This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 10449–10456 10449

Cite this: Phys. Chem. Chem. Phys., 2011, 13, 10449–10456

A multi-scale approach to spin crossover in Fe(II) compoundsw

Marcel Swart,*ab

Mireia Guellaand Miquel Sola

a

Received 7th March 2011, Accepted 22nd March 2011

DOI: 10.1039/c1cp20646j

We report here for the first time a multi-scale study on the concept of spin-crossover compounds,

which integrates improved density functionals, a polarizable force field and hybrid QM/MM

calculations. This multi-scale setup is applied to the temperature dependence of spin states of a

Fe(II) compound with trispyrazolylborate ligands that exhibits spin-crossover. Our study shows a

transition temperature of around 290 K, which is in perfect agreement with experimental results.

Moreover, based on our data we provide the origin of why spin transition occurs in this

iron-compound: it results directly from spin-state changes in the iron-compound that lead to

more favourable electrostatic interactions for the high-spin state.

I. Introduction

Molecular switching due to thermally induced spin crossover

(SCO) in transition metal (TM) compounds has raised much

interest,1–38 in part because of the potential applications in

technology and biomedicine. Many of these studies involve

Fe(II) compounds that switch from low spin at low temperatures

to high spin at high(er) temperatures, although also other

transition metals such as cobalt may be involved.29,32 The

switch from low to high spin is usually accompanied by a

change in metal–ligand bond-lengths, but without further

changes in the molecular geometry; for instance for the

TM-compound under study here both spin-state geometries

have the same symmetry (D3d). Moreover, for d6 systems

(e.g. Fe(II)-compounds) changes in Mossbauer parameters

and magnetic properties are observed, resulting from the

change from a diamagnetic compound in the low-spin to a

paramagnetic compound with four unpaired electrons in the

high-spin state. The thermal transition temperature where this

switching takes place varies for different compounds, and is

observed with a temperature range for the switching that is

between a few degrees (sudden switch) to hundreds (gradual

process). Multiple spin-crossovers are also possible within one

compound, and may involve between 6 and 30 (un)paired

electrons.39

The origin of (sudden) SCO is often described as resulting from

the cooperative effect of a large number of TM compounds,1,30

e.g. through long-range interactions within the solid state

(crystal). Although indeed the ‘‘sudden switch’’ takes place in

the solid state, this viewpoint is too limited: isolated TM

compounds in solution also show SCO behavior,26,40,41 albeit of

the gradual kind. Therefore, in the general sense (valid for both

the sudden switch and the gradual process) the SCO phenomenon

is associated with spin-state preferences of the isolated TM

compounds. Several studies have in the past tried to analyze

SCO by computations,17,18,38 but these were hampered because of

inherent problems42–44 of the computational methodologies

used for the correct description of spin ground-states of TM

complexes. For instance, early density functionals using the

generalized gradient approximation (GGA) overestimate the

stability of low spin states, while hybrid functionals (containing

a portion of Hartree–Fock exchange) overestimate the stability of

high spin states.42,45 Also the basis set used can have a profound

influence.46,47 More recently, other studies have highlighted the

appropriateness of more recent and improved density functionals,

such as OPBE,42,43,48–50 SSB-D,44,51 TPSSh52–54 or M06-L.44,55

In a recent study,30 we investigated the spin-state preferences

of isolated Fe(II) compounds, with either trispyrazolylborate

(Tb) or trispyrazolylmethane (Tc) ligands. For these compounds,

we studied how substitution patterns on the ligands altered the

spin ground-states and Mossbauer parameters, which in

turn were compared with experimentally observed magnetic

susceptibility data and/or Mossbauer spectra.30 Because of the

use of OPBE,48–50 good results had been obtained for the spin

ground-state42,44 and the Mossbauer parameters. However, no

attempt was made to study the SCO patterns, which would

involve a study of the system at different temperatures.

