Computational Modelling — Modeling energy transfer and absorption spectra in layered metal-organic frameworks based on a Frenkel-Holstein Hamiltonian

10 measurement groups · 67 results

Reported values remain attached to the sample, method, conditions, extraction quality and source location that produced them.

Numerical diagonalisation of the Holstein Hamiltonian and Gaussian line broadening

1D stack of 30 Ni3(HITP)2 SBU monomers · Model

Model set to S = 3.3 A and D = 1.85 A to compare calculated absorption spectrum with the experimental Ni3(HITP)2 spectrum reported in Ref. 21.

Context: model_system
Measurement source: article page 4 (rendered p005) · II.E · Fig. 3

Property	Reported value	Normalised value	Uncertainty	Origin and quality	Source
Displacement D for Fig. 3 model compatibility	D = 1.85 A	—	—	Text Exact Reported	article page 4 (rendered p005) · II.E · Fig. 3
Frenkel state energy E_S1 used in Fig. 3 absorption simulation	E_S1 = 2500 cm-1	—	—	Caption Exact Reported	article page 4 (rendered p005) · II.E · Fig. 3 caption
Charge-transfer state energy E_T used in Fig. 3 absorption simulation	E_T = 3900 cm-1	—	—	Caption Exact Reported	article page 4 (rendered p005) · II.E · Fig. 3 caption
Excitonic coupling J used in Fig. 3 absorption simulation	J = 1100 cm-1	—	—	Caption Exact Reported	article page 4 (rendered p005) · II.E · Fig. 3 caption
Absorption linewidth used in Fig. 3 simulation	650 cm-1	—	—	Caption Exact Reported	article page 4 (rendered p005) · II.E · Fig. 3 caption
Interlayer spacing S for Fig. 3 model compatibility	S = 3.3 A	—	—	Text Exact Reported	article page 4 (rendered p005) · II.E · Fig. 3
1D stack size used for Fig. 3 absorption simulation	N = 30 SBU monomers	—	—	Caption Exact Reported	article page 4 (rendered p005) · II.E · Fig. 3 caption
Electron transfer integral t_e used in Fig. 3 absorption simulation	t_e = 875 cm-1	—	—	Caption Exact Reported	article page 4 (rendered p005) · II.E · Fig. 3 caption
Hole transfer integral t_h used in Fig. 3 absorption simulation	t_h = 910 cm-1	—	—	Caption Exact Reported	article page 4 (rendered p005) · II.E · Fig. 3 caption

Holstein Hamiltonian absorption simulation parameterised by electronic-structure J, t_h, and t_e

1D stack of 30 Ni3(HITP)2 SBU monomers · Model

Spectra for monomer, eclipsed stack, short-axis sliding (0.7 and 1.2 A), and long-axis sliding (2 and 4 A); energies reported in wavenumbers.

Context: model_system
Measurement source: article page 7 (rendered p008) · III.C · Table I; Fig. 6

Property	Reported value	Normalised value	Uncertainty	Origin and quality	Source
Long-axis 2 A sliding absorption response	red shift with more visible profile difference around approximately 2 vibrational quanta	—	approximately	Text Approximate	article page 6 (rendered p007) · III.C · Fig. 6(c)
Long-axis 4 A sliding absorption response	overall spectrum shows a blue shift relative to the monomer	—	—	Text Qualitative	article page 6 (rendered p007) · III.C · Fig. 6(d)
Short-axis 0.7 A sliding absorption response	red shift; H-like features with A1/A2 below monomer 0-0/0-1 ratio	—	—	Text Qualitative	article page 6 (rendered p007) · III.C · Fig. 6(a)
Short-axis 1.2 A sliding absorption response	pronounced J-like behaviour with A1/A2 greater than monomer	—	—	Text Qualitative	article page 6 (rendered p007) · III.C · Fig. 6(b); Table I
Eclipsed stack J parameter	J = 1310 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Eclipsed stack t_e parameter	t_e = -772 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Eclipsed stack t_h parameter	t_h = 784 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Table I diabatic CT/Frenkel state energy E_S1	E_S1 = 600 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Table I Frenkel/charge-transfer state energy E_T	E_T = 6000 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Long-axis 2 A sliding J parameter	J = 1014 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Long-axis 2 A sliding t_e parameter	t_e = 290 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Long-axis 2 A sliding t_h parameter	t_h = -689 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Long-axis 4 A sliding J parameter	J = 714 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Long-axis 4 A sliding t_e parameter	t_e = -105 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Long-axis 4 A sliding t_h parameter	t_h = -287 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Short-axis 0.7 A sliding J parameter	J = 980 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Short-axis 0.7 A sliding t_e parameter	t_e = 293 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Short-axis 0.7 A sliding t_h parameter	t_h = 512 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Short-axis 1.2 A sliding J parameter	J = -605 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Short-axis 1.2 A sliding t_e parameter	t_e = 20 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Short-axis 1.2 A sliding t_h parameter	t_h = 192 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I
Table I absorption linewidth sigma	sigma = 250 cm-1	—	—	Table Exact Reported	article page 7 (rendered p008) · III.C · Table I

DFT, TD-DFT, CIS, and Gaussian 16 calculations

Density functional theory

Ni3(HITP)2 SBU monomer model · Model

Optimisation and excited-state calculations used M06-L/cc-pVTZ; T calculations used M06-L/cc-pVTZ; J calculations used CIS/cc-pVTZ; all computations used Gaussian 16.

