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On accuracy of BCS predictions for different classes of superconductors see: (r) B. Chakraverty, Ramakrishnan T., Physica C, 282-287, 290 (1997).
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On the "magic electronic state" in oxocuprates and its connection to Cu-O bond stretching see: (s) Burdett J.K., Inorg. Chem., 32, 3915 (1993).
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In some sense our paper is analogous to the review on periodicity in 120 first-and second-row diatomic molecules, by Boldyrev A.I., Gonzales N. and Simons J., J. Phys. Chem., 98, 9931 (1994).
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Chen, W.22
Wong, M.W.23
Andres, J.L.24
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C.A.C.A.O. (Computer Aided Composition of Atomic Orbitals), A Package of Programs for Molecular Orbital Analysis [PC Beta-Version 5.0, 1998], Mealli C. and Proserpio D.M., with a major contribution by Ienco A., J. Chem. Educ., 67, 399 (1990).
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The reader is referred to several classical texts on vibronic coupling in triatomic and multiatomic molecules, whose importance was brought to our attention by a reviewer: (a) Öpik U. and Pryce M.H.L., Proc. Roy. Soc. A, 238, 425 (1957)
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0001006389
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A dynamic model for mixed-valence compounds
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Lippard S.J. Ed.; John Wiley and Sons: NY
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(f) Wong K. Y. and Schatz P.N., A Dynamic Model for Mixed-Valence Compounds. Progress in Inorganic Chemistry, vol. 28; Lippard S.J. Ed.; John Wiley and Sons: NY 1981; p.369;
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Wong, K.Y.1
Schatz, P.N.2
-
36
-
-
0007344136
-
-
note
-
As shown in Table S2 in Supplement, we could not compute 8 of 100 molecules in this family. The reasons for failure varied: problems with convergence, failures of Coulomb series, and density matrix breaking symmetry problems.
-
-
-
-
37
-
-
0007278835
-
-
note
-
As shown in Table S2 in Supplement, we also could not compute 29 of the additional 240 molecules in this family. The reasons, as mentioned in Ref. 13, varied.
-
-
-
-
38
-
-
0033717885
-
-
(a) Murphy L.R., Meek T.L., Allred A.L. and Allen L.C., J. Phys. Chem. A, 104, 5867 (2000).
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J. Phys. Chem. A
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Murphy, L.R.1
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Allen, L.C.4
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39
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0007287224
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(b) Cao C.Z., Li Z.L. and Allen L.C., Chin. J. Inorg. Chem., 15, 218 (2000). On configuration energies, a modern concept related to electronegativity, see for example:
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Cao, C.Z.1
Li, Z.L.2
Allen, L.C.3
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41
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0034738165
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Mann J.B., Meek T.L., Knight E.T., Capitani J.F. and Allen L.C., J. Am. Chem. Soc., 122, 5132 (2000).
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Mann, J.B.1
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Allen, L.C.5
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50
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0000073570
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(a) Timoten R.S., Seetula J.A., Niiranen J. and Gutman D., J. Phys. Chem., 95, 4009 (1991).
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Timoten, R.S.1
Seetula, J.A.2
Niiranen, J.3
Gutman, D.4
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59
-
-
0007214450
-
-
note
-
The Pauling electronegativity (PEN) has been used in this paper to compute f. Since PEN has formally units of square root of energy, f has units of square root of energy per distance. This might explain why a correlation of f with square root of the force constant (see Fig. 12) is almost linear (square root of force constant also has square root of energy per distance units). There is another electronegativity definition, the Mulliken electronegativity (MEN, expressed in energy units). MEN correlates quite well with PEN for most of elements. f would formally have energy per distance, i.e. force units if one defined f using MEN. Note that we obtained a strongly nonlinear correlation between f and force in Ref. 4.
-
-
-
-
61
-
-
0007213865
-
-
note
-
As far as we know, there is no experimental data available for the symmetric linear radicals investigated in this paper. Such radicals are often not bound, and dissociate to a diatomic and an isolated atom. The species studied here might also be intermediates or transition states between two asymmetric linear, or two symmetric bent minima (these minima would correspond to "real" ground state molecules). Our study is not intended to predict the geometry of molecular radicals, but to discern trends in vibronic coupling.
-
-
-
-
62
-
-
0007272512
-
-
note
-
Dissociation of symmetric linear triatomic proceeds along a combination of antisymmetric and symmetric stretching coordinates. In this paper we study the potential energy surface of a triatomic along an antisymmetric stretching coordinate, with symmetric stretching coordinate optimized and then frozen.
-
-
-
-
63
-
-
0007342989
-
-
note
-
2. The presence of an unpaired electron in the species studied here usually results in strong vibronic coupling in these systems, in contrast to the closed-shell ones.
-
-
-
-
64
-
-
0007276694
-
-
note
-
An unequal distribution of points in the ABA and BAB regions contributes partially to the left-right asymmetry of Fig. 3, but is not its main cause.
-
-
-
-
65
-
-
0007214359
-
-
note
-
g for all triatomics investigated in this paper also correlates very well with f.
-
-
-
-
68
-
-
33645844435
-
-
(b) Cava R.J., Batlogg B., Krajewski J.J., Farrow R., Rupp L.W., White A.E., Short K., Peck W.F. and Kometani T., Nature, 332, 814 (1988).
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(1988)
Nature
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-
-
Cava, R.J.1
Batlogg, B.2
Krajewski, J.J.3
Farrow, R.4
Rupp, L.W.5
White, A.E.6
Short, K.7
Peck, W.F.8
Kometani, T.9
-
71
-
-
0007213866
-
-
note
-
As Table S2 details, we could not compute properly 24 among 120 molecules in this group.
