Contents. Introduction: what is CDFT and why use it? Theoretical basis of CDFT in brief. CDFT implementation in CP2K. Summary

Transcription

1 Cntents Intrductin: what is CDFT and why use it? Theretical basis f CDFT in brief CDFT implementatin in CP2K Algrithmic framewrk Overview f features using examples Summary

2 Intrductin CDFT allws creatin f charge and spin lcalized states Why are such states needed? Charge transfer phenmena Electrnic cuplings (key rle in charge transfer kinetics) Treating self-interactin errr due t spurius electrn delcalizatin Parametrizing mdel Hamiltnians (e.g. Heisenberg spin Hamiltnian) And mre [1] CDFT in CP2K [2] requires versin 5.1 r newer 1. Kaduk, B.; Kwalczyk, T.; van Vrhis, T., Chem. Rev., 2012, 112, Hlmberg, N.; Laasnen, K., J. Chem. Thery Cmput., 2017, 13,

3 Generatin f cnstrained states Enfrce density lcalizatin in atm-centered regins with cnstraint ptential(s) [3,4] EE CDFT λλ, ρρ = max λλ min ρρ EE KS ρρ + cc λλ cc ii=, Weight functin defines the type f cnstraint Lagrange multiplier (ptential strength) Ttal density cnstraint (ρρ + ρρ ): ww = ww = ww ww cc ii rr ρρ ii rr ddrr NN cc Magnetizatin density cnstraint (ρρ ρρ ): ww = ww = ww Spin specific cnstraint (ρρ ): ww = ww, ww = 0 Weight functin Target value 3. Wu, Q.; van Vrhis, T., Phys. Rev. A: At., Ml., Opt. Phys., 2005, 72, Wu, Q.; van Vrhis, T., J. Chem. Thery Cmput., 2006, 2,

4 CDFT weight functin Cnstructed as sum f nrmalized atmic weight functins ww cc ii rr = cc ii PP ii (rr) PP ii (rr) ii CC CP2K uses Becke partitining Smthed Vrni-like scheme Atmic sizes can be taken int accunt (recmmended) E.g. xygen has psitive charge in water withut adjustment NN ii 5

5 Optimizatin f the CDFT energy (1/2) Cnstraints are satisfied when cc λλ = ww ii 1 rr ρρ ii rr ddrr NN 1 ii=, = 00 In practice, λλ iteratively ptimized until mmaaaa cc λλ εε Uses rt-finding algrithms, e.g., Newtn s methd λλ nn+1 = λλ nn ααjj nn 1 cc λλ nn Step size [ 1, 0) JJ iiii = cc ii cc ii λλ + δδ ii λλ ii Jacbian matrix, apprximated by finite differences δδ ii cc ii (λλ) 6

6 Optimizatin f the CDFT energy (2/2) Input Cnstraints cnverged r max steps reached? CDFT lp Yes N Build Jacbian (ptinal) N/Dne New guess fr λλ Optimize step size? Yes Reduce step size Standard CP2K SCF Stre Yes data fr mixed CDFT Output 7

7 Defining cnstraints (1/2) &QS... &CDFT TYPE_OF_CONSTRAINT BECKE &OUTER_SCF ON TYPE BECKE_CONSTRAINT EXTRAPOLATION_ORDER 2 MAX_SCF 10! Cnvergence threshld EPS_SCF 1.0E-3! Optimizer selectin: nw Newtn's methd with backtracking line search OPTIMIZER NEWTON_LS! Optimizer step size STEP_SIZE -1.0! Line search settings MAX_LS 5 CONTINUE_LS FACTOR_LS 0.5! Finite difference settings fr calculatin f Jacbian matrix JACOBIAN_STEP 1.0E-2 JACOBIAN_FREQ 1 1 JACOBIAN_TYPE FD1 JACOBIAN_RESTART FALSE &END OUTER_SCF &END CDFT Full example files at 7

8 Defining cnstraints (2/2) &QS! Cnstraint definitins...! Each repetitin defines a cnstraint &CDFT &ATOM_GROUP... ATOMS 1 &END CDFT COEFF 1 &BECKE_CONSTRAINT CONSTRAINT_TYPE CHARGE! Take atmic radii int accunt? &END ATOM_GROUP ADJUST_SIZE FALSE Use e.g. cvalent radii! N cnstraint but calculate charges ATOMIC_RADII &DUMMY_ATOMS! Cmpute Becke charges? ATOMS 2 ATOMIC_CHARGES TRUE &END DUMMY_ATOMS! Cnstraint strength and target values! Print inf abut CDFT calculatin! Give ne value per cnstraint &PROGRAM_RUN_INFO ON STRENGTH ${BECKE_STR} &EACH TARGET ${BECKE_TARGET} QS_SCF 1! Cutff scheme &END EACH CUTOFF_TYPE ELEMENT COMMON_ITERATION_LEVELS 2 ELEMENT_CUTOFF 7.0 ADD_LAST NUMERIC! Perfrm Becke partitining nly within the space FILENAME./${NAME}! spanned by cnstraint atm centered spherical Gaussians &END PROGRAM_RUN_INFO! (reduces cst fr slvated systems) &END BECKE_CONSTRAINT CAVITY_CONFINE TRUE &END QS CAVITY_SHAPE VDW EPS_CAVITY 1.0E-7 IN_MEMORY TRUE SHOULD_SKIP TRUE

