Table 6 Static first hyperpolarizability tensor of Lycopene calculated using DFT at B3LYP/6-311 level of theory (in a.u. unit) and converted values to esu.

From: On the remarkable nonlinear optical properties of natural tomato lycopene

Static hyperpolarizability

a.u

esu

\(\beta_{xxx}\)

11,543.00000

99.72252 \(\times { }10^{ - 30}\)

\(\beta_{yyy}\)

− 11.75330

− 0.1015393 \(\times { }10^{ - 30}\)

\(\beta_{zzz}\)

− 200.58700

− 1.732915 \(\times { }10^{ - 30}\)

\(\beta_{xxy}\)

− 1285.84000

− 11.10865 \(\times { }10^{ - 30}\)

\(\beta_{xyy}\)

198.00000

1.710566 \(\times { }10^{ - 30}\)

\(\beta_{xxz}\)

944.66600

8.161177 \(\times { }10^{ - 30}\)

\(\beta_{xyz}\)

3.08147

0.02662150 \(\times { }10^{ - 30}\)

\(\beta_{yyz}\)

72.36650

0.6251901 \(\times { }10^{ - 30}\)

\(\beta_{xzz}\)

− 82.92250

− 0.7163857 \(\times { }10^{ - 30}\)

\(\beta_{yzz}\)

− 90.53260

− 0.7821310 \(\times { }10^{ - 30}\)

\(\beta_{x}\)

11,658.07750

100.717E \(\times { }10^{ - 30}\)

\(\beta_{y}\)

− 1388.12590

− 11.9923E \(\times { }10^{ - 30}\)

\(\beta_{z}\)

816.44550

7.05345E \(\times { }10^{ - 30}\)

\(\left\langle \beta \right\rangle\)

11,768.78276

101.6731 \(\times { }10^{ - 30}\)