Accurate Prediction of Lattice Energies and Structures of Molecular Crystals with Molecular Quantum Chemistry Methods

Abstract

We extend the generalized energy-based fragmentation (GEBF) approach to molecular crystals under periodic boundary conditions (PBC), and we demonstrate the performance of the method for a variety of molecular crystals. With this approach, the lattice energy of a molecular crystal can be obtained from the energies of a series of embedded subsystems, which can be computed with existing advanced molecular quantum chemistry methods. The use of the field compensation method allows the method to take long-range electrostatic interaction of the infinite crystal environment into account and make the method almost translationally invariant. The computational cost of the present method scales linearly with the number of molecules in the unit cell. Illustrative applications demonstrate that the PBC-GEBF method with explicitly correlated quantum chemistry methods is capable of providing accurate descriptions on the lattice energies and structures for various types of molecular crystals. In addition, this approach can be employed to quantify the contributions of various intermolecular interactions to the theoretical lattice energy. Such qualitative understanding is very useful for rational design of molecular crystals.

Generalized energy‐based fragmentation approach for modeling condensed phase systems

“…Then, a series of ‘derivative’ subsystems are generated using the inclusion–exclusion principle. The detailed procedure of generating these derivative subsystems has been described in our previous work . It is worth mentioning that the PBCs and the translation symmetry are always taken into account during the construction of subsystems.…”

“…To mimic the effect of the long‐range electrostatic interaction from the crystal environment, we need to add some compensating charges on the boundaries of the super cell. The guiding rule of determining the magnitudes of these compensating charges is that the overall dipole moment of each unit cell should be zero . With the values of embedding point charges and compensating charges, we complete the construction of ‘electrostatically embedded’ subsystems.…”

“…In comparison with the previous methods (a huge number of point charges are explicitly included in the Hamiltonian of a subsystem), the compensation field method provides a cost‐effective and efficient way of treating long‐range electrostatic interactions. With this method, the PBC‐GEBF results of periodic systems are almost translationally invariant . On the other hand, the PBC‐GEBF method can be potentially applied to condensed phase systems consisting of large molecules.…”

“…For instance, the binary interaction method (BIM) proposed by Hirata's group has been demonstrated to provide satisfactory descriptions on the crystal structure, lattice energy, and vibrational spectra for a few typical molecular crystals. Very recently, we have extended the generalized energy‐based fragmentation (GEBF) approach, which was designed for linear scaling electronic structure calculations of large molecules and molecular clusters, to molecular crystals with the PBC . In the so‐called PBC‐GEBF method, the energy (or properties) of a periodic condensed phase system can be evaluated as a linear combination of energies (or properties) of a series of small subsystems (which contains a few molecules), each of which is embedded in the electric field generated by a finite array of background point charges.…”

“…In the so‐called PBC‐GEBF method, the energy (or properties) of a periodic condensed phase system can be evaluated as a linear combination of energies (or properties) of a series of small subsystems (which contains a few molecules), each of which is embedded in the electric field generated by a finite array of background point charges. Our test applications demonstrated that the PBC‐GEBF approach, combined with advanced molecular quantum chemistry methods, can provide accurate descriptions on the structure, stability, and vibrational spectra of molecular crystals . In this review, we will give an overview of the basic ideas and implementation details of the PBC‐GEBF method and provide a few examples to illustrate the performance of the PBC‐GEBF approach in predicting the structures, stability, and vibrational spectra of molecular or ionic liquid crystals (ILCs).…”