An introductory tutorial on how to use the constrained density functional theory (CDFT) module in the CP2K open-source quantum chemistry and solid state physics software package. The talk was given at the CP2K UK User meeting on January 12, 2018, at the University of Lincoln.

1. Constrained DFT
(CDFT) in CP2K
CP2K UK User Meeting 2018, January 12
Nico Holmberg

2. Contents
• Introduction: what is CDFT and why use it?
• Theoretical basis of CDFT in brief
• CDFT implementation in CP2K
o Algorithmic framework
o Overview of features using examples
• Summary
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3. Introduction
• CDFT allows creation of charge and spin localized states
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3

4. Introduction
• CDFT allows creation of charge and spin localized states
• Why are such states needed?
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3

5. Introduction
• CDFT allows creation of charge and spin localized states
• Why are such states needed?
o Charge transfer phenomena
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3

6. Introduction
• CDFT allows creation of charge and spin localized states
• Why are such states needed?
o Charge transfer phenomena
o Electronic couplings (key role in charge transfer kinetics)
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3

7. Introduction
• CDFT allows creation of charge and spin localized states
• Why are such states needed?
o Charge transfer phenomena
o Electronic couplings (key role in charge transfer kinetics)
o Treating self-interaction error due to spurious electron delocalization
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3

8. Introduction
• CDFT allows creation of charge and spin localized states
• Why are such states needed?
o Charge transfer phenomena
o Electronic couplings (key role in charge transfer kinetics)
o Treating self-interaction error due to spurious electron delocalization
o Parametrizing model Hamiltonians (e.g. Heisenberg spin Hamiltonian)
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3

9. Introduction
• CDFT allows creation of charge and spin localized states
• Why are such states needed?
o Charge transfer phenomena
o Electronic couplings (key role in charge transfer kinetics)
o Treating self-interaction error due to spurious electron delocalization
o Parametrizing model Hamiltonians (e.g. Heisenberg spin Hamiltonian)
o And more… [1]
1. Kaduk, B.; Kowalczyk, T.; van Voorhis, T., Chem. Rev., 2012, 112, 321−370.
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3

10. Introduction
• CDFT allows creation of charge and spin localized states
• Why are such states needed?
o Charge transfer phenomena
o Electronic couplings (key role in charge transfer kinetics)
o Treating self-interaction error due to spurious electron delocalization
o Parametrizing model Hamiltonians (e.g. Heisenberg spin Hamiltonian)
o And more… [1]
• CDFT in CP2K [2] requires version 5.1 or newer
1. Kaduk, B.; Kowalczyk, T.; van Voorhis, T., Chem. Rev., 2012, 112, 321−370.
2. Holmberg, N.; Laasonen, K., J. Chem. Theory Comput., 2017, 13, 587−601. 12.1.2018
3

11. Generation of constrained states
• Enforce density localization in atom-centered regions with constraint
potential(s) [3,4]
𝐸𝐸CDFT 𝝀𝝀, 𝜌𝜌 = max
𝝀𝝀
min
𝜌𝜌
𝐸𝐸KS 𝜌𝜌 + �
𝑐𝑐
𝜆𝜆𝑐𝑐 �
𝑖𝑖=↑,↓
� 𝑤𝑤𝑐𝑐
𝑖𝑖
𝒓𝒓 𝜌𝜌𝑖𝑖
𝒓𝒓 𝑑𝑑𝒓𝒓 − 𝑁𝑁𝑐𝑐
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3. Wu, Q.; van Voorhis, T., Phys. Rev. A: At., Mol., Opt. Phys., 2005, 72, 024502.
4. Wu, Q.; van Voorhis, T., J. Chem. Theory Comput., 2006, 2, 765−774.

12. Generation of constrained states
• Enforce density localization in atom-centered regions with constraint
potential(s) [3,4]
𝐸𝐸CDFT 𝝀𝝀, 𝜌𝜌 = max
𝝀𝝀
min
𝜌𝜌
𝐸𝐸KS 𝜌𝜌 + �
𝑐𝑐
𝜆𝜆𝑐𝑐 �
𝑖𝑖=↑,↓
� 𝑤𝑤𝑐𝑐
𝑖𝑖
𝒓𝒓 𝜌𝜌𝑖𝑖
𝒓𝒓 𝑑𝑑𝒓𝒓 − 𝑁𝑁𝑐𝑐
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Weight
function
Lagrange multiplier (potential strength)
Target
value
3. Wu, Q.; van Voorhis, T., Phys. Rev. A: At., Mol., Opt. Phys., 2005, 72, 024502.
4. Wu, Q.; van Voorhis, T., J. Chem. Theory Comput., 2006, 2, 765−774.

