
151
-
-
85037449292
-
-
note
-
l/2. The explanation of the shortening of multiple bonds as well as rationalizations of electronegativity scales will follow in another communication, once the premises of this communication find some acceptance.
-
-
-
|