Proton-Transfer Regulated Magnetic Spin Couplings in Nitroxide

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Proton-Transfer Regulated Magnetic Spin Couplings in Nitroxide-Functionalized Porphycene Diradicaloids Qi Wang, Xinyu Song, Ping Li, and Yuxiang Bu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01221 • Publication Date (Web): 10 Apr 2019 Downloaded from http://pubs.acs.org on April 10, 2019

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The Journal of Physical Chemistry

Proton-Transfer Regulated Magnetic Spin Couplings in Nitroxide-Functionalized Porphycene Diradicaloids Qi Wang,† Xinyu Song,*,† Ping Li,‡ Yuxiang Bu †,‡ † School

of Chemistry and Chemical Engineering, Shandong University, Jinan, 250100, Peoples’ Republic of China

‡ School

of Chemistry and Chemical Engineering, Qufu Normal University, Jinan, 273165, Peoples’ Republic of China

Abstract. Porphycene has found lots of promising applications due to its unique structure including flexible proton transfer tautomerization, while its large conjugated configuration can also assure it as a coupler for the diradical systems.

In this work, we theoretically design

the porphycene diradicals using porphycene as the coupler and nitroxide radical groups as spin sources and explore their proton-transfer-regulated magnetic spin coupling characteristics at the density functional theory level.

Structurally, introduction of nitroxide

radicals does not change the planarity of porphycene which is beneficial to the spin coupling between two spin sources.

The calculated results verify that the porphycene coupler can

support quite large spin coupling interactions in a large range (J being from -1933 cm-1 to 729 cm-1) and proton transfers in the porphycene couplers can not only regulate the spin coupling degrees

(e.g.

-1037

cm-1

versus

-1832

cm-1)

but

also

realize

the

ferromagneticantiferromagnetic coupling interconversion (e.g. 647 cm-1 versus -320 cm-1). We also find that the linking position and orientation of the nitroxide radical groups can noticeably modify the magnetic spin coupling properties of the porphycene diradicals. Different porphycene diradicals featuring different nitroxide-linking modes possess different spin coupling pathways and thus different spin coupling characteristics.

Besides, spin

delocalization and SOMO-SOMO energy splittings of triplet state are used to analyze the magnetic spin coupling differences among these diradicals.

It should be noted that

compared with parent porphycene, nitroxide-diradicalized porphycene derivatives have considerably lower intramolecular proton transfer barriers in the core regions, favoring the regulation.

This work provides useful information for rational design of the 1

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bio-motifs-based magnetic molecular devices.



INTRODUCTION In the past few decades, organic magnetic molecules have attracted wide attention from

experimental and theoretical chemists owing to their unusual properties.1-5

Generally,

magnetic materials molecules contain radical groups as the spin sources and π-conjugated organic molecules as the coupler, and the spin-spin coupling interactions among the spin sources play a crucial role in determining the magnetic coupling properties of such organic magnets.6,7

Therefore, finding suitable couplers and stable radical groups is crucial for

designing the target-directed diradicals with expected magnetic spin coupling characteristics. In recent years, more and more organic molecules have been designed and explored as the couplers, such as polyacenes,8 oligopyridines,9 and porphyrins.10

Porphycene, as one of the

isomers of porphyrin (porphine), was synthesized in 1986 by Vogel and co-workers,11 and has been widely used in catalytic,12 Raman,13,14 optical properties15,16 and so on.

Structurally,

porphycene also consists of four pyrrole rings but the linking bridges are different from porphine and porphyrins.

Similarly, porphycene is also a highly conjugated macrocycle and

possesses high stability, aromaticity and good spintronics properties.17-20 Hence, porphycene can be utilized as the couplers in the design of organic magnetic molecules.

Besides, various

types of radical groups as the spin sources have been synthesized and applied experimentally and theoretically.21-26 In the single radical groups, nitroxide radical is the simplest in structure and can be introduced into porphycene without changing its original planar structure. On the other hand, the magnetic regulation of diradical molecules can be achieved in many ways, such as preparing as 4n π antiaromatic linear and angular polyheteroacenes,27 using different lengths of the aromatic coupler,28 and protonation.29

Since hydrogen

migration in porphycene can be easy to realize by some methods such as the force-induced,30 hot carrier-induced31 and single atoms or molecules-induced tautomerizations,32 and the effect of substituents on proton migration in porphycene and mechanisms of intramolecular proton-transfer reactions have been widely studied in recent years,33,34 porphycene should be a promising coupler with proton-transfer tunable electronic properties. 2


Thus, we can

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envision that the porphycene-based diradical systems should have the magnetic spin coupling properties tunable or switchable through intramolecular proton transfer tautomerization.

In

addition, the UV/Vis/NIR absorption spectra of porphycene diradicals have obvious characteristic peaks (e.g. Soret-like bands) compared with that of the porphycene monomer, and the absorptions at the long wave are obviously enhanced.35,36

Since different

porphycene diradicals exhibit different absorption, the tunability of absorbed light wavelengths for them was also discussed in recent years.20,35-37

Clearly, the porphycene

molecule featuring diradicals can have strong characteristic absorption spectra with appropriate wavelengths, and such absorptions can be reasonably regulated through intramolecular proton transfers. Inspired by unique structure and properties of porphycene, in this work, we design novel porphycene-based diradicals and explore their magnetic spin coupling characteristics at the B3LYP/6-311G(d,p) level.

Most importantly, we can realize the magnetic spin coupling

regulation of the porphycene diradicals through intramolecular proton transfers.

Besides, the

attaching position and orientation of the functionalizing nitroxide radical groups also considerably affect the spin coupling magnitude and even characteristics (ferromagnetic (FM) versus antiferromagnetic (AFM) coupling).

The achievability of magnetic spin coupling

regulation is verified by calculating the proton transfer energy barriers in the porphycene core which are lowered due to diradicalization.

Clearly, the present study on the magnetic spin

coupling interactions of these porphycene diradicals provides a theoretical guidance for their applications in magnetic electronic devices and relevant fields, and this kind of molecular materials has exhibited a huge application prospect.



DESIGN SCHEME AND COMPUTATIONAL DETAILS By considering the π-conjugation character and proton transfer properties of porphycene

and radicalization scheme of organic conjugated systems for diradicals, in this work, we design the diradical-functionalized porphycene molecules through attaching two nitroxide radical groups (as spin sources) to porphycene (as coupler) which may be structurally tautomerized by proton transfer in the core region.

These diradicals can be differentiated by

3



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their cis-trans positions of the added nitroxide radical groups and two protons within the porphycene core.

As shown in Scheme 1 and 2, porphycene has two C=C units in two

opposite edges, and thus four linking sites for substituents.

Taking the two parallel C=C

units in the porphycene macrocycle as a reference, two nitroxide radical groups can be connected to their same (cis) or different (trans) sides, respectively, denoted as NOc (the cis form) or NOt (the trans form).

Meanwhile, two hydrogens in the porphycene core can be

labeled by Hc (the cis form) in the same sides or Ht (the trans form) in the opposite sides, respectively.