13. Generation of constrained states
• Enforce density localization in atom-centered regions with constraint
potential(s) [3,4]
𝐸𝐸CDFT 𝝀𝝀, 𝜌𝜌 = max
𝝀𝝀
min
𝜌𝜌
𝐸𝐸KS 𝜌𝜌 + �
𝑐𝑐
𝜆𝜆𝑐𝑐 �
𝑖𝑖=↑,↓
� 𝑤𝑤𝑐𝑐
𝑖𝑖
𝒓𝒓 𝜌𝜌𝑖𝑖
𝒓𝒓 𝑑𝑑𝒓𝒓 − 𝑁𝑁𝑐𝑐
• Weight function defines the type of constraint
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4
Weight
function
Lagrange multiplier (potential strength)
Target
value
3. Wu, Q.; van Voorhis, T., Phys. Rev. A: At., Mol., Opt. Phys., 2005, 72, 024502.
4. Wu, Q.; van Voorhis, T., J. Chem. Theory Comput., 2006, 2, 765−774.

14. Generation of constrained states
• Enforce density localization in atom-centered regions with constraint
potential(s) [3,4]
𝐸𝐸CDFT 𝝀𝝀, 𝜌𝜌 = max
𝝀𝝀
min
𝜌𝜌
𝐸𝐸KS 𝜌𝜌 + �
𝑐𝑐
𝜆𝜆𝑐𝑐 �
𝑖𝑖=↑,↓
� 𝑤𝑤𝑐𝑐
𝑖𝑖
𝒓𝒓 𝜌𝜌𝑖𝑖
𝒓𝒓 𝑑𝑑𝒓𝒓 − 𝑁𝑁𝑐𝑐
• Weight function defines the type of constraint
o Total density constraint (𝜌𝜌↑
+ 𝜌𝜌↓
): 𝑤𝑤↑
= 𝑤𝑤↓
= 𝑤𝑤
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Weight
function
Lagrange multiplier (potential strength)
Target
value
3. Wu, Q.; van Voorhis, T., Phys. Rev. A: At., Mol., Opt. Phys., 2005, 72, 024502.
4. Wu, Q.; van Voorhis, T., J. Chem. Theory Comput., 2006, 2, 765−774.

15. Generation of constrained states
• Enforce density localization in atom-centered regions with constraint
potential(s) [3,4]
𝐸𝐸CDFT 𝝀𝝀, 𝜌𝜌 = max
𝝀𝝀
min
𝜌𝜌
𝐸𝐸KS 𝜌𝜌 + �
𝑐𝑐
𝜆𝜆𝑐𝑐 �
𝑖𝑖=↑,↓
� 𝑤𝑤𝑐𝑐
𝑖𝑖
𝒓𝒓 𝜌𝜌𝑖𝑖
𝒓𝒓 𝑑𝑑𝒓𝒓 − 𝑁𝑁𝑐𝑐
• Weight function defines the type of constraint
o Total density constraint (𝜌𝜌↑
+ 𝜌𝜌↓
): 𝑤𝑤↑
= 𝑤𝑤↓
= 𝑤𝑤
o Magnetization density constraint (𝜌𝜌↑
− 𝜌𝜌↓
): 𝑤𝑤↑
= −𝑤𝑤↓
= 𝑤𝑤
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Weight
function
Lagrange multiplier (potential strength)
Target
value
3. Wu, Q.; van Voorhis, T., Phys. Rev. A: At., Mol., Opt. Phys., 2005, 72, 024502.
4. Wu, Q.; van Voorhis, T., J. Chem. Theory Comput., 2006, 2, 765−774.

16. Generation of constrained states
• Enforce density localization in atom-centered regions with constraint
potential(s) [3,4]
𝐸𝐸CDFT 𝝀𝝀, 𝜌𝜌 = max
𝝀𝝀
min
𝜌𝜌
𝐸𝐸KS 𝜌𝜌 + �
𝑐𝑐
𝜆𝜆𝑐𝑐 �
𝑖𝑖=↑,↓
� 𝑤𝑤𝑐𝑐
𝑖𝑖
𝒓𝒓 𝜌𝜌𝑖𝑖
𝒓𝒓 𝑑𝑑𝒓𝒓 − 𝑁𝑁𝑐𝑐
• Weight function defines the type of constraint
o Total density constraint (𝜌𝜌↑
+ 𝜌𝜌↓
): 𝑤𝑤↑
= 𝑤𝑤↓
= 𝑤𝑤
o Magnetization density constraint (𝜌𝜌↑
− 𝜌𝜌↓
): 𝑤𝑤↑
= −𝑤𝑤↓
= 𝑤𝑤
o Spin specific constraint (𝜌𝜌↑): 𝑤𝑤↑ = 𝑤𝑤, 𝑤𝑤↓ = 0
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Weight
function
Lagrange multiplier (potential strength)
Target
value
3. Wu, Q.; van Voorhis, T., Phys. Rev. A: At., Mol., Opt. Phys., 2005, 72, 024502.
4. Wu, Q.; van Voorhis, T., J. Chem. Theory Comput., 2006, 2, 765−774.