Here, we report a multi-scale study on SCO in the iron

compound Fe(II)(Tb)2, using a sequential molecular dynamics

(MD) scheme. In this scheme, trajectories at different temperatures

are obtained from MD simulations employing a polarizable

force field, which is then followed by hybrid QM/MM

calculations on snapshots from these trajectories. Both the

force field parameterization as the QM/MM calculations

a Institut de Quımica Computacional and Departament de Quımica,Universitat de Girona, Campus Montilivi, 17071 Girona, Spain

b Institucio Catalana de Recerca i Estudis Avancats (ICREA),Pg. Lluıs Companys 23, 08010 Barcelona, Spain.E-mail: marcel.swart@icrea.cat

w Electronic supplementary information (ESI) available: Force fieldparameters for iron compound, radius of spherical box at differenttemperatures, and vibrational frequencies of analytical and IntraFFHessian. See DOI: 10.1039/c1cp20646j

PCCP Dynamic Article Links

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10450 Phys. Chem. Chem. Phys., 2011, 13, 10449–10456 This journal is c the Owner Societies 2011

involve improved density functionals for SCO studies in TM

complexes.

II. Computational methods

All of the density functional calculations were carried out with

the Amsterdam Density Functional (ADF) program, version

2010.01.56,57 Uncontracted basis sets of Slater-type orbitals

(STOs) of triple-B quality plus polarization (TZP) were used,

in some cases using the frozen-core (fc) approach.57 The

hybrid QM/MM calculations were performed always using

all-electron basis sets.

The molecular dynamics simulations with the polarizable force

field used the Discrete Reaction Field (DRF) approach58–68

within the DRF90 program.69 The parameters needed for

these simulations were specific for the systems under study,

which have been obtained in DFT calculations on the isolated

solvent and solutes (see below). The dichloromethane solvent

was in these MD simulations treated as a rigid body,

i.e. without internal (vibrational) degrees of freedom.

A. Polarizable force field setup

For the DRF approach, we need for each atom in the solvent

and the solutes (Fe(II)-compound in low and high spin

state), an atomic charge, an atomic radius and an atomic

polarizability. Details about the energy expressions, the setup

of the (QM/MM) DRF approach and how these result from

second-order perturbation theory are given in ref. 61 and 66.

For the dichloromethane solvent, we simply use standard

atomic polarizabilities60 that give a good representation of its

molecular value. This is different for the iron compound, for

which no standard polarizabilities are available. We therefore

computed first the molecular polarizability of Fe(II)(Tb)2 with

the ADF program,70 for both the low (singlet) and high

(quintet) spin-state. Because ADF allows the calculation of

molecular polarizability only for spin-restricted systems,

and not yet for unrestricted ones, these calculations were

performed using the finite field approach. Similar to a recent

study,71 we used electric field strengths of �1.0e–3, �2.0e–3,�3.0e–3 a.u. along the X-, Y- or Z-direction and measured the

change in dipole moments. The linear response then gives the

usual 3 � 3 polarizability tensor (see Table 1).

Although the tensor components are somewhat different

between the high and low spin states, the mean molecular

polarizability is virtually the same with values of 345.50 a.u.

for the low spin, and 345.55 a.u. for the high spin state. With

the standard value for the a-factor (2.1304) within the DRF

approach, we then used the polar60 program to obtain atomic

polarizabilities (a.u.) for the iron compounds: 2.1537 (H),

11.2741 (B), 10.0051 (C), 4.5261 (N) and 61.6579 (Fe).

With these atomic parameters the molecular tensors could be

perfectly reproduced.

The atomic charges and radii were taken directly from

calculations at OPBE/TZP,48 using the multipole derived

charge (MDC) analysis72 for the charges, and QCosmo radii.73,74

Indicated in Fig. 1 are the (D3d) symmetry-unique atoms with

their labels, and given in Table 2 are their charges and radii.