Their combinations lead to different isomers, as marked by these notations and

additional suffixes (1 or 2), e.g. NOc-Hc-1 and NOc-Ht-1.

Since the orientations of two

nitroxide radical groups also affect the spin coupling interactions, we further mark the orientation isomers of the radical groups by the suffixes a, b, c and d.

Thus, each above

diradical molecule has three structural isomers by changing the radical group orientation, e.g. NOc-Hc-1a, NOc-Hc-1b, NOc-Hc-1c for NOc-Hc-1 and NOc-Ht-1a, NOc-Ht-1b, NOc-Ht-1c for NOc-Ht-1 (Scheme 1 and 2).

Here, we explore in detail the effects of proton transfers,

position linking and orientation of nitroxide radical groups on the magnetic spin coupling properties of these designed porphycene diradicals.

In particular, we focus on the proton

transfer regulation of the spin coupling interactions, together with an analysis about the change of proton transfer energy barrier in the porphycene coupler induced by the introduction of two nitroxide radical groups. The configuration optimizations and frequency analyses were performed at the B3LYP/6-311G(d,p) level for the closed-shell singlet state (CS), broken-symmetry open-shell singlet state (BS), triplet state (T) of the diradicals and the energies and magnetic exchange coupling constants (J) were calculated at the same level (Figure 1 and Table S1 in the Supporting Information (SI)).

The BS state was determined by the Noodleman method,38

and J was calculated by the formula,39 J = (EBS - ET)/(T - BS), where EBS and ET are the total energies and BS and T are the average spin square values of the BS and T states, respectively.

As shown in Table S2 and S3 in the SI, for the purpose of verification

and reliability of the results at the B3LYP/6-311G(d,p) level, single point calculations were performed at the B3LYP/6-311++G(d,p) for all porphycene diradicals and the M06-2X/6-311++G(d,p) level for some porphycene diradicals. 4


The results have confirmed

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the reliability of the B3LYP/6-311G(d,p) results (Figure S1 in the SI). ■

RESULTS AND DISCUSSION We theoretically design porphycene diradical isomers through considering three factors

(protonation sites, and linking positions and orientation of radical groups), as shown in Scheme 1 and 2.

Clearly, there are two position isomers for the linkage of two nitroxide

radical groups to the two C=C units: the cis and trans ones, as mentioned above.

However,

for each position isomer, proton transfer could further lead to different tautomers which feature different protonated states of the cores of the porphycene coupler: also the cis and trans ones.

As shown in Scheme 1, for the cis-nitroxide radicals (NOc), different

porphycene diradical isomers can be obtained by intramolecular proton transfers, such as NOc-Hc-1a → NOc-Ht-1a → NOc-Hc-2a → NOc-Ht-2a, while for the trans-nitroxide radicals (NOt), proton transfers can lead to NOt-Hc-1a, NOt-Ht-1a, NOt-Hc-2a and NOt-Ht-2a. Moreover, for the nitroxide radical groups, there are also different orientations, which further lead to more porphycene diradical isomers, as donated by the suffixes a, b, c and d.

Scheme

2 shows the correlations among different nitroxide orientation isomers for possible porphycene diradicals.

For example, NOc-Hc-1a can produce NOc-Hc-1b and NOc-Hc-1c by

changing nitroxide radical orientations, while the others (e.g. NOc-Ht-1a, NOc-Hc-2a and NOc-Ht-1a) can also change to their corresponding radical orientation isomers.

But, the

porphycene isomers, NOc-Ht-2b and NOc-Ht-2c, obtained by rotating the radical groups of NOc-Ht-2a, are the same as NOc-Ht-1b and NOc-Ht-1c, and NOt-Ht-1b and NOt-Ht-2b are the same as NOt-Ht-1c and NOt-Ht-2c among NOt-Ht-1 and NOt-Ht-2 series nitroxide radical isoforms, respectively, and thus they are not repeatedly considered here.

In addition, for the

NOt-modified porphycene diradicals there are also other type of nitroxide radical oriented isomers (i.e. NOt-Hc-1d, NOt-Ht-1d, NOt-Hc-2d and NOt-Ht-2d, Scheme 2 and Figure S2 in the SI).

All relevant results including the energies of the BS and T states, ΔE(BS-T), the

values, and associated magnetic exchange coupling constants (J) calculated at the B3LYP/6-311G(d,p) level are given in Figure 1 and Table S1 in the SI.

Clearly, these

results have fully indicated intriguing changes of the spin coupling constants (J) and energies of the BS and T states for the porphycene diradicals due to proton transfers and changes of the 5



linking mode and orientations of radical groups. shown in Figure S2-S3 in the SI.

Page 6 of 36

Besides, the optimized geometries are

In order to better understand the magnetic transitions in

these porphycene diradicals, we conduct electronic origin analyses from spin alternation rule, SOMO-SOMO energy splitting and spin polarization and delocalization.

We also analyze

the effects of linking position and orientation of nitroxide radical groups.

Most importantly,

we analyze the proton transfer barriers and discuss the mechanism of proton transfer regulation of the magnetic spin coupling properties. Basic Geometric Character and Relative Stability Analyses.

The optimized

geometries indicate that all porphycene diradicals are coplanar where not only the coupler itself is planar but also the nitroxide radicals are coplanar with the porphycene coupler, which creates a favorable condition for the π-conjugation between the two nitroxide spin sources and porphycene coupler (Figure S2 in the SI).

The extended conjugation contributes to strong

spin coupling interaction between two unpaired electrons of the nitroxide radical groups and leads to a large degree of spin polarization for these porphycene derivatives in comparison with the non-planar porphyrin analogues.10 The backbone bond lengths of the optimized nitroxide-modified porphycene molecules are shown in Figure S3 in the SI.

Generally, the

standard length of a single bond C−C is ca. 1.540 Å and that of a double bond C=C is about 1.330 Å.

Here, all optimized C−C bond lengths are 1.350-1.460 Å which are between single

and double bonds (Figure S3 in the SI), demonstrating that each of the porphycene couplers is a large π-conjugated system.

Undoubtedly, the expanded π-conjugated structure is

beneficial to the conduction of electrons and thus these nitroxide-modified porphycene molecules are more likely to exhibit diradical characters.

As shown in Figure S3 in the SI,

for the NOc-modified porphycene diradicals (NOc-Hc-1a, NOc-Ht-1a, NOc-Hc-2a and NOc-Ht-2a), the C−N bonds (Ccoupler−Nradical) are about 1.392 Å, while those in the NOt-modified ones (NOt-Hc-1a, NOt-Ht-1a, NOt-Hc-2a and NOc-Ht-2a) are only 1.374-1.386 Å.

They all are shorter than the common C-N single bonds, further indicating effective

π-conjugation between the nitroxide groups and the porphycene coupler which favors the spin delocalization and thus the spin coupling of the nitroxide radical groups.