17. CDFT weight function
• Constructed as sum of normalized
atomic weight functions
𝑤𝑤𝑐𝑐
𝑖𝑖
𝒓𝒓 = ��
𝑖𝑖∈𝒞𝒞
𝑐𝑐𝑖𝑖 𝑃𝑃𝑖𝑖(𝒓𝒓) �
𝑖𝑖
𝑁𝑁
𝑃𝑃𝑖𝑖(𝒓𝒓)
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18. CDFT weight function
• Constructed as sum of normalized
atomic weight functions
𝑤𝑤𝑐𝑐
𝑖𝑖
𝒓𝒓 = ��
𝑖𝑖∈𝒞𝒞
𝑐𝑐𝑖𝑖 𝑃𝑃𝑖𝑖(𝒓𝒓) �
𝑖𝑖
𝑁𝑁
𝑃𝑃𝑖𝑖(𝒓𝒓)
• CP2K uses Becke partitioning
o Smoothed Voronoi-like scheme
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19. CDFT weight function
• Constructed as sum of normalized
atomic weight functions
𝑤𝑤𝑐𝑐
𝑖𝑖
𝒓𝒓 = ��
𝑖𝑖∈𝒞𝒞
𝑐𝑐𝑖𝑖 𝑃𝑃𝑖𝑖(𝒓𝒓) �
𝑖𝑖
𝑁𝑁
𝑃𝑃𝑖𝑖(𝒓𝒓)
• CP2K uses Becke partitioning
o Smoothed Voronoi-like scheme
o Atomic sizes can be taken into account
(recommended)
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20. CDFT weight function
• Constructed as sum of normalized
atomic weight functions
𝑤𝑤𝑐𝑐
𝑖𝑖
𝒓𝒓 = ��
𝑖𝑖∈𝒞𝒞
𝑐𝑐𝑖𝑖 𝑃𝑃𝑖𝑖(𝒓𝒓) �
𝑖𝑖
𝑁𝑁
𝑃𝑃𝑖𝑖(𝒓𝒓)
• CP2K uses Becke partitioning
o Smoothed Voronoi-like scheme
o Atomic sizes can be taken into account
(recommended)
− E.g. oxygen has positive charge in water
without adjustment
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21. Optimization of the CDFT energy (1/2)
• Constraints are satisfied when
𝒄𝒄 𝝀𝝀 =
�
𝑖𝑖=↑,↓
� 𝑤𝑤1
𝑖𝑖
𝒓𝒓 𝜌𝜌𝑖𝑖
𝒓𝒓 𝑑𝑑𝑑𝑑 − 𝑁𝑁1
⋮
= 𝟎𝟎
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22. Optimization of the CDFT energy (1/2)
• Constraints are satisfied when
𝒄𝒄 𝝀𝝀 =
�
𝑖𝑖=↑,↓
� 𝑤𝑤1
𝑖𝑖
𝒓𝒓 𝜌𝜌𝑖𝑖
𝒓𝒓 𝑑𝑑𝑑𝑑 − 𝑁𝑁1
⋮
= 𝟎𝟎
• In practice, 𝝀𝝀 iteratively optimized until 𝐦𝐦𝐚𝐚𝐚𝐚 𝒄𝒄 𝝀𝝀 ≤ 𝝐𝝐
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23. Optimization of the CDFT energy (1/2)
• Constraints are satisfied when
𝒄𝒄 𝝀𝝀 =
�
𝑖𝑖=↑,↓
� 𝑤𝑤1
𝑖𝑖
𝒓𝒓 𝜌𝜌𝑖𝑖
𝒓𝒓 𝑑𝑑𝑑𝑑 − 𝑁𝑁1
⋮
= 𝟎𝟎
• In practice, 𝝀𝝀 iteratively optimized until 𝐦𝐦𝐚𝐚𝐚𝐚 𝒄𝒄 𝝀𝝀 ≤ 𝝐𝝐
o Uses root-finding algorithms, e.g., Newton’s method
𝝀𝝀𝑛𝑛+1 = 𝝀𝝀𝑛𝑛 − 𝛼𝛼𝑱𝑱𝑛𝑛
−1
𝒄𝒄 𝝀𝝀𝑛𝑛
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24. Optimization of the CDFT energy (1/2)
• Constraints are satisfied when
𝒄𝒄 𝝀𝝀 =
�
𝑖𝑖=↑,↓
� 𝑤𝑤1
𝑖𝑖
𝒓𝒓 𝜌𝜌𝑖𝑖
𝒓𝒓 𝑑𝑑𝑑𝑑 − 𝑁𝑁1
⋮
= 𝟎𝟎
• In practice, 𝝀𝝀 iteratively optimized until 𝐦𝐦𝐚𝐚𝐚𝐚 𝒄𝒄 𝝀𝝀 ≤ 𝝐𝝐
o Uses root-finding algorithms, e.g., Newton’s method
𝝀𝝀𝑛𝑛+1 = 𝝀𝝀𝑛𝑛 − 𝛼𝛼𝑱𝑱𝑛𝑛
−1
𝒄𝒄 𝝀𝝀𝑛𝑛
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Jacobian matrix,
approximated by
finite differences
Step size ∈ [−1, 0)
𝑱𝑱𝑖𝑖𝑖𝑖 =
𝜕𝜕𝒄𝒄𝑖𝑖
𝜕𝜕𝝀𝝀𝑗𝑗
≈
𝒄𝒄𝑖𝑖 𝝀𝝀 + 𝜹𝜹𝑗𝑗 − 𝒄𝒄𝑖𝑖(𝝀𝝀)
𝜹𝜹𝑗𝑗