Context: model_system
Measurement source: SI page 5 (rendered p005) · III. Computational details

Property	Reported value	Normalised value	Uncertainty	Origin and quality	Source
Computational software	Gaussian 16	—	—	Text Qualitative	SI page 5 (rendered p005) · III. Computational details
Excitonic coupling J calculation level	CIS/cc-pVTZ	—	—	Text Qualitative	SI page 5 (rendered p005) · III. Computational details
Optimisation and excited-state electronic-structure level	DFT and TD-DFT using M06-L with cc-pVTZ	—	—	Text Qualitative	SI page 5 (rendered p005) · III. Computational details
Charge-transfer coupling T calculation level	M06-L/cc-pVTZ	—	—	Text Qualitative	SI page 5 (rendered p005) · III. Computational details

Vibronic progression simulations with varied Huang-Rhys factor lambda and optional random onsite-energy disorder

1D stack of 30 Ni3(HITP)2 SBU monomers · Model

Lambda varied from 0.82 to 0.86; S fixed; D varied from 0 to 1 A; some cases add 20 degree rotation and random fluctuation in [0, epsilon].

Context: model_system
Measurement source: article page 8 (rendered p009) · III.D · Fig. 9

Property	Reported value	Normalised value	Uncertainty	Origin and quality	Source
Eclipsed stack lambda minus	lambda- = 0.43	—	—	Text Exact Reported	article page 6 (rendered p007) · III.C · Fig. 6 discussion
Eclipsed stack lambda plus	lambda+ = 0.46	—	—	Text Exact Reported	article page 6 (rendered p007) · III.C · Fig. 6 discussion
Lower lambda value in Fig. 9 simulations	lambda1 = 0.82	—	—	Text Exact Reported	article page 8 (rendered p009) · III.D · Fig. 9
Higher lambda value in Fig. 9 simulations	lambda2 = 0.86	—	—	Text Exact Reported	article page 8 (rendered p009) · III.D · Fig. 9
Effect of increasing lambda on spectral centroid	spectral centroid slightly red-shifted by increasing lambda	—	—	Text Qualitative	article page 8 (rendered p009) · III.D · Fig. 9(a)
Rotation angle added to sliding in Fig. 9 simulations	theta = 20 degrees	—	—	Text Exact Reported	article page 8 (rendered p009) · III.D · Fig. 9
Sliding displacement in Fig. 9 lambda simulations	D1 = 1 A	—	—	Text Exact Reported	article page 8 (rendered p009) · III.D · Fig. 9
Monomer lambda value used to explain first two vibronic peak intensities	lambda = 0.82	—	—	Text Exact Reported	article page 6 (rendered p007) · III.C · Fig. 6 discussion
Symmetric stretching mode energy used for spectral scaling	1568 cm-1	—	—	Text Exact Reported	article page 6 (rendered p007) · III.C · Fig. 6 discussion

Atomic transition charge (ATC) evaluation of long-range excitonic coupling J

Adjacent Ni3(HITP)2 SBU dimer model · Model

J calculated as a function of SBU displacement along short/long molecular axes, in-plane rotational angle, and tilt angle; centre of mass between adjacent monomers fixed at 3.3 A for Fig. 4.

Context: model_system
Measurement source: article page 5 (rendered p006) · III.A · Fig. 4

Property	Reported value	Normalised value	Uncertainty	Origin and quality	Source
Long-axis displacement J at D = 2 A	approximately 10.1 x 10^2 cm-1 at D = 2 A	—	visual estimate from axis	Figure Axis Approximate	article page 5 (rendered p006) · III.A · Fig. 4(a)
Native-configuration excitonic coupling JMarked as a best value within this paper	J = 1310 cm-1	—	—	Text Exact Reported	article page 5 (rendered p006) · III.A · Fig. 4(b)
Rotational-angle J-profile span	approximately 700 cm-1	—	approximately	Text Approximate	article page 5 (rendered p006) · III.A · Fig. 4(b)
Tilt angle where J sign changes	about 45 degrees	—	about	Text Approximate	article page 5 (rendered p006) · III.A · Fig. 4(c)

HOMO and LUMO energetic splitting as proxy for charge-transfer integrals

Adjacent Ni3(HITP)2 SBU dimer model · Model

SBU dimer spacing S increased from an eclipsed configuration along the stacking direction.