Certainly, the

differences in the C-N bond lengths can yield different effects on the spin coupling 6


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interactions between two spin sources, depending on the actual structures of the diradicals. In general, a shorter spacer (a shorter C-N bond here) is more favorable to the spin coupling.7 Further, we also compare the ground state energies of all considered diradicals and find that the most stable diradical is NOt-Ht-1d with an open-shell singlet (BS) ground state, although it energetically is only slightly lower than NOt-Ht-1b and NOt-Ht-1a by 0.63 and 1.13 kcal/mol, respectively.

For other NOt-modified diradicals, the ground state energies of

NOt-Ht-2a and NOt-Ht-2b are only 1.27 and 2.88 kcal/mol higher than the most stable structure, respectively, while NOt-Hc-1c with relatively small coupling constant is energetically higher only by 4.41 kcal/mol.

However, the ground states of the cis-nitroxide

diradicals (the NOc-Hc-1 family) are higher than that of NOt-Ht-1d by 6.59 (NOc-Hc-1a), 7.04 (NOc-Hc-1b) and 6.15 (NOc-Hc-1c) kcal/mol, respectively.

NOc-Hc-2c has the highest

energy and is 9.69 kcal/mol higher than the most stable NOt-Ht-1d among those diradicals (NOc-Ht-1, NOc-Hc-2, and NOc-Ht-2) with a T ground state.

The diradicals with the

NOt-modified structures have higher symmetry and their ground states are relatively lower and are more supportive of the spin coupling interactions between two radical groups through the porphycene coupler (Table S5 in the SI).

The fact that the most unstable NOc-Hc-2c is

only 9.69 kcal/mol higher than the most stable isomer indicates that these diradical isomers have comparable stability.

In other word, the proton transfer tautomerization does not yield

significant thermodynamic effect (i.e. only being less endothermic or exothermic), and thus these diradicals could be utilized for the molecular magnet design. Diradical Characters and Magnetic Spin Couplings.

Porphycene itself is a large

π-conjugated structure that could exhibit magnetic spin coupling properties after diradicalization.

From Figure 1 and Table S1 (in the SI), we can find that some of the

porphycene diradicals have the BS ground states with the values close to 1.0 and the others have a T ground state ( = ca. 2.0) and a low-lying BS excited state.

Undoubtedly,

these indicate that all molecules are standard diradicals and have the expected magnetic spin coupling characteristics (AFM or FM).

Interestingly, different proton-transfer structures of

porphycene diradicals have different magnetic spin coupling magnitudes or characteristics (Scheme 1-2 and Figure 1), indicating that proton transfers could modulate the spin coupling 7



interactions.

Page 8 of 36

For the NOc-structured porphycene diradicals, the NOc-Hc-1 family (i.e.

NOc-Hc-1a, NOc-Hc-1b and NOc-Hc-1c) exhibit AFM spin coupling characteristics (-321.4 cm-1, -43.9 cm-1 and -661.6 cm-1), while their corresponding proton transfer tautomers (NOc-Ht-1a, NOc-Ht-1b and NOc-Ht-1c) exhibit the FM spin coupling characteristics (647.5 cm-1, 703.7 cm-1 and 590.7 cm-1).

Besides, the other series of diradicals including the

NOc-Hc-2 and NOc-Ht-2 families all also exhibit strong FM spin couplings (J = 401.6 - 728.9 cm-1, Figure 1).

The Hc-structured porphycene coupler can undergo a proton transfer

process to obtain a Ht-structured one, and the diradical exhibits a magnetic conversion from AFM to FM and also an increase of the magnetic spin coupling strength |J|.

For example,

for the NOc-Ht-1 family of diradicals (NOc-Ht-1c, NOc-Ht-1a, and NOc-Ht-1b), the J values (590.7 cm-1, 647.5 cm-1, and 703.7 cm-1) mildly increase, in contrast to the corresponding NOc-Hc-1 family (J= -661.6 cm-1, -321.5, and -43.9).

These results also indicate that the

orientation of nitroxide groups also considerably affects the magnitudes of J and thus the magnetic spin coupling transition magnitudes (e.g. from 647.5 cm-1/NOc-Ht-1a to -321.5 cm-1/NOc-Hc-1a with change of 969.0 cm-1 for the orientation a, versus from 703.7 cm-1/NOc-Ht-1b to -43.9 cm-1/NOc-Hc-1b with change of 747.7 cm-1 for the orientation b). Similarly, for the NOt-structured porphycene diradicals, proton transfers also considerably modulate the magnetic spin coupling interactions but do not cause a magnetic transition.

That is, all trans-nitroxide-modified porphycene diradicals including the families

of NOt-Hc-1, NOt-Ht-1 and NOt-Ht-2 have the BS ground states and exhibit the AFM spin coupling characteristics.

For NOt-Hc-1a, NOt-Hc-1b, NOt-Hc-1c and NOt-Hc-1d, the

coupling constants (J) have quite large negative values (-1037.5 cm-1, -1368.5 cm-1, -996.6 cm-1 and -1364.94 cm-1), and after proton transfers the negative J values further enlarge (NOt-Ht-1a/-1832.25 cm-1, NOt-Ht-1b(c)/-1933.03 cm-1 and NOt-Ht-1d/-2125.85 cm-1). Further, for each series of diradicals, different orientations of the nitroxide groups also noticeably affect the sizes of the coupling constants J (increasing from left to right as shown in Scheme 2 and Figure 1).

Clearly, for the NOt-structured porphycene diradicals, proton

transfers only noticeably change the sizes of the spin coupling constants, but does not change their signs. We also find that the linking position of nitroxide groups also affects the size of J. 8


As

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shown in Scheme 1, for a porphycene coupler (Hc or Ht), the different position linkage of the nitroxide radicals leads to considerable differences in the magnetic spin coupling properties. When two nitroxide groups are connected to two C=C units in the cis form (NOc), the formed NOc-Ht-1a, NOc-Hc-2a and NOc-Ht-2a present the FM spin coupling characteristics, while for the connection in the trans form (NOt), the formed NOt-Ht-1a, NOt-Hc-2a and NOt-Ht-2a exhibit the AFM spin coupling characteristics and the magnitudes of spin couplings are correspondingly enhanced after changing the linking positions of nitroxide groups from the cis form to the trans form.

For example, NOc-Ht-1a, NOc-Hc-2a and NOc-Ht-2a have the J

values of 647.5 cm-1, 570.5 cm-1, and 728.9 cm-1, respectively, while NOt-Ht-1a, NOt-Hc-2a and NOt-Ht-2a have large negative values (-1832.3cm-1, -1037.5cm-1 and -1486.8 cm-1). However, NOc-Hc-1a (-321.4 cm-1) after changing the linking position of nitroxide groups converts to NOt-Hc-1a (-1037.5 cm-1) but without a transition of magnetic spin coupling characteristics and only leads to an increase in the magnitude of spin coupling.

The origin of

the spin coupling transition is discussed in detail in the following spin alternation rule.

Here,

we simply attribute the enhancement of magnetic spin coupling to the differences in structural symmetry of these diradicals.

