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VibSpec

# VibSpec - Vibrational Spectroscopy E = he = he k 1 2 m1m2 =...

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Colby College Vibrational Spectroscopy E υ = h ν e ( υ + ½) = h - ϖ e ( υ + ½) ν e = 1 2 π k μ ϖ e = 2 πν e = k μ μ = m 1 m 2 m 1 + m 2 G ~ υ = ν ~ e ( υ + ½) ν ~ e = ν e c in cm -1 Anharmonicity E υ = h ν e ( υ + ½) – χ e h ν e ( υ + ½) 2 + Y e h ν e ( υ + ½) 3 +... χ e = anharmonicity get weak ∆υ = ±2 and even weaker ∆υ = ±3 transitions called overtones Morse Potential V = D e [ 1 – e –a(R-R e ) ] 2 a = ϖ e μ 2D e ½ χ e = a 2 h - 2 μϖ e = h - ϖ e 4D e = ν ~ e 4D ~ e E υ = h ν e ( υ + ½) – χ e h ν e ( υ + ½) 2 E υ +1 – E υ = h ν e ( υ +1+½) – χ e h ν e ( υ +1+½) 2 – h ν e ( υ +½) + χ e h ν e ( υ +½) 2 E = h ν e χ e h ν e 2( υ +1) G ~ = ν ~ e χ e ν ~ e 2( υ +1) υ = lower level D e = D o + ½ h ν e – ¼ χ e h ν e D ~ e = D ~ o + ½ ν ~ e – ¼ ν ~ e χ e in cm -1 Relationship between χ e and D ~ e : E = h ν e χ e h ν e 2( υ cl + 1) = 0 1 = χ e 2( υ cl + 1) υ cl + 1 = 1 2 χ e upper level or υ cl = 1 2 χ e – 1 lower level
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