The Realization Of The Program For The Internal Contraction Of MRPT2 And The First Principle Of The NH4 Sub-BH ₃ Crystal

The main work of this paper can be divided into two parts.:In part I:Multi-reference second order perturbation theory, MRPT2 is an efficient method to deal with the small and medium-sized molecular electronic structure. Especially in the study of excited state, MRPT2 is one of the commonly used method. Earlier, based on the configuration, We developed a new algorithm for MRPT2, and then present an improved version of the configuration-based multi-reference second-order perturbation approach (referred to as DPD-MRPT2); by employing the graphical unitary group approach (referred to as GUGA) and hole-particle duality, the effective Hamiltonian matrix calculation algorithms is efficiently improved. And this new approach has some significant advantages:such as high efficiency, can handle larger systems (such as{[Cu(NH3)3]2}2+), give a correct description of the quasi-degenerate potential curve (such as the LiF molecular potential curves), and can efficiently avoid the intrude state (such as the AgH molecular potential energy surface) and so on. In order to make this method applicable to a larger system, we employed the internal contraction approximation algorithm, which is successfully used in MRCI, and designed a suitable internal contraction algorithm for MRPT2. And by applied in some typical examples, we have checked the internal contraction MRPT2 (referred to as IC-MRPT2)method.In part II, we use the plane-wave pseudo-potential Density Functional Theory (referred to as DFT) method implemented in the MedeA-VASP package to explore the theoretical geometry structure of Ammonia Borane (NH3BH3, referred to as AB) molecular crystal, the electronic structure, the elastic properties, the thermodynamic properties and especially to explore the phase transition of NH3BH3, from a tetragonal I4mm (C94v) phase with disordered orientation of hydrogen to an orthorhombic phase with Pmn21 (C2v7) symmetry, as a function of temperature based on Density Functional Theory calculations with semi-empirical dispersion potential correction. NH3BH3 form an molecular crystal, and for which the van der Waals (vdW) weak interactions are essential. It is well known that pure DFT with local or semilocal functional cannot give a crrect description on the van der Waals interaction, but DFT-D2 gives an improve description to the vdW interaction correction using a semi-empirical dispersion potential to the Kohn-Sham DFT energy. In high temperature environments, the hydrogen atoms were found to be disordered in both the amine [NH3]-and borane [BH3]-groups. We define a series of substructures with the NH3BH3 moiety always in C3v symmetry and the partially occupied high temperature state can be described as a continuous transformation between these substructures. In order to describe the phase transition as a function of temperature, we need to determine the minimal free energy as a function of temperature. With optimization of crystal structures based on electronic structure calculations, the minimal energy structures can be determined. However, minimal free energy structures at different temperatures are in general different from the minimal energy structure determined from optimization based on electronic structure calculations. To determine the minimal free energy structure at each temperature, we thus need to take into account the phonon effects explicitly, based on the harmonic approximation. Combining the total energies with phonon spectrum of each substructure can give an essential support about the stability of crystal vibration. As A3 lies in the bottom of the potential energy surface (referred to as PES), here we explore the transition process from the other six structures to A3 as a function of rotation angle. This structure had been detected by Raman spectra of single crystal AB from 88 to 300 K, which also suggested an intermediate phase in the narrow temperature range of 210-225 K. With knowledge of free energy surfaces along rotations of the [NH3]-and [BH3]-groups, complete transformation paths are mapped out. The phase transition is found to follow the sequence of partially occupied tetragonal system (I4mm) of a mixture of states with monoclinic (Cc), (CM) and orthorhombic (Pmn2j) symmetries to fully occupied quasitetragonal system (the intermediate phase, Pmn2i) to fully occupied orthorhombic system (Pmn21).