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See Refs. 13(g) and 16 where the definition of a weight for the edges of a graph and the construction of the minimum spanning tree is given in detail. The value p = 2 used in Eq. (7) specifies the metric used, in this case the Euclidean metric.
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85034152624
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note
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5 (p= 1.124281, 0.109462, 0.034155, d = 0.109462). The centers are coded as in Fig. 1.
-
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76
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85034145458
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note
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See Ref. 24. The reader should also consider other experimental determinations of the geometry of trans-butadiene. See the papers by A. Almenningen, O. Bastiansen, and M. Traetteberg, Acta Chem. Scand. 12, 1221 (1958); K. Kveseth, R. Seip, and D. A. Kohl, A34, 31 (1980); Researchers relying exclusively on a specific choice of molecular geometry should examine carefully the entry for trans-butadiene in the CRC Handbook of Chemistry and Physics, 78th ed. (Chemical Rubber Corp., Boca Raton, 1997) and the cautious introductory note in 9-15 therein.
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85034133215
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note
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80
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85034133377
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note
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It is obvious from the cluster analysis of the performance of theoretical methods for a series of molecules presented in Ref. 16 that MP2 stands apart from other MP methods or CC techniques in electric property calculations.
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81
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85034152313
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note
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See Refs. 15(a) and 15(d). See also the discussion on the second hyperpolarizability of ethene in Ref. 13(d).
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82
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85034150605
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note
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xxxy component in the molecular orientation adopted in Ref. 12.
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85
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85034140214
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note
-
See Ref. 10. Only mean hyperpolarizability values are given.
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87
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0043231303
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See also the exchange of advanced ideas in Refs. 11 and 9(b)
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The reader should turn to Bishop's lucid dissection of the subject, published in Rev. Mod. Phys. 62, 343 (1990). See also the exchange of advanced ideas in Refs. 11 and 9(b).
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89
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See also S. P. Kama, G. B. Talapatra, W. M. K. P. Wijekoon, and P. N. Prasad, Phys. Rev. A 45, 2763 (1992); Y. Luo, H. Agren, H. Koch, P. Jørgensen, and T. Helgaker, Phys. Rev. B 51, 14949 (1995).
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