For the NOt-structured porphycene diradicals, their symmetry

is significantly higher than that of the NOc-structured diradicals (i.e. centrosymmetric versus noncentrosymmetic backbone), which is favorable to delocalization of spin electrons on nitroxide radical groups (spin polarization) and thus the spin coupling interactions. Spin Alternation Rule Analysis and Spin Coupling Channels.

The spin alternation

rule40,41 has been widely used as a standard to predict the magnetic coupling characteristics of diradicaloids, especially for the polycyclic systems with diradical characters.

However, in

existence of some couplers with five-membered rings or their heteroatoms-doped derivatives, the spin density distributions of diradicals do not comply with the standard spin alternation rule.

Therefore, the extended spin alternation rules were suggested10,40 and have been

applied to the special diradical molecules.

The basic principle is that the sign of the

magnetic exchange coupling constant is determined by the numbers of conjugated bonds and their contributed electrons in the coupling pathway.40,42 According to the previous work,40 a molecule exhibits the AFM coupling if the number of bonds is odd. 9


On the contrary, if the


number of bonds is even, it exhibits the FM coupling.

Page 10 of 36

Here, the porphycene coupler has two

main coupling pathways (left versus right side, Figure 2) for the present cases, and for each five-membered pyrrole ring there are also two pathways (through –C-C– or through –N(H)–). Clearly, the numbers of bonds in these possible coupling pathways are different, thus resulting in different magnetic spin coupling characteristics.

As shown in Figure 2, the red

numbers and arrows donate the distribution and direction of α spin, while the purple numbers and arrows denote those of the β spin electron.

The pink and blue bonds show the spin

coupling channels, and the blue and pink lines represent the FM and AFM coupling pathways, respectively.

According to the spin density distribution of the diradicals, we can draw the

spin alternation maps of them which clearly show the magnetic spin coupling mechanism of diradicals.

For NOc-Hc-1a, each of the nitrogen atoms (>NH, the amino N) on two pyrrole

rings provides two π electrons, which is equivalent to a π bond, while for the nitrogen atoms (=N, the imino N) on other two pyrrole-like each provides only one π electron.

There are

odd number of bonds on two coupling pathways that are mutually supportive and jointly promote the diradical to show the AFM spin coupling characteristics for NOc-Hc-1a. However, after single proton transfer, NOc-Hc-1a becomes NOc-Ht-1a.

Since the molecule

(NOc-Ht-1a) has a pyrrole nitrogen (>NH) structure on each of the two coupling pathways, two coupling pathways have even number of bonds, which contributes to the FM spin coupling in NOc-Ht-1a.

However, the orbital energies and shapes of two or more atoms of

porphycene are similar and form degenerate orbitals, resulting in the presence of a “pseudoatom”.

As shown in Figure S4 in the SI, in the HOMO of the CS state, two pπ

orbitals are of the same type as red-cycled, thus forming the “pseudoatom”.

For NOc-Hc-2a

(Figure S4 in the SI) which is the double proton transfer product of NOc-Hc-1a, two pπ orbitals of the C=C bond region that links two five-membered rings are of the same type and form an orbital, which makes the two carbon atoms have same spin orientations and merge into one “pseudoatom”.

Due to the presence of pseudoatom, the number of bonds on each coupling

pathway in NOc-Hc-2a is reduced by one relative to NOc-Hc-1a, resulting in a positive J value (FM). Similarly, NOt-Hc-1a increases or decreases a bond correspondingly in the two coupling pathways due to the change of the position of the radical group, which causes the molecule to 10


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exhibit opposite magnetic properties to NOc-Hc-1a. But also due to the presence of the pseudoatom in the C=C region, NOt-Hc-1a still exhibits the AFM coupling.

Other

NOt-modified porphycene diradicals obtained by linkage position change of nitroxide radical exhibit opposite magnetic properties to the corresponding cis-linked nitroxide radicals (NOc), as shown in Figure S6 in the SI.

Clearly, the spin alternation rule has been further extended

by introducing the concept of pseudoatom and now can explain the magnetic spin coupling properties of all porphycene diradicals well (Figure S6 in the SI). As shown in Figure S5 in the SI, we mainly show the spin density maps of ground states of all porphycene diradicals.

In order to clarify the ground states of different porphycene

diradicals, the spin density plots of higher spin state are shown in Figure S5b in the SI. According to the way of the mismatching of spin polarization for spin density distribution to understand the ground spin states in organic diradicals including 5-memberd ring couplers used by Lee and coworkers,6,42 we compare the spin density distributions of the BS and T states of all porphycene diradicals and find that the spin densities of the triplet states of the NOt-Ht-modified porphycene diradicals (NOt-Ht-1a/b/c/d and NOt-Ht-2a/b/c/d) do not match the spin polarization, and thus the spin couplings of the triplet states are hindered.

The

remaining porphycene diradical isomers do not possess the mismatching spin polarization, but different ground states and magnetic properties of different proton transfer isomers are well explained in terms of spin alternation rules.

Therefore, we find that porphycene diradicals

change the structure of the porphycene coupler by intramolecular proton transfer(s), which changes the number of chemical bonds on the coupling paths on both sides and thus realizes the magnetic regulation of the porphycene diradicals. SOMO−SOMO Energy Level Splitting.

The energy level splitting of two singly

occupied molecular orbitals (SOMO) is an empirical rule that can be used to explain the signs and magnitudes of the magnetic coupling constants for diradical molecules.27,43-45

At first,

Hoffmann43 suggested that if ΔESS < 1.5 eV, the diradical molecule has a triplet ground state and when ΔESS > 1.3 eV, the molecule has a singlet ground state, where ΔESS means the SOMO-SOMO energy gap associated with two single electrons in the triplet state.

Similarly,

we perform a ΔESS analysis of the nitroxide-modified porphycene molecules with diradical 11



character.

Page 12 of 36

Table S4 (in the SI) gives the ΔESS energy gaps of all porphycene diradicals

(given in Scheme 1) that undergo the proton transfers and linking position changes.

From

Table S4 (in the SI) we can find that ΔESS for diradicals (NOc-Ht-1, NOc-Hc-2 and NOc-Ht-2) with the FM spin coupling characteristics are very small (only ca. 0.2 eV) and far less than 1.5 eV.

However, for the molecules (NOc-Hc-1, NOt-Hc-1, NOt-Ht-1 and NOt-Ht-2), their ΔESS

are relatively large (0.65 -1.23 eV) and close to 1.3 eV, which correspond to the singlet ground states.

Although these results (Table S4 in the SI) do not obey the above

Hoffmann’s criterions (which should be modified for different systems with large structural differences), the basic tendency is in good agreement, as evidenced by a good linear correlation between ΔESS and ΔEST (the singlet-triplet (S-T) energy gaps) which is shown in Figure 3.

That is, as the increase of ΔESS, ΔEST gradually decreases, obeying a linear

relationship, which is also in good agreement with that between ΔESS and ΔEST proposed by Constantinides et al.27

Further, large ΔESS values in NOc-Ht-1, NOc-Hc-2 and NOc-Ht-2

result in small J values (the FM coupling characteristics), but large those in NOc-Hc-1, NOt-Hc-1, NOt-Ht-1 and NOt-Ht-2 lead to strong AFM coupling interaction.