B. Molecular mechanics parameters for Fe(II)-compounds

Apart from the parameters for the polarizable force field, we

also need molecular mechanics parameters for the bonded

interactions (bonds, angles, dihedrals). For this we use the

IntraFF method75 that takes these parameters from the

computed Hessian. The basic philosophy behind IntraFF75

is that the force constant gives an estimate for the curvature

around the minimum, just as the Hessian matrix (a 3N � 3N

matrix with second derivatives of the energy with respect to

atomic coordinates) does. Therefore, by choosing appropriate

direction vectors for the different internal coordinates (bonds,

angles, dihedrals), reliable and consistent force constant values

can be obtained directly from the computed QM Hessian.

Here we use the analytical76 Hessian matrix obtained at

OPBE/TZP, from which the force field parameters for the

bonded interactions were obtained (see Supplementary Infor-

mation).w As an example, the Fe-N bonds had force constant

values (using the Amber77 convention) of 146.96 kcal mol�1

A�2 (low spin) and 120.01 kcal mol�1 A�2 (high spin).

C. Molecular dynamics setup

The MD simulations were performed with the DRF90

program,69 using a timestep of 1 fs. At each temperature

between 200 K and 450 K (with steps of 10 K) an initial

equilibration run was done of 100 ps, which was followed by a

production run of 100 ps. A Nose–Hoover thermostat78 within

the NVT-ensemble79 was used for obtaining the desired

temperature, and a soft wall-force potential69 was used to

keep the solvent molecules from evaporating from the

spherical box. The centre of mass of the solute was fixed at

Table 1 Molecular polarizability tensors (a.u.) of Fe(II)(Tb)2

Low spin High spin

320.61 0.0 0.0 317.25 0.0 0.00.0 320.61 0.0 0.0 317.25 0.00.0 0.0 395.27 0.0 0.0 402.16

Fig. 1 Fe(II)(Tb)2 with symmetry-unique atomlabels.

This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 10449–10456 10451

the center of the box at all times. The size of the box was

adapted at the different temperatures in such a way as to retain

the macroscopic density of the solvent at these different

temperatures (see Supplementary information).w Quaternions

were used to treat the rigid body motions of the solvents.79

D. Hybrid QM/MM setup with polarizable force field

The hybrid QM/MM calculations using the DRF approach61,66,68

for the polarizable force field were performed with a locally

modified version of ADF2010.01. The major difference with

the implementation by Jensen and co-workers66 was the input

handling, which is now merged into the general QM/MM

setup of ADF.80,81 Moreover, the interaction between the QM

and MM systems, and within the MM systems were modified

at two places: (i) the electric field of the QM electrons at the

polarizable (MM) particles is now screened for overlapping

charge densities (using the error function);82 (ii) the dipole field

tensor between the induced MM dipoles is now screened for

overlapping charge densities (using Thole’s model).83 These

changes were needed to make the interactions consistent with

the DRF approach,61 where all of them are screened for

overlapping densities. More details of these changes in the

DRF-QM/MM setup within ADF will be given elsewhere.81

Note that because we have studied the spin-states at temperatures

between 200 and 450 K, and have selected 100 snapshots from

the MD trajectories, in total we have been running over 5000

single-point QM/MM calculations.

III. Results and discussion

We have studied the low-spin singlet and high-spin quintet

state of the Fe(II)(Tb)2 compound in a multi-scale approach

that closely integrates quantum-chemistry84 with molecular

dynamics simulations79 with a polarizable force field.61,69 The

iron compound studied here has at 0 K a low-spin singlet

ground-state, as identified before by us30 and others17 with

computational studies. Unlike other SCO-compounds in the

solid state, in a solution of dichloromethane it does not

show a sudden switch from low to high spin within a short

temperature range, but instead shows a gradual process of

switching.26 The transition temperature is therefore not as well

defined as in the solid state, but is roughly estimated to be

around 285–290 K for the Fe(II)(Tb)2 compound in a solution

of dichloromethane.26

In the current contribution, we attempt to analyze the SCO

phenomenon from a computational point of view using a

multi-scale approach where a density functional method

(OPBE) is used that is appropriate43,44,51 for the description

of spin-state preferences of transition-metal complexes.