25. Optimization of the CDFT energy (2/2)
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Input
Constraints
converged
or max steps
reached?
Yes
New guess
for 𝝀𝝀
Output
CDFT loop
Store data for
mixed CDFT
Build Jacobian
(optional)
Optimize step
size?
Standard
CP2K SCF
Reduce
step size
No/Done
Yes
Yes
No

26. Defining constraints (1/2)
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&QS
...
&CDFT
TYPE_OF_CONSTRAINT BECKE
&OUTER_SCF ON
TYPE BECKE_CONSTRAINT
EXTRAPOLATION_ORDER 2
MAX_SCF 10
! Convergence threshold
EPS_SCF 1.0E-3
! Optimizer selection: now Newton's method 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 for calculation of Jacobian 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 https://www.cp2k.org/howto:cdft

27. Defining constraints (2/2)
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&QS ! Constraint definitions
... ! Each repetition defines a constraint
&CDFT &ATOM_GROUP
... ATOMS 1
&END CDFT COEFF 1
&BECKE_CONSTRAINT CONSTRAINT_TYPE CHARGE
! Take atomic radii into account? &END ATOM_GROUP
ADJUST_SIZE FALSE ! No constraint but calculate charges
ATOMIC_RADII 0.63 0.32 &DUMMY_ATOMS
! Compute Becke charges? ATOMS 2
ATOMIC_CHARGES TRUE &END DUMMY_ATOMS
! Constraint strength and target values ! Print info about CDFT calculation
! Give one value per constraint &PROGRAM_RUN_INFO ON
STRENGTH ${BECKE_STR} &EACH
TARGET ${BECKE_TARGET} QS_SCF 1
! Cutoff scheme &END EACH
CUTOFF_TYPE ELEMENT COMMON_ITERATION_LEVELS 2
ELEMENT_CUTOFF 7.0 ADD_LAST NUMERIC
! Perform Becke partitioning only within the space FILENAME ./${NAME}
! spanned by constraint atom centered spherical Gaussians &END PROGRAM_RUN_INFO
! (reduces cost for solvated systems) &END BECKE_CONSTRAINT
CAVITY_CONFINE TRUE &END QS
CAVITY_SHAPE VDW
EPS_CAVITY 1.0E-7
IN_MEMORY TRUE
SHOULD_SKIP TRUE

28. Defining constraints (2/2)
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&QS ! Constraint definitions
... ! Each repetition defines a constraint
&CDFT &ATOM_GROUP
... ATOMS 1
&END CDFT COEFF 1
&BECKE_CONSTRAINT CONSTRAINT_TYPE CHARGE
! Take atomic radii into account? &END ATOM_GROUP
ADJUST_SIZE FALSE ! No constraint but calculate charges
ATOMIC_RADII 0.63 0.32 &DUMMY_ATOMS
! Compute Becke charges? ATOMS 2
ATOMIC_CHARGES TRUE &END DUMMY_ATOMS
! Constraint strength and target values ! Print info about CDFT calculation
! Give one value per constraint &PROGRAM_RUN_INFO ON
STRENGTH ${BECKE_STR} &EACH
TARGET ${BECKE_TARGET} QS_SCF 1
! Cutoff scheme &END EACH
CUTOFF_TYPE ELEMENT COMMON_ITERATION_LEVELS 2
ELEMENT_CUTOFF 7.0 ADD_LAST NUMERIC
! Perform Becke partitioning only within the space FILENAME ./${NAME}
! spanned by constraint atom centered spherical Gaussians &END PROGRAM_RUN_INFO
! (reduces cost for solvated systems) &END BECKE_CONSTRAINT
CAVITY_CONFINE TRUE &END QS
CAVITY_SHAPE VDW
EPS_CAVITY 1.0E-7
IN_MEMORY TRUE
SHOULD_SKIP TRUE
Use e.g. covalent radii