Hence,

porphycene diradicals with negative J values have relatively large ΔESS, which are also in keeping with the close relationship between the S-T energy gaps and SOMO-SOMO energy level splittings.

In short, by means of and SOMO-SOMO energy level splittings of triplet

state, we can explain the changes in magnetic spin coupling constants caused by proton transfers and different position linking of nitroxide radical groups for these diradicals. Spin Polarization Analysis.

To further understand different J coupling magnitudes and

characteristics of these cis/trans isomers of the porphycene diradicals, spin polarization or delocalization is analyzed.

In general, most of spin densities are concentrated on the spin

sources (i.e. nitroxide radical groups), but spin polarization is observed through spin delocalization over the entire diradical backbone including the spin sources and coupler. Spin density map (Figure S5 in the SI) shows that the spin density of each porphycene diradical spreads out on the whole molecule with a relatively large polarizability of two unpaired electrons.

Previous studies indicated that large spin polarization can motivate the

spin coupling interaction between two nitroxide radical groups, and thus yield a large |J| 12


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value.29

In order to fully understand the effect of the linking position of nitroxide radicals on

spin polarization, we first make a comparison of spin densities for the cis/trans-linked structures of nitroxide radicals.

The trans-structured nitroxide radicals have relatively high

symmetry and a high degree of conjugation, and thus have large spin polarization.

As

shown in Figure 4, only 22.1% -24.9% of spin densities are delocalized to the porphycene coupler for the cis-form linkage (NOc) of nitroxide groups (NOc-Hc-1a, NOc-Ht-1a, NOc-Hc-2a and NOc-Ht-2a), while spin polarization considerably increases to be about 28-38% for the trans-form (NOt-Hc-1a, NOt-Ht-1a, NOt-Hc-2a and NOt-Ht-2a).

All results

indicate that the trans-form linkage (NOt) of two nitroxide groups (NOt-Hc-1a, NOt-Ht-1a and NOt-Ht-2a) have large spin polarization and thus large magnetic spin coupling constants (|J|). Besides, large magnitudes of atomic density distributions (blue-circled) of the connecting carbons between the nitroxide groups and coupler also further demonstrate strong spin polarization from the spin sources (the nitroxide groups) to the porphycene coupler. Therefore, we can get a conclusion that large degree of delocalization of spin density corresponds to a strong magnetic spin coupling interaction featuring a large |J| value.

It

should be noted that shifting the linking position of nitroxide radical groups (e.g. converting NOc-Ht-1a to NOt-Ht-1a) not only changes the size of |J| value but also may change its sign (i.e. magnetic coupling characteristics conversion), which can be predicted by means of the SOMO−SOMO energy level splitting and spin alternation rule as mentioned above. Coincidentally, the rule can be also applied to other porphycene diradicals (Figure S8 in the SI).

For the porphycene diradicals with same nitroxide-linked configurations, different

radical group orientations also cause changes in spin polarization.

This is because that the

radical orientations in some configurations are favorable to the formation of weak intramolecular >N-OH-C hydrogen bond(s), improving the conjugation between the porphycene coupler and nitroxide groups and thus enlarging spin delocalization.

For

example, as shown in Figure S8 (in the SI), spin polarization gradually increases for the diradicals (24.5% in NOc-Hc-1b, 26.4 % in NOc-Hc-1a and 32.0% in NOc-Hc-1c) and correspondingly the numbers of their intramolecular hydrogen bonds also increase (0, 1 and 2 for them), in good agreement with the coupling constant changes (-44.9 cm-1, -321.5 cm-1 and -661.6 cm-1 for them, Scheme 1). 13



Page 14 of 36

The Effect of Orientation of the Nitroxide Radical Groups. the radical orientation change can regulate the J coupling.

Besides, we also find that

As shown in Scheme 2, the

change of nitroxide orientation causes an increase in the coupling constant and does not change the magnetic characteristics of porphycene diradicals.

Nitroxide radical rotation has

different effects on the changes of magnetic coupling constants of different proton transfer isomers.

First, for the NOc-modified porphycene diradicals, the magnetic spin coupling

constants of Hc-structured porphycene molecules (NOc-Hc-1 and NOc-Hc-2) increase from NOc-Hc-1b (NOc-Hc-2b) to NOc-Hc-1a (NOc-Hc-2a) to NOc-Hc-1c (NOc-Hc-2c), (i.e. NOc-Hc-1b/-43.99 cm-1 to NOc-Hc-1a/-321.36 cm-1 to NOc-Hc-1b/-661.59 cm-1).

For the

NOt-modified ones, the magnetic exchange coupling constants of Ht-structured porphycene molecules (NOt-Ht-1 and NOt-Ht-2) are the smallest for the a-oriented porphycene molecules (NOt-Ht-1a/-1832.25 cm-1 and NOt-Ht-2a/1486.84cm-1), and the largest for the d-oriented ones (NOt-Ht-1d/-2125.85 cm-1 and NOt-Ht-2d/1704.36 cm-1).

As shown in Figure 5, some

structures of porphycene diradicals (e.g. NOc-Hc-1c and NOc-Hc-1c) favor the formation of intramolecular hydrogen bonds (>N-OH-C) between the radical(s) and porphycene coupler, forming a stable additional six-membered ring structure.

This structure allows the

porphycene coupler to be better conjugated with the radical groups, which is mainly reflected in the N-O bond lengths.

As shown in Figure S3 (in the SI), the bond lengths of the N-O

bonds forming the intramolecular hydrogen bonds are significantly shortened and are in between the single and double bonds (NOc-Hc-1b/1.266 Å, NOc-Hc-1a/1.262 Å and NOc-Hc-1c/1.261 Å), which clearly supports the magnetic spin couplings quite well.

The

intramolecular hydrogen bonds make the spin electrons on the nitroxide groups better delocalize to the coupler, leading to higher spin polarizability.

According to the spin density

distributions and spin polarization analysis mentioned above, we can find that the spin polarizabilities of the diradicals increase gradually (e.g. from 24.5% of NOc-Hc-1b, 26.4% of NOc-Hc-1a to 32.0% of NOc-Hc-1c, Figure S8 in the SI).

Similarly, the formation of two

intramolecular hydrogen bonds in NOt-Ht-1d and NOt-Ht-2d further increases spin polarization, resulting in larger spin coupling constants in them than those in NOt-Ht-1b/NOt-Ht-2b featuring an intramolecular hydrogen bond and NOt-Ht-1a/NOt-Ht-2a without hydrogen bonds.

Thus, the spin coupling constants of the diradicals gradually 14


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increase following the increase of the numbers of intramolecular hydrogen bonds. However, for the NOc-Ht-1 and NOt-Hc-1 series molecules, the magnetic spin coupling constants of different nitroxide-orientated structures increase from NOc-Ht-1c/NOt-Hc-1c to NOc-Ht-1a/NOt-Hc-1a to NOc-Ht-1b/NOt-Hc-1b and are not affected by intramolecular hydrogen bonds.