Because our previous study30 used the OPBE functional, and

to be able to compare directly with that study, we have used

the OPBE functional in this study as well. This notwithstanding,

we have checked that SSB-D51 provides similar results. Thus,

for instance, the spin-state splitting at 0 K is almost the same

for the two functionals, with a value of 5.9 kcal mol�1 at

OPBE/TZP(fc), and 6.0 kcal mol�1 at SSB-D/TZP(fc).

A. Force field parameterization

The gas-phase D3d-symmetric structures of the Fe(II)(Tb)2compound in the low and high spin state were taken directly

from our previous study,30 where these were optimized

already. Here we have calculated the analytical Hessian for

obtaining the molecular mechanics (MM) parameters of the

bonded interactions, which were obtained with the IntraFF

program.75 The vibrational frequencies from these Hessians

showed positive values only, and were adequately reproduced

by our IntraFF parameters (with mean absolute deviations of

30 and 41 cm�1, see Supplementary information).

The force constants for the Fe–N bonds were some 20%

larger for the low spin-state (147 kcal mol�1 A�2) than for the

high spin-state (120 kcal mol�1 A�2), which is probably mainly

related to the larger Fe–N distance in the latter. For Cu–N

bonds in a blue-copper protein, an exponential decay of the

force constant was observed with increasing equilibrium

distance.85 For the copper systems, these values could be fitted

nicely by the anharmonic bond potential by Frost,86,87 which

only has two parameters (A, B). With only one set of

parameters for Cu–His bonds, the force constants for several

azurin mutants with varying copper-nitrogen distances could

be matched perfectly.85 However, one set was needed for the

reduced state of the copper proteins, and one for the oxidized

state. A similar situation is observed here, where we find

different A/B parameters for the low and high spin state

(see Table 3). Note that in the MD simulations the harmonic

bond potential was used in all cases.

The atomic charges72 and radii73,74 needed for the force field

were taken directly from single-point calculations on the

isolated iron compounds and a solvent molecule, and are

derived directly from the charge-density (de)localization in

Table 2 Atomic charges (a.u.) and radii (a.u.)a

Charges radii

SolventC �0.1472 3.2358H 0.4180 2.0593Cl �0.3444 3.5289Solute Low High Low HighB0 1.4520 1.4794 3.4859 3.4741H0 �0.4762 �0.4801 2.1535 2.1550N1 �0.3912 �0.3859 2.8269 2.8317N2 �0.3565 �0.4001 2.7562 2.8005C3 0.0771 0.0809 3.2787 3.2959H3 0.1573 0.1464 2.0599 2.0674C4 �0.2488 �0.2371 3.3434 3.3414H4 0.1434 0.1409 2.0646 2.0700C5 0.0417 0.0568 3.3410 3.3386H5 0.1227 0.1266 2.0660 2.0611Fe 0.7870 0.8301 3.8458 3.8506

a for atomlabels of solute see Fig. 1.

Table 3 Anharmonic Frost parametersa (a.u.) for Fe–N and Cu–Nbonds

A B Z1 Z2

Fe–N, low spin 1.43 58.4 26 7Fe–N, high spin 1.22 52.1 26 7Cu–N, reducedb 1.61 � 0.01 65.3 29 7Cu–N, oxidizedb 1.52 � 0.01 65.3 � 0.3 29 7

a UFrost(R) = e�A�R(Z1�Z2/R � B), see ref. 86 and 75. b from ref. 85.

