In fragmentation approaches, a large system is divided into small subsystems on which separate ab initio calculations are performed. In the FMO method, there are two different fragmentation schemes, the hybrid orbital projection (HOP) method and the adaptive frozen orbitals (AFO) method. The main difference between the two fragmentation treatments is that AFO features a frozen molecular orbital on each fragmented bond, whereas HOP uses an unconstrained orbital. If several fragmented bonds are located near each other, the electron density is significantly disrupted around the detached bonds. Therefore, the HOP scheme is suitable for proteins since atoms are connected in chains, whereas the AFO scheme is used for species like nanoparticles where atoms are linked three dimensionally. The FMO/AFO method has been used to study zeolites, a silicon nano-wire (SiNW) and mesoporous silica nanoparticles.  In the AFO approach, the frozen orbital is treated using a Fock matrix transformation. The occupied orbitals in the bond being fragmented are frozen and do not mix with virtual orbitals in the Fock matix. However, the virtual orbitals are free to mix with other orbitals because these orbitals are projected out of the Fock space. To use fragmentation methods in various applications, fully analytic gradients are required to perform geometry optimizations, follow reaction paths, and perform molecular dynamics (MD) simulations. However, the fully analytic AFO gradient has not been derived or coded. The FMO/AFO analytic energy gradient is not trivial due to the coupling of the electronic states of fragments and pairs. The analytic energy gradient is derived by using Z-vector equations.<br/>

Analytic energy gradient derivation of the fragment molecular orbital method in the adaptive frozen orbital treatment (FMO/AFO)

2019 Fall National Meeting

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