The position changes of nitroxide radicals in the NOc-Ht-1 and NOt-Hc-1

series result in increases in the coupling constants, which can be reflected from the degrees of spin polarization (Figure S8 in the SI).

The spin polarizations of all diradicals reveal that if

molecular spin polarizations are large, the corresponding spin coupling constants are also large, presenting a positive correlation which is essentially determined by the nitroxide orientations.

For example, the spin polarization of three nitroxide-rotamers (NOt-Hc-1c,

NOt-Hc-1a and NOt-Hc-1b) are 29.1%, 32.0% and 33.6%, respectively, and the spin coupling constants of them are -996.3 cm-1, -1037.5 cm-1 and -1368.5 cm-1 in the same order.

For the

NOc-Ht-1c, NOc-Ht-1a and NOc-Ht-1b rotamers, spin polarizations have quite small changes (23.8%, 24.4% and 24.9% for them), and their spin coupling constants change little (590.7 cm-1, 647.5 cm-1 and 703.7 cm-1), indicating that the orientation effect of the radical groups are not noticeable in this case. On the other hand, to describe the conformational stability of these diradicals, we examine the BS ground state energy profile as a function of radical-porphycene torsion angle of porphycene diradicals (Figure S7 in the SI).

All geometry optimizations and energy

calculations were simultaneously done at the B3LYP/6-311G(d,p) level by scanning the dihedral angle from 0° to 180° with a stepsize of 10°.

Two stable local minima with the

dihedral angles of 0° and 180° are observed (Figure S7 in the SI), respectively, indicating that the coplanar structures of the nitroxide group and coupler are stable and nonplanar orientation of the radical groups relative to the porphycene coupler is unfavorable to the structural stability and also to the magnetic spin coupling interaction between two radical groups. In short, the orientation effect of nitroxide groups originates from the possibility of forming intramolecular hydrogen bonds in some rotamers of the diradicals. The formation of intramolecular hydrogen bonds between the nitroxide groups and their proximate pyrrole rings can effectively improve the spin polarization and unpaired electron delocalization and thus enhance the magnetic spin couplings for some cases. 15


Undoubtedly, the orientation


Page 16 of 36

effects of the radical groups should be taken into account in designing such kinds of diradical magnets although the radical groups could be further fixed in practical applications. Proton Transfer Regulation.

Our intriguing finding in this work should be the proton

transfer regulation of the magnetic spin couplings in these diradicals.

Comparison among

various protonation states of the diradicals reveals that proton transfers can regulate the magnetic spin coupling magnitudes and characteristics of them.

Certainly, different proton

transfer tautomers featuring different linking positions and orientations of nitroxide groups exhibit different proton transfer effects.

The proton transfer regulation effects present in two

aspects: the variation only in magnetic spin coupling magnitude versus conversion of magnetic spin coupling characteristics.

For the NOc-structured porphycene diradicals

(NOc-Hc-1a, NOc-Hc-1b and NOc-Hc-1c), they have the AFM spin couplings, and other isomers exhibit the FM ones.

Here, the porphycene diradicals change the molecular

configurations by intramolecular proton transfers with the energy changes of the ground state and excited states and further the spin coupling constant J changes.

As shown in Figure 6,

when the AFM spin coupling is strong, the energy of the BS state is lower, the energy of the corresponding T state increases, and the energy gap between the BS and T state (ΔEBS-T) increases, and vice versa.

In Scheme 1, for the NOc-modified porphycene molecules, the

molecule NOc-Hc-1a (-321.4 cm-1) undergoes proton transfer to obtain NOc-Ht-1a (647.5 cm-1), the magnetic properties of the associated molecules vary, and the spin coupling constant increases.

The origin is, as shown in Table S1 (in the SI) and Figure 6, that the

energy of the BS state of the molecule increases during the proton transfer process, and the corresponding T state energy decreases, making NOc-Ht-1a be FM.

At the same time, the

energy gap increases and the spin coupling constant increases accordingly.

Similarly, for the

proton transfer process from NOc-Ht-1a (647.5 cm-1) to NOc-Hc-2a (570.5 cm-1), the T-state energy is still smaller than the BS state, but the energy gap (ΔEBS-T) is reduced and the spin coupling constant is thus reduced.

For the NOt-modified porphycene molecules, the BS state

energies are always reduced during proton transfer process, and the corresponding T-state energies are increased, and thus only the spin coupling constant increases but without magnetic conversion (Figure 6). 16


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In general, the relative ground state energy of a molecule is smaller, its structure is more stable, and the corresponding coupling constant is larger, as shown in Table S5 in the SI. Thus, the Ht-structured porphycene coupler has a relatively stable symmetric structure with a large coupling constant, and proton transfer could cause large changes in the J coupling constants.

For example, the J values of NOc-Hc-1a, NOc-Hc-1b and NOc-Hc-1c with poor

relative stability (6.59, 7.03 and 6.15 kcal/mol) are -321.4, -43.9 and -661.6 cm-1, respectively, but after single proton transfers, the J values of the corresponding proton transfer isomers (NOc-Ht-1a, NOc-Ht-1b and NOc-Ht-1c) with slightly small relative ground state energies (5.54, 3.40 and 5.93 kcal/mol) are 647.5, 703.7 and 590.7 cm-1, respectively.

In particular,

due to very strong intramolecular hydrogen bonds in NOc-Hc-1c, the magnetic spin coupling constant is larger than that of the corresponding single proton transferred structure (NOc-Ht-1c).

In general, the Ht-structured porphycene diradicals have good relative stability,

and large coupling constants compared with Hc-structured diradicals.

Clearly, this

observation reveals the proton transfer regulation of magnetic spin coupling properties. On the other hand, the proton transfer of porphycene diradical changes its molecular structure, thereby changing the spin coupling pathway, and contributes to different coupling modes, as mentioned in the spin alternation rule analysis.

For example, from the spin

alternation rule analysis, NOc-Hc-1a has the AFM spin coupling, but for NOc-Ht-1a, the change in the nitrogen linkage on pyrrole of porphycene due to proton transfer contributes to the spin orientation change of spin electrons, resulting in a conversion from the AFM to FM spin coupling.

That is, the structure change of the porphycene coupler (NOc-Hc-2a) leads to

the appearance of pseudoatom, and thus the J value change from the negative to positive one. Clearly, this reveals a regulation possibility of magnetic properties through intramolecular proton transfer.

However, for porphycene diradicals that nitroxide radical groups are

connected in the trans form (NOt-Hc-1a), only the magnitude of coupling constant changes when proton transfers.

Similarly, from the relative ground state energies and structural

differences, we find that the magnetic spin coupling strength of a Ht-structured porphycene diradical is greater than that of a cis-hydrogen (Hc) structured one.

Since proton transfers

can change the internal structures of the porphycene coupler, the spin density distributions of porphycene diradicals are different, which leads to different spin polarizations. 17


As shown in


Page 18 of 36

Figure S8 (in the SI), the spin polarizability of NOt-Hc-1a is 32.0%, and that of the proton-transferred NOt-Ht-1a increases to 37.7% where the coupling constant of the latter is -1832.3 cm-1, considerably larger than that (-1037.5 cm-1) of the former.

