namd¶
-
libra_py.namd.compute_Hvib(ham_old, ham_cur, orb, dt)[source]¶ Computes the vibronic Hamiltonian - in the MO basis - this is equivalent to the general version below with the 1-electron “Slater determinant” basis functions. This function is going to be deprecated, but let keep it here, for backward compatibility
- Parameters
ham_old (Hamiltonian) – Hamiltonian at time t-dt [units: a.u. of energy]
ham_cur (Hamiltonian) – Hamiltonian at time t [units: a.u. of energy]
orb (list of ints) – indices of the orbitals included in the active space. The Hvib dimensions will be determined by the N_act = len(orb) and the elements of Hvib will reflect only the orbitals included in this active state. Indexing starts with 0.
dt (float) – Time step [units: a.u. of time]
- Returns
vibronic Hamiltonian matrix in the MO basis: Hvib = Hel - i*hbar*d_ij
- Return type
CMATRIX(N_act,N_act)
-
libra_py.namd.compute_Hvib_sd(ham_old, ham_cur, orb, SD_basis, dt)[source]¶ Computes the vibronic Hamiltonian - in the MO basis
- Parameters
ham_old (Hamiltonian) – Hamiltonian at time t-dt [units: a.u. of energy]
ham_cur (Hamiltonian) – Hamiltonian at time t [units: a.u. of energy]
orb (list of ints) – indices of the orbitals included in the active space. The Hvib dimensions will be determined by the norb = len(orb) and the elements of Hvib will reflect only the orbitals included in this active state. Indexing starts with 0.
SD_basis (list of lists of ints) – Slater determinant (SD) basis - are defined in terms of the indices withing the active space, with the numbering starting from 0. In no-SOC case, the numbers smaller than N_act = len(orb) will correspond to alpha orbitals other - to beta orbitals
dt (float) – Time step [units: a.u. of time]
- Returns
vibronic Hamiltonian matrix in the SD basis: Hvib = Hel - i*hbar*d_ij. Here, N = len(SD_basis)
- Return type
CMATRIX(N,N)
Example
If we have a system with HOMO being the orbital with index 20, LUMO - with 21, then if we want to consider a minimal 2-state system, we can choose orb = [20, 21] Mapping:
0 1 2 3 H(alp) L(alp) H(bet) L(bet) GS = |H(alp),H(beta)| S1 = |H(alp),L(beta)| and SD_basis = [ [0, 2], [0, 3] ] /\ /\ /\ / | | | | H alp H bet H alp L beta
Example
If we have a system with HOMO being the orbital with index 20, LUMO - with 21, then if we want to consider a minimal 2-state system with spin-flip, we can choose orb = [20, 21] Mapping:
0 1 2 3 H(alp) L(alp) H(bet) L(bet) GS = |H(alp),H(beta)| S1 =|H(alp),L(beta)| T0 = |H(alp),L(alp)| T1 = |H(bet),L(bet)| and SD_basis = [ [0, 2], [0, 3] , [0, 1] , [ 2, 3 ] ] /\ /\ /\ /\ /\ /\ /\ / | | | | | | | | H alp H bet H alp L beta H alp L alp H bet L bet
Example
If we have a radiacl in a system with 3 electrons, occuplying HOMO-1 (doubly) and HOMO (singly). Say, the HOMO is the orbital with index 20, HOMO-1 - with 19, then if we may want to consider the active space of 3 orbitals: [19, 20, 21] Mapping:
0 1 2 3 4 5 H-1(alp) H(alp) L(alp) H-1(bet) H(bet) L(bet) GS = |H-1(alp),H-1(beta), H(alp)| and SD_basis = [ [0, 3, 1], [0, 3, 4], ... ] /\ /\ /\ /\ /\ /\ | | | | | | H-1 alp H-1 bet H alp H-1 alp H-1 bet H bet
Example
We may consider a transition between certain orbitals, say we are interested in transition between LUMO+10 (index 30) and LUMO+15 (index 35), then we can choose orb = [30, 35] Note, the definition of the SD basis used in Example #1 can be re-used. Mapping:
0 1 2 3 L+10(alp) L+15(alp) L+10(bet) L+15(bet) GS = |L+10(alp),L+10(beta)| S1 = |L+10(alp),L+15(beta)| and SD_basis = [ [0, 2], [0, 3] ] /\ /\ /\ / | | | | L+10 alp L+15 bet L+10 alp L+15 beta