29. Defining constraints (2/2)
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&QS ! Constraint definitions
... ! Each repetition defines a constraint
&CDFT &ATOM_GROUP
... ATOMS 1
&END CDFT COEFF 1
&BECKE_CONSTRAINT CONSTRAINT_TYPE CHARGE
! Take atomic radii into account? &END ATOM_GROUP
ADJUST_SIZE FALSE ! No constraint but calculate charges
ATOMIC_RADII 0.63 0.32 &DUMMY_ATOMS
! Compute Becke charges? ATOMS 2
ATOMIC_CHARGES TRUE &END DUMMY_ATOMS
! Constraint strength and target values ! Print info about CDFT calculation
! Give one value per constraint &PROGRAM_RUN_INFO ON
STRENGTH ${BECKE_STR} &EACH
TARGET ${BECKE_TARGET} QS_SCF 1
! Cutoff scheme &END EACH
CUTOFF_TYPE ELEMENT COMMON_ITERATION_LEVELS 2
ELEMENT_CUTOFF 7.0 ADD_LAST NUMERIC
! Perform Becke partitioning only within the space FILENAME ./${NAME}
! spanned by constraint atom centered spherical Gaussians &END PROGRAM_RUN_INFO
! (reduces cost for solvated systems) &END BECKE_CONSTRAINT
CAVITY_CONFINE TRUE &END QS
CAVITY_SHAPE VDW
EPS_CAVITY 1.0E-7
IN_MEMORY TRUE
SHOULD_SKIP TRUE
Use e.g. covalent radii

30. Example: 𝐙𝐙𝐧𝐧𝟐𝟐
+
(1/2)
• When 𝑹𝑹𝐙𝐙𝐙𝐙−𝐙𝐙𝐙𝐙 grows, charge should localize onto one Zn atom
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9

31. Example: 𝐙𝐙𝐧𝐧𝟐𝟐
+
(1/2)
• When 𝑹𝑹𝐙𝐙𝐙𝐙−𝐙𝐙𝐙𝐙 grows, charge should localize onto one Zn atom
• Standard GGA/hybrid functionals place +0.5 charge on both atoms
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9

32. Example: 𝐙𝐙𝐧𝐧𝟐𝟐
+
(1/2)
• When 𝑹𝑹𝐙𝐙𝐙𝐙−𝐙𝐙𝐙𝐙 grows, charge should localize onto one Zn atom
• Standard GGA/hybrid functionals place +0.5 charge on both atoms
• Force charge localization on first atom
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! Set initial constraint strength to 0 (restarting from DFT)
STRENGTH 0.0
! Constraint target is the number of valence electrons – 1
TARGET 11.0
&ATOM_GROUP
ATOMS 1
COEFF 1
CONSTRAINT_TYPE CHARGE
&END ATOM_GROUP

33. Example: 𝐙𝐙𝐧𝐧𝟐𝟐
+
(2/2)
• The default output file contains the CDFT SCF iterations
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New guess
for 𝝀𝝀
CDFT loop
Build Jacobian
(optional)
Optimize step
size?
Standard
CP2K SCF
Reduce
step size
No/Done
Yes

34. Example: 𝐙𝐙𝐧𝐧𝟐𝟐
+
(2/2)
• The default output file contains the CDFT SCF iterations
o Each iteration corresponds to standard CP2K energy optimization
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New guess
for 𝝀𝝀
CDFT loop
Build Jacobian
(optional)
Optimize step
size?
Standard
CP2K SCF
Reduce
step size
No/Done
Yes

35. Example: 𝐙𝐙𝐧𝐧𝟐𝟐
+
(2/2)
• The default output file contains the CDFT SCF iterations
o Each iteration corresponds to standard CP2K energy optimization
o Uses optimized solution from line search as restart if available
• The following files are created with (quasi-)Newton optimizers
o *.LineSearch.out: Electronic structure SCF and optimization of step size
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New guess
for 𝝀𝝀
CDFT loop
Build Jacobian
(optional)
Optimize step
size?
Standard
CP2K SCF
Reduce
step size
No/Done
Yes

36. Example: 𝐙𝐙𝐧𝐧𝟐𝟐
+
(2/2)
• The default output file contains the CDFT SCF iterations
o Each iteration corresponds to standard CP2K energy optimization
o Uses optimized solution from line search as restart if available
• The following files are created with (quasi-)Newton optimizers
o *.LineSearch.out: Electronic structure SCF and optimization of step size
o *.cdftLog: Summary of CDFT parameters and computed partial charges
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37. Example: 𝐙𝐙𝐧𝐧𝟐𝟐
+
(2/2)
• The default output file contains the CDFT SCF iterations
o Each iteration corresponds to standard CP2K energy optimization
o Uses optimized solution from line search as restart if available
• The following files are created with (quasi-)Newton optimizers
o *.LineSearch.out: Electronic structure SCF and optimization of step size
o *.cdftLog: Summary of CDFT parameters and computed partial charges
o *.JacobianInfo.out: Calculation of Jacobian matrix with perturbed 𝝀𝝀
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38. Example: 𝐙𝐙𝐧𝐧𝟐𝟐
+
(2/2)
• The default output file contains the CDFT SCF iterations
o Each iteration corresponds to standard CP2K energy optimization
o Uses optimized solution from line search as restart if available
• The following files are created with (quasi-)Newton optimizers
o *.LineSearch.out: Electronic structure SCF and optimization of step size
o *.cdftLog: Summary of CDFT parameters and computed partial charges
o *.JacobianInfo.out: Calculation of Jacobian matrix with perturbed 𝝀𝝀
o *.inverseJacobian: Restart file for inverse Jacobian matrix
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39. Standard CP2K SCF with
fixed values of constraint
strength and step size
CDFT SCF iteration
information
Constraint
information
Restarted from converged
density obtained during
line search