-
-
-
-
72
-
-
0007269433
-
-
note
-
2Li, which surprisingly is computed to be vibronically unstable.
-
-
-
-
73
-
-
0033449808
-
Calculations on open-shell molecules: A beginner's guide
-
Lipkowitz K.B., Boyd D.B., Eds.; John Wiley and Sons: NY
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Bally T. and Borden W.T., Calculations on Open-Shell Molecules: A Beginner's Guide, Rev. Comput. Chem., vol. 13, Lipkowitz K.B., Boyd D.B., Eds.; John Wiley and Sons: NY, 1999, p. 1.
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Rev. Comput. Chem.
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, pp. 1
-
-
Bally, T.1
Borden, W.T.2
-
74
-
-
0007344533
-
-
note
-
ii, between 5s of Cs and 2p of F is about 15 eV, except F bonding is mainly through 2p.
-
-
-
-
76
-
-
0000121790
-
-
A general perturbation theory for a one-electron LCAO-MO method, including change of the overlap integrals, has been developed by Imamura (Imamura A., Mol. Phys., 15, 225 (1968)).
-
(1968)
Mol. Phys.
, vol.15
, pp. 225
-
-
Imamura, A.1
-
77
-
-
0007276695
-
-
note
-
We will discuss this point further in Ref. 7.
-
-
-
-
81
-
-
0007275408
-
-
th Internationa Jahn-Teller Symposium Vibronic Interactions in Crystals and Molecules, Boston, submitted
-
th Internationa] Jahn-Teller Symposium Vibronic Interactions in Crystals and Molecules, Boston, 2000, Atanasov M. and Reinen D., Chem. Eur. J., submitted. The authors conclude that the hardest molecules are the most susceptible to vibronic coupling (hardness is used by them in the chemical sense of Pearson's hardness η).
-
(2000)
Chem. Eur. J.
-
-
Atanasov, M.1
Reinen, D.2
-
82
-
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0007213290
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personal communication
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Ayers P.W. and Parr R.G., personal communication, 2000.
-
(2000)
-
-
Ayers, P.W.1
Parr, R.G.2
-
83
-
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0007274227
-
-
note
-
Some people see red when "hypervalence" is mentioned. We find this term to be heuristically useful and use it interchangeably with three-center four-electron bonding.
-
-
-
-
84
-
-
0029769453
-
-
(a) Feretti V., Gilli P., Bertolasi V. and Gilli G., Crystallogr. Rev., 5, 3 (1996);
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Crystallogr. Rev.
, vol.5
, pp. 3
-
-
Feretti, V.1
Gilli, P.2
Bertolasi, V.3
Gilli, G.4
-
88
-
-
0007286128
-
-
note
-
A formal negative sign has been introduced for the force constant if the corresponding computed frequency is imaginary.
-
-
-
-
89
-
-
0007217596
-
-
note
-
Of course, Hi wants to be triangular. But in the spirit of our studies we keep it linear here.
-
-
-
-
94
-
-
0007213294
-
-
note
-
right is relatively small, and not relevant to our discussion.
-
-
-
-
95
-
-
0007342991
-
-
note
-
There is some s-p mixing at the terminal F's, which "shapes" these orbitals a little.
-
-
-
-
96
-
-
0007276696
-
-
note
-
The s orbital of central F atom does contribute to the vibronic coupling along the normal coordinate for bending, however.
-
-
-
-
99
-
-
0007214136
-
-
note
-
ii (sp).
-
-
-
-
101
-
-
0000112034
-
-
c Superconductors and Related Materials, ed. by Salje E.K.H, Alexandrov A.S. and Liang W.Y., Cambridge University Press, Cambridge 1995).
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Rev. Mod. Phys.
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, pp. 218
-
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Varma, C.M.1
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103
-
-
0007214138
-
-
note
-
One should consider in a more rigorous approach also nonadiabatic corrections, which are important in the vicinity of curve crossing region.
-
-
-
-
104
-
-
0007272515
-
-
note
-
Of course, the model used by us to simulate "ionic/covalent curve crossing" may be substituted by other approaches. A rigorous model for an ABA triatomic should show how the "ionic/covalent curve crossing" along the symmetric stretching coordinate influences the vibronic stability along the antisymmetric stretching coordinate.
-
-
-
-
106
-
-
0000644136
-
-
(b) Maitre P., Hiberty P.C., Ohanessian G. and Shaik S.S., J. Phys. Chem., 94, 4089 (1990).
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Maitre, P.1
Hiberty, P.C.2
Ohanessian, G.3
Shaik, S.S.4
-
108
-
-
0007209488
-
-
note
-
From both computations and theoretical models we know how to reach the goal of large vibronic coupling. However, there is a limit to the extent and significance of large vibronic coupling. This limit is determined by the thermodynamic stability of a molecule toward asymmetric dissociation. If the coupling is so large that it leads to an ABA molecule's dissociation (such dissociation proceeds along a combination of antisymmetric and symmetric stretching coordinates), then that coupling in a way has no real physical importance. A linear symmetric structure (the point at which G is determined) is then too far away from any real equilibrium geometry. Hence, "prodissociative", enormously large coupling constants might not be useful in pointing to molecules which may have interesting properties.
-
-
-
-
109
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0004290937
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-
John Wiley and Sons: NY, Chichester, Brisbane, Toronto
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rd Ed., John Wiley and Sons: NY, Chichester, Brisbane, Toronto, 1978).
-
(1978)
rd Ed.
-
-
Nakamoto, K.1
-
110
-
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0007287227
-
-
note
-
We have made some progress toward a physical justification of the use of f; this work will be published elsewhere.
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-
-
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