Context: model_system
Measurement source: article page 6 (rendered p007) · III.B · Fig. 5

Property	Reported value	Normalised value	Uncertainty	Origin and quality	Source
HOMO splitting at S = 3.1 A	approximately 2.4 x 10^-1 eV	—	visual estimate from axis	Figure Axis Approximate	article page 6 (rendered p007) · III.B · Fig. 5
HOMO splitting at S = 4.1 A	approximately 1.3 x 10^-1 eV	—	visual estimate from axis	Figure Axis Approximate	article page 6 (rendered p007) · III.B · Fig. 5
LUMO splitting at S = 3.1 A	approximately 1.9 x 10^-1 eV	—	visual estimate from axis	Figure Axis Approximate	article page 6 (rendered p007) · III.B · Fig. 5
LUMO splitting at S = 4.1 A	approximately 0.9 x 10^-1 eV	—	visual estimate from axis	Figure Axis Approximate	article page 6 (rendered p007) · III.B · Fig. 5

DFT optimisation and Huang-Rhys lambda evaluation for hypothetical amine-substituted SBU

Density functional theory

Hypothetical amine-substituted SBU model · Model

Table S1(b) reports optimisation energies, Ni-N distances, and lambda values for neutral, cationic, and anionic states of a hypothetical amine-substituted SBU.

Context: model_system
Measurement source: SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(b)

Property	Reported value	Normalised value	Uncertainty	Origin and quality	Source
Anionic hypothetical amine-substituted SBU lambda	lambda = 0.61	—	—	Visual Estimate Rounded Reported	SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(b)
Cationic hypothetical amine-substituted SBU lambda	lambda = 0.65	—	—	Visual Estimate Rounded Reported	SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(b)
Neutral hypothetical amine-substituted SBU lambda	lambda = 0.53	—	—	Visual Estimate Rounded Reported	SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(b)

Frenkel/charge-transfer Holstein Hamiltonian model for through-space energy transfer

1D stack of 30 Ni3(HITP)2 SBU monomers · Model

Linear array of n SBUs with periodic boundary conditions along the non-covalent stacking direction; includes long-range excitonic coupling J and short-range charge-transfer coupling T.

Context: model_system
Measurement source: article page 2 (rendered p003) · II.A · Fig. 2

Property	Reported value	Normalised value	Uncertainty	Origin and quality	Source

Absorption simulations varying E_T/E_S1 and switching off Coulomb interaction J

1D stack of 30 Ni3(HITP)2 SBU monomers · Model

0.7 A short-axis slide compared between perturbative E_T/E_S1 = 10 and resonance E_T/E_S1 = 1 cases; no-J diabatic limit assessed.

Context: model_system
Measurement source: article pages 7-8 (rendered p008-p009) · III.C · Figs. 7 and 8

Property	Reported value	Normalised value	Uncertainty	Origin and quality	Source
Resonance-regime broad spectral peak position	broad peak centered approximately at five vibrational quanta	—	approximately	Text Approximate	article page 7 (rendered p008) · III.C · Fig. 7
Perturbative regime E_T/E_S1 ratio	E_T/E_S1 = 10	—	—	Text Exact Reported	article page 7 (rendered p008) · III.C · Fig. 7
Resonance regime E_T/E_S1 ratio	E_T/E_S1 = 1	—	—	Text Exact Reported	article page 7 (rendered p008) · III.C · Fig. 7

DFT optimisation and Huang-Rhys lambda evaluation for neutral, cationic, and anionic Ni3(HITP)2 SBU

Density functional theory

Ni3(HITP)2 SBU monomer model · Model

Table S1(a) reports optimisation energies, equilibrium Ni-N distances, and lambda values for the neutral, cationic, and anionic Ni3(HITP)2 SBU.

Context: model_system
Measurement source: SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(a)

Property	Reported value	Normalised value	Uncertainty	Origin and quality	Source
Anionic Ni3(HITP)2 SBU optimisation energy	A energy = -2189.49	—	—	Visual Estimate Rounded Reported	SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(a)
Anionic Ni3(HITP)2 SBU lambda	lambda = 0.43	—	—	Visual Estimate Rounded Reported	SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(a)
Anionic Ni3(HITP)2 SBU equilibrium Ni-N distance	d_Ni-N = 1.90 A	—	—	Visual Estimate Rounded Reported	SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(a)
Cationic Ni3(HITP)2 SBU optimisation energy	C energy = -2190.34	—	—	Visual Estimate Rounded Reported	SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(a)
Cationic Ni3(HITP)2 SBU lambda	lambda = 0.46	—	—	Visual Estimate Rounded Reported	SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(a)
Cationic Ni3(HITP)2 SBU equilibrium Ni-N distance	d_Ni-N = 1.91 A	—	—	Visual Estimate Rounded Reported	SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(a)
Neutral Ni3(HITP)2 SBU optimisation energy	N energy = -2192.04	—	—	Visual Estimate Rounded Reported	SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(a)
Neutral Ni3(HITP)2 SBU lambda	lambda = 0.40	—	—	Visual Estimate Rounded Reported	SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(a)
Neutral Ni3(HITP)2 SBU equilibrium Ni-N distance	d_Ni-N = 1.88 A	—	—	Visual Estimate Rounded Reported	SI page 2 (rendered p002) · I. Insights on the SBU relaxation energies · Table S1(a)