40. Fragment constraints (1/2)
• Number of valence electrons per
molecule not necessarily well
defined
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12

41. Fragment constraints (1/2)
• Number of valence electrons per
molecule not necessarily well
defined
o Case for overlapping, strongly
interacting molecules
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12

42. Fragment constraints (1/2)
• Number of valence electrons per
molecule not necessarily well
defined
o Case for overlapping, strongly
interacting molecules
o How to set constraint target value?
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12

43. Fragment constraints (1/2)
• Number of valence electrons per
molecule not necessarily well
defined
o Case for overlapping, strongly
interacting molecules
o How to set constraint target value?
• Use a fragment based constraint
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12
�𝜌𝜌A(𝒓𝒓) �𝜌𝜌B(𝒓𝒓)
�𝑁𝑁𝑐𝑐 = �
𝑖𝑖=↑,↓
�𝑤𝑤𝑖𝑖
𝒓𝒓 �𝜌𝜌A
𝑖𝑖
𝒓𝒓 + �𝜌𝜌B
𝑖𝑖
𝒓𝒓 𝑑𝑑𝒓𝒓

44. Fragment constraints (1/2)
• Number of valence electrons per
molecule not necessarily well
defined
o Case for overlapping, strongly
interacting molecules
o How to set constraint target value?
• Use a fragment based constraint
o Only single-point calculations
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12
�𝜌𝜌A(𝒓𝒓) �𝜌𝜌B(𝒓𝒓)
�𝑁𝑁𝑐𝑐 = �
𝑖𝑖=↑,↓
�𝑤𝑤𝑖𝑖
𝒓𝒓 �𝜌𝜌A
𝑖𝑖
𝒓𝒓 + �𝜌𝜌B
𝑖𝑖
𝒓𝒓 𝑑𝑑𝒓𝒓

45. Fragment constraints (1/2)
• Number of valence electrons per
molecule not necessarily well
defined
o Case for overlapping, strongly
interacting molecules
o How to set constraint target value?
• Use a fragment based constraint
o Only single-point calculations
• Cube read/write accelerated with
MPI I/O since r18131
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12
�𝜌𝜌A(𝒓𝒓) �𝜌𝜌B(𝒓𝒓)
�𝑁𝑁𝑐𝑐 = �
𝑖𝑖=↑,↓
�𝑤𝑤𝑖𝑖
𝒓𝒓 �𝜌𝜌A
𝑖𝑖
𝒓𝒓 + �𝜌𝜌B
𝑖𝑖
𝒓𝒓 𝑑𝑑𝒓𝒓

46. Fragment constraints (2/2)
• Charge transfer energies of
strongly interacting complexes
−Δ𝐸𝐸CT = 𝐸𝐸CDFT − 𝐸𝐸DFT
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13

47. Fragment constraints (2/2)
• Charge transfer energies of
strongly interacting complexes
−Δ𝐸𝐸CT = 𝐸𝐸CDFT − 𝐸𝐸DFT
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13
Energy of system with
charge transfer prevented

48. Fragment constraints (2/2)
• Charge transfer energies of
strongly interacting complexes
−Δ𝐸𝐸CT = 𝐸𝐸CDFT − 𝐸𝐸DFT
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13
Energy of system with
charge transfer prevented
Fragment Becke with atomic size adjustments
Becke
Becke with atomic size adjustments
BW:
BW+A:
FBB+A:

49. Fragment constraints (2/2)
• Charge transfer energies of
strongly interacting complexes
−Δ𝐸𝐸CT = 𝐸𝐸CDFT − 𝐸𝐸DFT
• Magnitude of charge transferred,
Δ𝑞𝑞 , overestimated by non-
fragment constraints
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13
Energy of system with
charge transfer prevented
Fragment Becke with atomic size adjustments
Becke
Becke with atomic size adjustments
BW:
BW+A:
FBB+A:

50. Combining multiple CDFT states
• Additional properties can be computed from the interactions between
CDFT states
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14