10452 Phys. Chem. Chem. Phys., 2011, 13, 10449–10456 This journal is c the Owner Societies 2011

these. The multipole derived charge analysis72 was designed to

give the best possible description for the electrostatic potential

and field inside and outside the molecule, when using atomic

fractional charges as the sources for them. Therefore, the

atomic multipole moments (up to the dipole moment) that

result directly from the charge density distribution were

distributed into fractional atomic MDC-d charges.72 Likewise,

the radii were taken from the QCosmo model,74 which

determines the atomic radii for use within a dielectric continuum

model based on the distribution of charge density around the

nuclei. i.e., they are based on the second-order moments ri�Ria2,

where ri is the charge density at a grid point i, and Ria is the

distance between grid point i and nucleus a. Since the

(de)localization of charge density is governed by the total

molecular charge and/or total molecular spin, these radii

should be adequate representations of the atomic sizes for

either anionic, neutral or cationic species. This was indeed

found to be the case for the solvation energy (within the

QCosmo approach)74 of a series of ions and molecules. For

the neutral molecules we study here, we do indeed find atomic

radii that are quite close to ‘‘normal’’ van der Waals radii, of

ca. 1.5 A for nitrogen, 1.7 A for carbon, 1.9 A for chloride and

ca. 2.0 A for iron (see Table 2).

The atomic polarizabilities for the polarizable part of the

force field were determined from fitting to the molecular

polarizability of the iron complex in the low and high

spin-state (see section II.A). These atomic values are within

the DRF approach used not only for the interaction of the

induced dipole moments with the source field (induction

energy), but also for screening61 the other energy components69

(dispersion, repulsion, electrostatics, soft wall-force) for

overlapping charge densities (Thole’s model).83

B. Molecular dynamics simulations

We have surrounded the iron-complexes within a spherical

box with 160 dichloromethane solvent molecules, in order to

have at least two solvent layers surrounding it (see Fig. 2). The

size of the box was adapted at each temperature (between 200 K

and 450 K in steps of 10 K) according to the macroscopic

density of the solvent at that temperature. These were estimated

from the experimental values within a temperature range of

0 1C to 100 1C,88 with a second order polynomial fitted to

them. This gave the following relationship: rmacro = 1.361685�0.001732�T � 2.331e�6�T2. This relationship then gave the

total solvent volume at a certain temperature, which together

with the solute volume (estimated with the rangenconf

program69) gave the total volume, from which the radius of

the spherical box was obtained (ranging from 29.48 to 33.62

Bohr, see Supplementary information).wThe initial configuration of the solvent molecules around the

solute was done with the rangenconf program,69 and a pre-

equilibration run of 10 ps at a temperature of 200 K was

performed for both the low and high spin state separately.

Afterwards, at each temperature an equilibration run was

performed for 100 ps, followed by a production run of another

100 ps, again for both spin states separately. The length of the

equilibration run was deliberately chosen to be long, in order

to let the system adjust itself to the new temperature and

spherical box size. From the trajectory of the production run,

at every 1000 steps (i.e. every ps) the configuration was kept

for subsequent snapshots with hybrid QM/MM (see below).

During the MD simulations the iron compound moved

freely, apart from its center of mass that was fixed at the

center of the spherical box at all times. The IntraFF75 parameters

for the bonded parameters worked well with e.g. average

Fe–N2 distances of e.g. 1.96 � 0.03 A at 200 K and 1.96 �0.04 at 400 K for the low spin, and 2.20 � 0.03 A at 200 K and

2.21 � 0.04 at 400 K for the high spin state. At the same time,

the temperature was recovered correctly, e.g. at 289.8� 13.0 K

for the target of 290 K, because of the use of the Nose-Hoover

thermostat.78 The total dipole moment of the system varied

from 12 Debye at 200 K to ca. 21 Debye at 450 K, which is

coming mainly from the expansion of the box. i.e. the ‘‘static’’

dipole moment resulting from the (re)orientation of the

fractional charges increases synchronously with the increase

of the temperature (and hence box size), while the total

‘‘induced’’ dipole moment (i.e. the sum of all induced dipoles

at the polarizable particles) oscillates between 3.5 and 6.0

Debye, but without a clear correlation with the temperature.