Similarly, the

coupling constants of NOt-Ht-1b/c with large spin polarizations (40%) are -1933.03 cm-1, and the corresponding Hc-structured porphycene diradicals (NOt-Hc-1b and NOt-Hc-1c ) have relatively small J values (-1368.47 cm-1 and -996.63 cm-1) and small spin polarizations (33.6% and 29.1% ).

In short, the increases of coupling constants caused by proton transfers

can be explained well by the increases of spin polarizability (Figure S8 in the SI).

Thus, we

can conclude that the magnetic spin couplings can be regulated for these porphycene diradicals by proton transfers. To clarify the magnetic coupling differences among these systems, we should explore the spin coupling mechanism between two unpaired electrons in the diradicals. As shown in previous studies,10,46 two unpaired electrons of two radical groups undergo the spin coupling interaction through the lowest unoccupied empty orbital (LUMO) of the intermediate coupler. Thus, the coupling mechanism is displayed in Figure 7(a) for the present systems.

The small

energy difference between the LUMO of the coupler and the HOMO (SOMO, the singly occupied molecular orbital) of the radical groups certainly is in favor of strong magnetic exchange coupling interactions.

The porphycene coupler in all the porphycene diradical has

two isomers: one is the Hc-modified porphycene coupler and the other is the Ht-modified one. We calculated the LUMO energies and HOMO-LUMO energy gaps of the Hc-modified and Ht-modified porphycene couplers at the B3LYP/ 6-311G(d,p) level.

The results indicate that

the HOMO-LUMO gap of the Hc-modified porphycene coupler is 2.47 eV, which is higher than that of the Ht-modified porphycene coupler (2.44 eV).

Therefore, the Ht-modified

porphycene as the coupler is beneficial to a large magnetic coupling in the porphycene diradicals.

The energy gaps between HOMOs (SOMOs) of the nitroxide radical groups and

LUMOs of the couplers were calculated at the B3LYP/ 6-311G(d,p) level.

As shown in

Figure 7, the LUMO of the Ht-modified porphycene coupler is energetically 0.40 kcal/mol lower than that of the Hc-modified porphycene coupler, leading to a small HOMO-LUMO gap between the radical groups and Ht-modified porphycene coupler.

Clearly, the porphycene

coupler provides a more favorable energetic basis for the spin coupling between two spin 18


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centers in a diradical through the LUMO in the Ht-modified form. Thermodynamics and Kinetics of Proton Transfers. proton transfer energetics for these diradical systems.

It is necessary to discuss the

There have been many theoretical and

experimental studies on the energy barriers for intramolecular double proton transfer of porphycene in recent years.30,34,47,48

For example, Dai et al. studied that the energy barrier of

porphycene intramolecular proton transfer can reach 5.41 kcal/mol under excited conditions.34 For the present systems, a key question is whether the attachment of two radical groups could affect the proton transfer barrier.

Therefore, we further explore the energy barriers of

intramolecular proton transfers in porphycene diradicals.

The proton transfer energetics at

different stages for porphycene diradicals were obtained through optimizations of the transition state (TS) and steady state structures at the B3LYP/6-311G(d,p) level.

For the

proton transfer isomers, the energy of the reactant is selected as the zero point and relative energies of the transition states, intermediate and product are displayed in Figure 8.

Our

calculations of the minimum energy paths (MEPs) show that the diproton transfer of two cis-hydrogen (Hc) isomers can be realized through a near degenerate trans-hydrogen (Ht) intermediate (Figure 8) and two transition states.

Thermodynamically, the ground state

energies of all porphycene diradicals are slightly low, but they are not quite different, and the reaction heats of double proton transfer are very small.

The ground state energy of the most

stable diradical differs from that of the highest ground state diradical by only 9.69 kcal/mol. As shown Figure 8, although the proton transfer reactions of diradicals (NOc-Hc-1a and NOc-Hc-1c) are endothermic, the reaction heat are only 0.03 kcal/mol and 1.30 kcal/mol, respectively.

However, for NOc-Hc-1b and NOc-Ht-1b, the proton transfer process is

exothermic by 1.39 kcal/mol and 1.59 kcal/mol, respectively. transfer is neither exothermic nor endothermic.

NOt-Hc-1a after proton

From the above comparison, we find that the

Ht-structured intermediate with a low ground state energy is more stable, which demonstrates that the proton transfer is more favorable for porphycene diradicals.

This is in agreement

with the calculated spin coupling constants of the trans-hydrogen (Ht) structured diradicals which are larger than those of the cis-hydrogen (Hc) structured ones. For the NOc-modified porphycene diradicals, the energy gap between the Hc-structured 19



Page 20 of 36

(NOc-Hc-1a or NOc-Hc-1b) and its corresponding Ht-structured diradical is larger (4.09 kcal/mol or 3.76 kcal/mol), and the change of the corresponding J is larger compared with the J change in NOc-Hc-1c with a small energy gap (2.45 kcal/mol).

Similarly, for the

NOt-structured diradical, the ground state energy of the intermediate (with trans-hydrogen) produced during proton transfer is significantly reduced, which leads to a large spin coupling constant. significantly

Kinetically, the energy barriers for NOc-modified porphycene diradicals are reduced.

NOc-Hc-1a

may

convert

into

NOc-Hc-2a

through

two

trans-intermediates (NOc-Ht-1a or NOc-Ht-2a) in two double proton transfer processes, and the transfer energy barriers (TS1/TS2) are 1.96/1.11 kcal/mol and 1.85/1.20 kcal/mol for two channels, respectively (Figure 8(a)).

In addition, two proton transfer energy barriers for

NOc-Hc-1b and NOc-Hc-1c are 1.25/0.45 kcal/mol and 1.74/2.45 kcal/mol, respectively, smaller than those (2.18/2.18 kcal/mol) in porphycene (Figure 8(a) and Figure S9 in the SI). However, the energy barriers of the proton transfers for two channels (via the NOt-Ht-1a or NOt-Ht-2a intermediates) are 4.93 kcal/mol and 5.54 kcal/mol, respectively (Figure 8(b)), slightly larger than those in porphycene.

The above analyses indicate that it is possible to

realize the proton transfer modulation of magnetic spin coupling interactions in such porphycene diradicals.

Simultaneously, these observations also show that the porphycene

diradicals can achieve the transition or variation of their magnetic properties through the easily realized intramolecular proton transfers. 

CONCLUSION We theoretically design the porphycene diradicals through introducing two nitroxide

groups to porphycene and explore their magnetic spin coupling properties in this work. Structurally, attachment of two nitroxide radical groups does not change the planarity of the porphycene unit, which is supportive to the magnetic spin couplings between the added radical groups.

Besides, the position linking and orientation of the introduced nitroxide

radical groups can significantly affect the intramolecular magnetic spin couplings.

In

particular, porphycene itself can undergo proton transfer isomerization, which can be utilized to regulate or switch the magnetic spin couplings through proton transfers in the porphycene diradicals.