9 Example: ZZnn 22 + (1/2) When RR ZZnn ZZnn grws, charge shuld lcalize nt ne Zn atm Standard GGA/hybrid functinals place +0.5 charge n bth atms Frce charge lcalizatin n first atm! Set initial cnstraint strength t 0 (restarting frm DFT) STRENGTH 0.0! Cnstraint target is the number f valence electrns 1 TARGET 11.0 &ATOM_GROUP ATOMS 1 COEFF 1 CONSTRAINT_TYPE CHARGE &END ATOM_GROUP 9

10 Example: ZZnn 22 + (2/2) The default utput file cntains the CDFT SCF iteratins Each iteratin crrespnds t standard CP2K energy ptimizatin Uses ptimized slutin frm line search as restart if available The fllwing files are created with (quasi-)newtn ptimizers *.LineSearch.ut: Electrnic structure SCF and ptimizatin f step size *.cdftlg: Summary f CDFT parameters and cmputed partial charges *.JacbianInf.ut: Calculatin f Jacbian matrix with perturbed λλ *.inversejacbian: Restart file fr inverse Jacbian matrix 10

11 Standard CP2K SCF with fixed values f cnstraint strength and step size Restarted frm cnverged density btained during line search CDFT SCF iteratin infrmatin Cnstraint infrmatin

12 Fragment cnstraints (1/2) Number f valence electrns per mlecule nt necessarily well defined Case fr verlapping, strngly interacting mlecules Hw t set cnstraint target value? ρρ A (rr) ρρ B (rr) Use a fragment based cnstraint Only single-pint calculatins Cube read/write accelerated with MPI I/O since r18131 NN cc = ii=, ww ii rr ρρ A ii rr + ρρ B ii rr ddrr

13 Fragment cnstraints (2/2) Charge transfer energies f strngly interacting cmplexes ΔEE CT = EE CDFT EE DFT Energy f system with charge transfer prevented BW: BW+A: FBB+A: Becke Becke with atmic size adjustments Fragment Becke with atmic size adjustments Magnitude f charge transferred, Δqq, verestimated by nnfragment cnstraints 13

14 Cmbining multiple CDFT states Additinal prperties can be cmputed frm the interactins between CDFT states Charge transfer kinetics (Marcus thery) kk ab = 2ππ ħ HH ab 2 TT 4ππkkππξξ exp ξξ + ΔAA 2 4ππkkππξξ Cnfiguratin interactin within the basis f CDFT states Electrnic cupling Slvent rerganizatin energy Reactin free energy Apprximate electrnic cupling with CDFT Khn-Sham determinants after rthgnalizatin [5] i j HH ij ΦΦ CDFT HH KS ΦΦ CDFT = EE i j CDFT + EE CDFT i λλ i SS 2 iiii ΦΦ cc ww i j j cc (rr) + λλ ccwwcc(rr) CDFT 2 cc j ΦΦ CDFT 5. Wu, Q.; van Vrhis, T., J. Chem. Phys., 2006, 125,

15 The mixed CDFT mdule &MULTIPLE_FORCE_EVALS # Zn+ Zn FORCE_EVAL_ORDER 2 3 &FORCE_EVAL MULTIPLE_SUBSYS WFN_FILE ${WFN_FILE_1} RESTART ${RESTART_1} NAME ${PROJECT_NAME}-state1 METHOD BECKE_TARGET ${BECKE_TARGET_1} BECKE_STR ${BECKE_STR_1} MIXING_TYPE MIXED_CDFT METHOD QS NGROUPS ${DFT_FILE} &MIXED_CDFT &END FORCE_EVAL! Calculate mixed CDFT prperties every COUPLING step # Zn Zn+ COUPLING 1 &FORCE_EVAL! Settings determining hw frces are WFN_FILE ${WFN_FILE_2} FORCE_STATES 1 RESTART ${RESTART_2} LAMBDA NAME ${PROJECT_NAME}-state2! Orthgnalize CDFT states with Lwdin's BECKE_TARGET ${BECKE_TARGET_2} LOWDIN BECKE_STR ${BECKE_STR_2}! Cnfiguratin interactin? METHOD QS CI ${DFT_FILE} &PRINT &END FORCE_EVAL &PROGRAM_RUN_INFO ON &END &END PRINT &END MIXED_CDFT &END subsys.inc &END FORCE_EVAL Additinal settings available and explained in the manual 15

16 Electrnic cupling in ZZnn 22 + Zn + Zn HH ZnZn + Different rthgnalizatin algrithms 16

17 Electrnic cupling in ZZnn 22 + Zn + Zn HH ZnZn + Agrees with 5.49 mhartree estimate frm mre expensive wavefunctin based methd CASSCF/MRCI+Q Different rthgnalizatin algrithms 17

18 CDFT in slvated systems Cmputatinal efficiency f GPW/OT allws study f slvated charge transfer prcesses at full DFT level Evaluating intramlecular charge transfer kinetics in QTTFQ 258 water, 12 ps (0.5 fs timestep) MPI cres (~120k cre hurs)

19 List f CDFT capabilities in CP2K GPW and GAPW (n fragment cnstraint) Full DFT r QM/MM Primarily fr OT, diagnalizatin is supprted but difficult t cnverge Energies and frces fr an unlimited number f cnstraints (any type) Mixed CDFT mdule supprts Electrnic cuplings with varius rthgnalizatin methds Cnfiguratin interactin Remval f linearly-dependent MOs via SVD decmpsitin Electrnic cupling reliability metrics

20 Summary CDFT is a tl t study charge transfer phenmena Available in latest release versin Tutrial at that cmplements regtests Summaries f CDFT thery and the CP2K implementatin Walk thrughs f example calculatins Help prvided n Ggle grups if yu encunter issues with CDFT features

21 Questins?