A modified ADMA linear scaling macromolecular method for enhanced detection of induced molecular shape changes

Divide-and-Conquer Linear-Scaling Quantum Chemical Computations

“…Then, the neighboring atoms of each subsystem are defined as the buffer region, and the AOs associated with the atoms in the buffer region of subsystem s are adopted as B ( s ). The density matrix of the entire system appearing in eq is approximated as the sum of the subsystem density matrices weighted by the partition matrix, P s P μ ν s = true{ .25ex2ex 1 goodbreak0em1em⁣ ( μ ∈ S false( s false) ∧ ν ∈ S false( s false) ) 1 / 2 goodbreak0em1em⁣ ( μ ∈ S false( s false) ∧ ν ∈ B false( s false) ⁡ or vice versa ) 0 goodbreak0em1em⁣ ( otherwise ) as D μ ν ent ≈ ∑ s subsystem P μ ν s D μ ν s The partition matrix was first introduced in the Lego approach or ADMA method. − Here, the density matrix of subsystem s , D s , is defined in the finite temperature regime as D μ ν s …”

“…Then, the neighboring atoms of each subsystem are defined as the buffer region, and the AOs associated with the atoms in the buffer region of subsystem s are adopted as B ( s ). The density matrix of the entire system appearing in eq is approximated as the sum of the subsystem density matrices weighted by the partition matrix, P s as The partition matrix was first introduced in the Lego approach or ADMA method. − Here, the density matrix of subsystem s , D s , is defined in the finite temperature regime as where ε F represents the Fermi level and f β ( x ) = [exp­(− β x ) + 1] −1 is the Fermi distribution function. The reason for introducing the finite temperature regime in the DC method was to conserve the number of electrons, n e , in the entire system in the DC method that adopt overlapped fragmentation, by solving the following equation of the Fermi level ε F : …”

“…Therefore, various fragmentation schemes have been developed to reduce scaling. − Li et al categorizes fragmentation schemes into energy-based and density-based approaches. Many fragmentation schemes correspond to the first category, such as molecular fragmentation with conjugate caps (MFCC), − generalized energy-based fragmentation (GEBF), ,, fragment molecular orbital (FMO), − molecular tailoring approach (MTA), − systematic molecular fragmentation (SMF), , and molecules-in-molecules (MIM) methods. , The latter category includes the divide-and-conquer (DC), − adjustable density matrix assembler (ADMA), − elongation, − and MFCC density matrix (MFCC-DM) methods . The latter category is normally applied at the mean-field (i.e., HF or DFT) level of theory because it is based on the one-body density matrix, whereas several extensions to the electron correlation theory partly hiring energy-based approaches have been proposed, for example, the DC electron correlation − and elongation local MP2 methods.…”