Method of identifying properties of molecules under open boundary conditions
A method of determining a property of a liquid system, the liquid system including at least one molecule in a solvent, comprises: generating a quantum model of the liquid system, the quantum model including a device region and a lead region, the device region being spherical, paraboloid, cubic or arbitrary in shape and encompassing the at least one molecule and a portion of the solvent of the liquid system, the lead region encompassing a region of the solvent surrounding the device region, determining a first property of the device region by solving a first quantum equation for the device region, determining the first property of the lead region by solving the first quantum equation under open boundary conditions for the lead region, and combining the first property of the device region with the first property of the lead region to arrive at a total first property for the liquid system.
1. A method for simulating a nanoscale device using a processor, the nanoscale device including system having at least one molecule in a solvent, the method comprising:
receiving model parameters for the system as input to the processor, the model parameters identifying at least one of a type of molecule and a type of solvent to be modeled for the system;
generating a quantum model of the system using the processor, the quantum model partitioning the system into including a device region and a lead region, the device region being spherical in shape and encompassing the at least one molecule and a portion of the solvent of the system, the lead region being further partitioned into a plurality of nested shell regions, each nested shell region having a spherical shell shape and encompassing a respective region of the solvent surrounding the device region in the system, the plurality of nested shell regions being arranged in a nested manner starting from a device-lead interface and extending outward from the device region, the device-lead interface defining where the device region meets the lead region; and
simulating the nanoscale device using the processor based on the quantum model, the simulating including:
determining a first property of the lead region using Non-Equilibrium Green's Function methods under open boundary conditions for the lead region using the processor, a recursive Green's function algorithm being applied to the plurality of nested shell regions to determine Green's functions for the plurality of nested shell regions of the lead region;
determining the first property of the device region using Non-Equilibrium Green's Function methods using the processor, a Green's function for the device region being determined based on a Green's function for the device-lead interface, the Green's function for the device-lead interface being determined based on the Green's functions for the plurality of nested shell regions of the lead region; and
combining the first property of the device region with the first property of the lead region to arrive at a total first property for the system using the processor.
2. The method of claim 1 , wherein the solvent comprises at least one of hydrophobic membranes, organic molecules, inorganic molecules, emulsions, solids, and alloys.
3. The method of claim 1 , further comprising:
determining a Hamiltonian for the system; and
determining the Green's function for the device region with reference to the Hamiltonian.
4. The method of claim 3 , wherein the Hamiltonian is determined using a Wannierization procedure.
5. The method of claim 1 , wherein dephasing increases with distance from the device region which results in the nested shell regions that are farther away from the device region having less non-locality than the nested shell regions that are closer to the device region, and
wherein a number of matrix inversions required to solve Green's functions for a given region depends in part on the amount of non-locality in the region.