51. Combining multiple CDFT states
• Additional properties can be computed from the interactions between
CDFT states
o Charge transfer kinetics (Marcus theory)
𝑘𝑘ab =
2𝜋𝜋
ℏ
𝑯𝑯ab
2
𝑇𝑇
4𝜋𝜋𝜋𝜋𝜋𝜋𝜉𝜉
exp −
𝜉𝜉 + Δ𝐴𝐴 2
4𝜋𝜋𝑘𝑘𝑇𝑇𝜉𝜉
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14

52. Combining multiple CDFT states
• Additional properties can be computed from the interactions between
CDFT states
o Charge transfer kinetics (Marcus theory)
𝑘𝑘ab =
2𝜋𝜋
ℏ
𝑯𝑯ab
2
𝑇𝑇
4𝜋𝜋𝜋𝜋𝜋𝜋𝜉𝜉
exp −
𝜉𝜉 + Δ𝐴𝐴 2
4𝜋𝜋𝑘𝑘𝑇𝑇𝜉𝜉
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Electronic coupling
Solvent reorganization energy
Reaction free energy

53. Combining multiple CDFT states
• Additional properties can be computed from the interactions between
CDFT states
o Charge transfer kinetics (Marcus theory)
𝑘𝑘ab =
2𝜋𝜋
ℏ
𝑯𝑯ab
2
𝑇𝑇
4𝜋𝜋𝜋𝜋𝜋𝜋𝜉𝜉
exp −
𝜉𝜉 + Δ𝐴𝐴 2
4𝜋𝜋𝑘𝑘𝑇𝑇𝜉𝜉
o Configuration interaction within the basis of CDFT states
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Electronic coupling
Solvent reorganization energy
Reaction free energy

54. Combining multiple CDFT states
• Additional properties can be computed from the interactions between
CDFT states
o Charge transfer kinetics (Marcus theory)
𝑘𝑘ab =
2𝜋𝜋
ℏ
𝑯𝑯ab
2
𝑇𝑇
4𝜋𝜋𝜋𝜋𝜋𝜋𝜉𝜉
exp −
𝜉𝜉 + Δ𝐴𝐴 2
4𝜋𝜋𝑘𝑘𝑇𝑇𝜉𝜉
o Configuration interaction within the basis of CDFT states
• Approximate electronic coupling with CDFT Kohn-Sham determinants
after orthogonalization [5]
𝑯𝑯ij ≈ 𝚽𝚽CDFT
i �𝐻𝐻KS 𝚽𝚽CDFT
j
=
𝐸𝐸CDFT
i
+ 𝐸𝐸CDFT
j
2
𝑺𝑺𝑖𝑖𝑖𝑖 − �
𝑐𝑐
𝚽𝚽CDFT
i 𝜆𝜆𝑐𝑐
i
𝑤𝑤𝑐𝑐
i
(𝒓𝒓) + 𝜆𝜆𝑐𝑐
j
𝑤𝑤𝑐𝑐
j
(𝒓𝒓)
2 𝚽𝚽CDFT
j
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Electronic coupling
Solvent reorganization energy
Reaction free energy
5. Wu, Q.; van Voorhis, T., J. Chem. Phys., 2006, 125, 164105.

55. The mixed CDFT module&MULTIPLE_FORCE_EVALS # Zn+ Zn
FORCE_EVAL_ORDER 2 3 &FORCE_EVAL
MULTIPLE_SUBSYS FALSE @SET WFN_FILE ${WFN_FILE_1}
&END @SET RESTART ${RESTART_1}
&FORCE_EVAL @SET NAME ${PROJECT_NAME}-state1
METHOD MIXED @SET BECKE_TARGET ${BECKE_TARGET_1}
&MIXED @SET BECKE_STR ${BECKE_STR_1}
MIXING_TYPE MIXED_CDFT METHOD QS
NGROUPS 1 @include ${DFT_FILE}
&MIXED_CDFT &END FORCE_EVAL
! Calculate mixed CDFT properties every COUPLING step # Zn Zn+
COUPLING 1 &FORCE_EVAL
! Settings determining how forces are mixed @SET WFN_FILE ${WFN_FILE_2}
FORCE_STATES 1 2 @SET RESTART ${RESTART_2}
LAMBDA 1.0 @SET NAME ${PROJECT_NAME}-state2
! Orthogonalize CDFT states with Lowdin's method @SET BECKE_TARGET ${BECKE_TARGET_2}
LOWDIN TRUE @SET BECKE_STR ${BECKE_STR_2}
! Configuration interaction? METHOD QS
CI FALSE @include ${DFT_FILE}
&PRINT &END FORCE_EVAL
&PROGRAM_RUN_INFO ON
&END
&END PRINT
&END MIXED_CDFT
&END MIXED
@include subsys.inc
&END FORCE_EVAL
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Additional settings available and
explained in the manual