The average of the purely classical total energy (Utot =Upot +

Ukinetic, where Upot = Uelst + Udisp + Urep + Uinduct + UMM

+Ucavit, see ref. 69) from the MD simulations goes up steadily

with temperature (because of both an increase of the kinetic

energy and a reduction of the interaction energy), for both

spin states (see Fig. 3). At low temperatures (250 K and

below), the low-spin singlet state has the lowest energy. On

the other hand, at more elevated temperatures (350 K and

above) there is a clear preference (20 kcal mol�1 or more) for

the high-spin quintet state. Most interestingly, the transition

temperature where the quintet state energy profile crosses with

the singlet state profile, is found in the region of 280–290 K

(see Fig. 3), exactly where it was also observed experimentally.26

Of course, in Fig. 3 we have not yet taken into account the

Fig. 2 Solvated Fe(II)(Tb)2 complex.

This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 10449–10456 10453

contribution of the electronic energy, which could shift the

quintet state upwards by ca. 6 kcal mol�1 (vide supra). However,

at 290 K the MM energy difference (9.8 kcal mol�1) is already

larger than this shift, so the transition temperature would not

change much. This electronic effect we will take into account in

the QM/MM snapshots below. Furthermore, note that we report

here the energies U, not the Helmholtz free energies A or Gibbs

free energies G. In principle, these latter might be obtained

using e.g. free energy perturbation techniques, thermodynamic

integration, meta-dynamics, etc.However, neither one of these is

implemented yet in the programs we use (with polarizable force

fields). Moreover, this would lead to an enormous increase of the

computational effort, easily leading up to 100.000 single-point

QM/MM calculations, which is clearly outside our current

possibilities. Nevertheless, we have looked at the Helmholtz

free energies as coming directly from the partition function Z

(keeping in mind that our simulation times of 100 ps are

obviously too short to get reliable quantitative results), which

gave qualitatively similar results as the energies U: the low-spin

state was favored at low temperatures, the high-spin state at high

temperatures, and the transition between the two takes place

around 280–300 K.

C. Single-point hybrid QM/MM snapshots

From the production run MD simulations, we have kept at

every ps the configuration of solvent molecules and iron

complexes. With these coordinates, we then performed 100

single-point QM/MM calculations using the adapted DRF

implementation in the ADF program. All interactions between

QM and MM systems, and within the MM system, were

consistently61 treated and screened for overlapping charge

densities (see section II.D).

Before discussing the results that we obtained, we focus first

on the similarities between the MM and QM/MM interactions.

We have monitored the electrostatic and induction energies for

the interaction between the QM and MM regions, both within

the purely classical calculations with the DRF90 program and

within the hybrid QM/MM calculations with ADF. These

interactions are obtained in a significantly different manner.

i.e., within the DRF90 program69 the interactions are obtained

based on empirical atomic interactions, while in the polarizable

hybrid QM/MM calculations66,68 it is the electrons of the QM

system that ‘‘feel’’ and ‘‘feed’’ the interactions. i.e., it is not just

that the electrons ‘‘feel’’ the (screened) electrostatic potential

from the classical charges, they also ‘‘feed’’ back the interactions

through their electrostatic field to the polarizable particles,

and induce dipoles in these. These latter lead to an additional

electrostatic potential for the electrons, and therefore leads to

an iterative scheme that has to be solved self-consistently on

top of the usual SCF scheme within QM calculations.66

This however does not lead to problems, as the QM/MM

calculations converge normally within 15–30 SCF cycles.

Interestingly enough, for the sum of the electrostatic and

induction energies between the QM and MM systems, the

difference between either a purely classical description or a

polarizable QM/MM description is quite small (of typically

2–7 kcal mol�1). And this despite the fact that because of the

dynamic behavior of both the solute and the solvent

molecules, there is a large variation in this sum (taken from

those of the 100 snapshots) of some 40 kcal mol�1. The

screening for overlapping charge densities is done in

completely different ways, e.g. with Thole’s model60,67,69,73,83

for the purely classical MD simulations, and within the MM

system in hybrid QM/MM. However, the potential of the

electrostatic field in the QM region, and its feeding back, is

screened using the error function, i.e. following Jensen’s

model.82 Given the large similarity between MM and QM/MM

interactions, it is therefore again61,67,73 proof that the polarizable

DRF approach gives a consistent picture at both the polarizable

MM and QM/MM level.

