Second-Order Nonlinear Optical Susceptibilities of Metal–Organic Frameworks Using a Combined Local Field Theory/Charge Embedding Electrostatic Scheme

The linear (χ (1) ) and second-order nonlinear (χ (2) ) optical properties of metal–organic frameworks (MOFs) have been evaluated and interpreted by employing the combined local field theory/charge embedding approach. Three MOFs have been selected, the isostructural bis{4-[2-(4-pyridyl)ethenyl]benzoato}-zinc(II) (PEB-Zn) and bis{4-[2-(4-pyridyl)ethenyl]benzoato}-cadmium(II) (PEB-Cd) and bis{4-[3-(4-pyridyl)ethenyl]benzoato}-cadmium(II) (PEB′-Cd). The simulations, employing the Møller–Plesset second-order perturbation theory level to describe the ion properties, conclude that (i) χ (2) of PEB-Zn (∼60 pm/V at 1064 nm) is about 10% larger than that of PEB-Cd, (ii) χ (2) of PEB′-Cd attains 100 pm/V at 1064 nm [i.e., twice more than that of PEB-Cd or an amplitude similar to that of the 4-( N, N -dimethylamino)-3-acetamidonitrobenzene (DAN) molecular crystal] and (iii) the change of crystal structure accompanying an increase of temperature from 173 to 298 K leads to a decrease of χ (2) by ca. 10%. For the isostructural PEB-Zn and PEB-Cd, the outcome of Kurtz-Perry SHG powder method has been simulated as a function of the grain size, demonstrating that differences between the two MOFs only show up for room temperature structures. A value of 1.29 was estimated for the PEB-Zn/PEB-Cd contrast ratio, in qualitative agreement with experiment (1.16). This work opens the way toward a theoretically based design of MOFs with outstanding second-order nonlinear optical responses.