56. Electronic coupling in 𝐙𝐙𝐧𝐧𝟐𝟐
+
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16
Zn+
Zn �𝐻𝐻 ZnZn+

57. Electronic coupling in 𝐙𝐙𝐧𝐧𝟐𝟐
+
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16
Zn+
Zn �𝐻𝐻 ZnZn+

58. Electronic coupling in 𝐙𝐙𝐧𝐧𝟐𝟐
+
10.1.2018
16
Zn+
Zn �𝐻𝐻 ZnZn+
Different
orthogonalization
algorithms

59. Electronic coupling in 𝐙𝐙𝐧𝐧𝟐𝟐
+
10.1.2018
17
Zn+
Zn �𝐻𝐻 ZnZn+
Different
orthogonalization
algorithms
Agrees with 5.49 mHartree
estimate from more expensive
wavefunction based method
CASSCF/MRCI+Q

60. CDFT in solvated systems
• Computational efficiency of
GPW/OT allows study of solvated
charge transfer processes at full
DFT level
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18

61. CDFT in solvated systems
• Computational efficiency of
GPW/OT allows study of solvated
charge transfer processes at full
DFT level
• Evaluating intramolecular charge
transfer kinetics in QTTFQ–
• 258 water, 12 ps (0.5 fs timestep)
• 48 s/timestep @ 384 MPI cores
(~120k core hours)
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18

62. List of CDFT capabilities in CP2K
• GPW and GAPW (no fragment constraint)
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19

63. List of CDFT capabilities in CP2K
• GPW and GAPW (no fragment constraint)
• Full DFT or QM/MM
12.1.2018
19

64. List of CDFT capabilities in CP2K
• GPW and GAPW (no fragment constraint)
• Full DFT or QM/MM
• Primarily for OT, diagonalization is supported but difficult to converge
12.1.2018
19

65. List of CDFT capabilities in CP2K
• GPW and GAPW (no fragment constraint)
• Full DFT or QM/MM
• Primarily for OT, diagonalization is supported but difficult to converge
• Energies and forces for an unlimited number of constraints (any type)
12.1.2018
19

66. List of CDFT capabilities in CP2K
• GPW and GAPW (no fragment constraint)
• Full DFT or QM/MM
• Primarily for OT, diagonalization is supported but difficult to converge
• Energies and forces for an unlimited number of constraints (any type)
• Mixed CDFT module supports
12.1.2018
19

67. List of CDFT capabilities in CP2K
• GPW and GAPW (no fragment constraint)
• Full DFT or QM/MM
• Primarily for OT, diagonalization is supported but difficult to converge
• Energies and forces for an unlimited number of constraints (any type)
• Mixed CDFT module supports
o Electronic couplings with various orthogonalization methods
12.1.2018
19

68. List of CDFT capabilities in CP2K
• GPW and GAPW (no fragment constraint)
• Full DFT or QM/MM
• Primarily for OT, diagonalization is supported but difficult to converge
• Energies and forces for an unlimited number of constraints (any type)
• Mixed CDFT module supports
o Electronic couplings with various orthogonalization methods
o Configuration interaction
12.1.2018
19

69. List of CDFT capabilities in CP2K
• GPW and GAPW (no fragment constraint)
• Full DFT or QM/MM
• Primarily for OT, diagonalization is supported but difficult to converge
• Energies and forces for an unlimited number of constraints (any type)
• Mixed CDFT module supports
o Electronic couplings with various orthogonalization methods
o Configuration interaction
o Removal of linearly-dependent MOs via SVD decomposition
12.1.2018
19

70. List of CDFT capabilities in CP2K
• GPW and GAPW (no fragment constraint)
• Full DFT or QM/MM
• Primarily for OT, diagonalization is supported but difficult to converge
• Energies and forces for an unlimited number of constraints (any type)
• Mixed CDFT module supports
o Electronic couplings with various orthogonalization methods
o Configuration interaction
o Removal of linearly-dependent MOs via SVD decomposition
o Electronic coupling reliability metrics
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19

71. Summary
• CDFT is a tool to study charge transfer phenomena
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20

72. Summary
• CDFT is a tool to study charge transfer phenomena
• Available in latest release version
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20

73. Summary
• CDFT is a tool to study charge transfer phenomena
• Available in latest release version
• Tutorial at https://www.cp2k.org/howto:cdft that complements regtests
12.1.2018
20

74. Summary
• CDFT is a tool to study charge transfer phenomena
• Available in latest release version
• Tutorial at https://www.cp2k.org/howto:cdft that complements regtests
o Summaries of CDFT theory and the CP2K implementation
o Walk throughs of example calculations
12.1.2018
20

75. Summary
• CDFT is a tool to study charge transfer phenomena
• Available in latest release version
• Tutorial at https://www.cp2k.org/howto:cdft that complements regtests
o Summaries of CDFT theory and the CP2K implementation
o Walk throughs of example calculations
• Help provided on Google groups if you encounter issues with CDFT
features
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20

76. Questions?