The (averaged) QM/MM energy profile for both the low

and high spin- state is given in Fig. 4. Similar to the situation

in the MD simulations, the transition between low and high

spin takes place in the region around 280–300 K. The energy

profile and the transition region are not as clear as in the

profile from the MD simulations, probably due to the much

smaller number of points taken into account (100 vs. 100,000).

Therefore, also with the QM/MM calculations do we

reproduce the experimentally observed transition temperature

very well. This is not that surprising, since we already saw this

emerging in the MD simulations with the polarizable force

field. Moreover, we also saw that describing these systems with

either polarizable MM, or with polarizable QM/MM gives

basically the same results.

D. Spin crossover patterns

The SCO from low to high spin of the Fe(II)(Tb)2 complex in a

solution of dichloromethane takes place around 290 K, both

Fig. 3 Energy profile (Utot, kcal mol�1) from MD simulations.

Fig. 4 Hybrid QM/MM energy profile.

10454 Phys. Chem. Chem. Phys., 2011, 13, 10449–10456 This journal is c the Owner Societies 2011

experimentally26 and with our current computational study.

There are many different ways to probe the spin-state of

a system at a certain temperature,1 such as e.g. magnetic

susceptibility, Mossbauer spectroscopy, Raman spectroscopy,

Fourier Transform Infrared spectroscopy, UV–vis, etc. And

many focus on stimulating the system with either thermal

perturbations, pressure,89 or light. Indeed, one of main

characteristics of the transition is the change in metal-ligand

bond distances,30 that gives quite different spectroscopic

features (see e.g. ref. 90). But so far, not much attention has

been paid as to the origin of the transition with thermal

perturbations. It is often assumed that because some (but

not all!) of the vibrational frequencies are lower for the

high spin-state than for the low spin, it is merely the entropy

that causes the spin transition. However, this is not what is

coming out of our calculations. The electronic contribution

to the entropy for multiplet states (3.2 cal mol�1 K�1, e.g. ca.

1.0 kcal mol�1 at 300 K) is negligible compared to the

differences shown in Fig. 3 and 4. Furthermore, the entropy

of the total simulated system, when obtained from the parti-

tion function Z, is similar for both spin states with sometimes a

larger value for the singlet, and sometimes for the quintet.

Although we directly admit that the time-scale of our simulation

is much too short to get an accurate estimate of the entropy, it

is clear from our simulations that the driving force for the

transition is not entropy.

Our simulations reveal a different cause for the spin transition,

which is directly connected to the spin-state and changes related

with it. As the temperature goes up, the kinetic energy increases

and this has a direct effect on the system size, e.g. macroscopic

density (vide supra). Not only that, also the interaction energy

(Upot) between the solute and the solvent molecules, and between

the solvent molecules themselves, decreases drastically from e.g.

around �4100 kcal mol�1 at 200 K (low spin-state) to around

�3700 kcal mol�1 at 450 K. This is again a direct result from the

increasing kinetic energy, leading to larger distances between

solute and solvent molecules, and between solvent molecules

themselves. The reduction of the interaction energy takes place

for both spin states, but it does so more slowly for the high spin-

state. e.g. at 200 K, the total interaction energy (electrostatics,

dispersion, repulsion and induction) is ca. 20 kcal mol�1 more

favorable for the singlet than for the quintet; at 450 K it is

reversed, and the interaction of the quintet is more favorable by

ca. 20 kcal mol�1. This change results almost entirely from

electrostatics that is some 15–20 kcal mol�1 more favorable for

the singlet at low temperatures, and some 10 kcal mol�1 more

favorable for the quintet at higher temperatures.

The origin of this change in electrostatics can be attributed

to the nitrogens of the pyrazolyls and the hydrogens of the

solvent molecules. The hydrogens are at lower temperature

closer to the pyrazolyl rings (as measured by the Npyrazolyl–

Hsolvent distances) in the low spin than in the high spin-state. In

contrast, at higher temperatures they are closer in the high

spin-state than in the low spin-state. In itself, this should have

no effect on the electrostatics, but because the fractional

charge on nitrogen N2 is significantly larger (see Table 2) for

the high-spin (�0.40) than for the low-spin state (�0.35),the electrostatic interaction with these hydrogens is more

favorable for the high-spin state. At low temperatures this is

not allowed to happen because of the reduction of volume,

which makes that the bulkier chlorines of the solvent are

‘‘pushed’’ inwards. Only at elevated temperatures, when this

inwards pressure is released, can the solvent adapt itself to its

more favored orientation. i.e., the hydrogens will then be

found closer to the solute, which favors the high-spin state

over the low-spin state.

IV. Conclusions

We have investigated spin-crossover (SCO) behavior in a

iron(II) compound that is experimentally known to show

SCO in a solution of dichloromethane. The structures of

the Fe(II)(Tb)2 compound were already obtained in our

previous study, where we looked at spin ground-states and

Mossbauer parameters of a number of Fe(II) complexes with

trispyrazolylborate and trispyrazolylmethane ligands, and

how these are affected by substitution patterns. In that study,

we showed that the OPBE functional works very well for

predicting the spin-state of these complexes.

Here, we extend that study by taking into account the

temperature effects through the use of molecular dynamics

simulations using a polarizable force field. All of the

parameters for both the polarizable part, as for the bonded

molecular mechanics part were obtained in single-point

calculations on the isolated solutes and solvent. We have

studied the energy profile for both the low and high spin-state

from 200 K to 450 K, and find that the transition from low to

high spin takes place around 290 K, which is in excellent

agreement with experimental data that places it around

285–290 K.

Based on our data, we find that the transition from low to

high spin is not governed by entropy, but a much simpler

picture emerges. Because of the larger iron-nitrogen distances

in the high spin-state, there is a subtle but significant change in

the charge distribution in which the N2 nitrogen atom ‘‘gains’’

charge density (its fractional charge increases from �0.35 for

the low spin-state to �0.40 for the high spin-state). This is

logical because of the reduction of covalent interactions with

iron at these larger Fe–N distance. At the same time, the

solvent reorients itself at elevated temperatures whereby

the protons are on average closer to these nitrogens in the

high-spin state than in the low-spin state. This makes that the

electrostatic interactions between the solute and solvent is more

favorable for the high-spin state at elevated temperatures. At

lower temperatures, the kinetic energy is smaller and the total

volume available for the solvent reduces as well. This makes

that the bulkier chlorines are ‘‘pushed’’ inwards, and hence this

subtle effect favorable for the high-spin state is reduced. Future

studies will clarify if this ‘‘electrostatics’’ argument is limited to

the transition-metal compounds in solution, or if it is generally

applicable also in the ‘‘sudden’’ switch within the solid state.

Acknowledgements

The following organizations are thanked for financial

support: the Ministerio de Ciencia e Innovacion (MICINN,

project numbers CTQ2008-03077/BQU and CTQ2008-06532/

BQU) and the DIUE of the Generalitat de Catalunya

This journal is c the Owner Societies 2011 Phys. Chem. Chem. Phys., 2011, 13, 10449–10456 10455

(project numbers 2009SGR637 and 2009SGR528). Excellent

service by the Centre de Supercomputacio de Catalunya

(CESCA) is gratefully acknowledged. Support for the research

of M. Sola was received through the ICREA Academia 2009

prize for excellence in research funded by the DIUE of the

Generalitat de Catalunya. Part of this study (the adaptation of

the QM/MM implementation) was financially supported by

the HPC-Europa Transnational Access program.

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