For the proton transfer tautomers with same linking and orientation modes, 20


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different protonated states exhibit different protonation effects.

Diradicals (NOc-Hc-1a,

NOc-Hc-1b and NOc-Hc-1c) possess the AFM spin couplings with the J values ranging from -43.9 cm-1 to -661.6 cm-1, whereas after proton transfer they convert to the FM coupling NOc-Ht-1a, NOc-Ht-1b and NOc-Ht-1c with positive J values (590.7 cm-1-703.7 cm-1), respectively.

Definitely, such conversions in the magnetic spin coupling properties can be

explained by the generalized spin alternation rule.

Proton transfers change the structures of

porphycene diradicals, and further change the coupling pathways of spin unpaired electrons. Thus, the proton transfer tautomerization can be viewed as a switch that regulates the intramolecular magnetic spin coupling.

As for the linking mode and orientation effects of

nitroxide radicals, different position linkages could change the spin coupling channel lengths, modes and even spin polarizations of the attaching radical groups and thus control the spin coupling strengths and even characteristics.

For example, the NOc-structured porphycene

diradical series (NOc-Ht-1, NOc-Hc-2 and NOc-Ht-2) exhibit the FM spin couplings, while their corresponding NOt-structured ones (NOt-Ht-1, NOt-Hc-2 and NOt-Ht-2) present the AFM spin coupling characteristics. change.

Both the strength and characteristics of the spin couplings

In addition, the orientation of the radical groups also considerably affects the spin

couplings mainly through forming intramolecular hydrogen bonds which improve not only the system stability but also the spin polarization of the radical groups, as evidenced by the spin coupling increase in the NOt-Hc-1c, NOt-Hc-1a and NOt-Hc-1b series (-996.6 cm-1, -1037.5 cm-1 and -1368.5 cm-1) and the corresponding increase in spin polarization (29.1%, 32.0% and 33.6%).

The other more important is that introduction of the nitroxide radical

groups can significantly reduce the proton transfer energy barriers (1.11-3.05 kcal/mol) in the porphycene couplers, making the proton transfers easier, and also hardly change the proton transfer thermodynamics.

Clearly, the present work reports a rational design for the

porphycene-based molecular magnets with the spin coupling tunable properties through proton transfers.

Certainly, this theoretical prediction needs further experimental supports

including the syntheses of these nitroxide-functionalized porphycene derivatives which should be easily realized.

But, we believe that the reported information here should be

reliable and the designed molecular magnets could find their promising applications in the spintronics materials fields. 21





ASSOCIATED CONTENT

(S) Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.******. All optimized molecular geometries and main bond lengths, relevant energy data for all diradicals, HOMO map of the CS states of all diradicals, spin density maps of the ground states of all diradicals, spin alternation rule and spin density distributions, potential energy surface scan of the BS state for the selected dihedral angles, the spin density distribution and comparison of spin polarization for the matching porphycene diradicals, the proton transfer energy profile of porphycene (PDF). 

AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected] ORCID Xinyu Song: 0000-0002-7486-9388 Yuxiang Bu: 0000-0002-6445-5069 Notes The authors declare no competing financial interest. 

ACKNOWLEDGMENTS

This work was supported by NSFC (21773137, 21873056, and 21573128) and the calculations in this work were carried out on the HPC Cloud Platform of Shandong University.

22


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

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Kato, K.; Furukawa, K.; Osuka, A. A Stable Trimethylenemethane Triplet

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(Radical–Coupler–Radical): Standardization of Couplers for Strong Ferromagnetism. J. Phys. Chem. A 2014, 118, 5112-5121. (43) Hoffmann, R.; Zeiss, G. D.; Van Dine, G. W. The Electronic Structure of Methylenes. J. Am. Chem. Soc. 1968, 90, 1485-1499 (44) Zhang, G.; Li, S.; Jiang, Y. Effects of Substitution on the Singlet−Triplet Energy Splittings and Ground-State Multiplicities of m-Phenylene-Based Diradicals: a Density Functional Theory Study. J. Phys. Chem. A 2003, 107, 5573-5582. (45) Zhang, F. Y.; Song, X. Y.; Bu, Y. X. Redox-Modulated Magnetic Transformations between Ferro- and Antiferromagnetism in Organic Systems: Rational Design of Magnetic Organic Molecular Switches. J. Phys. Chem. C 2015, 119, 27930-27937. (46) Shil, S.; Roy, M.; Misra, A. Role of the Coupler to Design Organic Magnetic Molecules: Lumo Plays an Important Role in Magnetic Exchange. RSC Adv. 2015, 5, 105574-105582. (47) Ciąćka, P.; Fita, P.; Listkowski, A.; Radzewicz, C.; Waluk, J. Evidence for Dominant Role of Tunneling in Condensed Phases and at High Temperatures: Double Hydrogen Transfer in Porphycenes. J. Phys. Chem. Lett. 2016, 7, 283-288. (48) Homayoon, Z.; Bowman, J. M.; Evangelista, F. A. Calculations of Mode-Specific Tunneling of Double-Hydrogen Transfer in Porphycene Agree with and Illuminate Experiment. J. Phys. Chem. Lett. 2014, 5, 2723-2727.

27



Page 28 of 36

Proton Transfers and Magnetic Modulation and Interconversion for the NOc/NOt-Porphycene Diradicals O

O H

H

N

NH

N

N

HN O

N

H O

N

NH

N

O H

N

HN

O

N

H

O H

N

H

NH

N

NH

N

O

O

NOc-Ht-1a J= 647.45 cm-1 O H

HN

N

NH

O

HN

NH

N

N

HN

NH

N

NOt-Ht-1a J= -1832.25 cm-1 O H

O H

N

N

N

NOc-Hc-1a J= -321.46 cm-1

H

N

N

N

N

N

N H

NOc-Hc-2a J= 570.45 cm-1

N

HN

N

HN

N

H

O

NOt-Hc-1a J= -1037.46 cm-1

N N

NH

N

H

NOt-Hc-2a J= -1037.46 cm-1

N

N

H

O

HN

H

O

NOc-Ht-2a J= 728.99 cm-1

NOt-Ht-2a J= -1486.84 cm-1

Scheme 1. Design scheme and schematic structures of representative porphycene diradicals for the linking position and proton transfer isomers.

NOc/NOt denote the two NO in the

cis/trans form with respect to the parallel two C=C units, while Hc/Ht denote the two H in the porphycene core in the cis/trans form. For the suffixes, 1 and 2 denote the numberings of the corresponding isomers, while a, b, and c denote the orientation isomers of the nitroxide radical groups.

28


Page 29 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Scheme 1b. the process of the change of radical orientation O

O H

H

H

N

NH

N

NH

N

the change of radical orientation

NOc-Hc-1b J= -43.99 cm-1

N O

NH

N

NH

N

H

H O

H

N

O

NH

HN

N

NOc-Ht-1c J= 590.70 cm-1

N

O

N

N

HN

NH

N

N

HN


N

N

NOc-Ht-1a J= 647.45 cm-1

H

N O

O


N

N

HN

N

O

HN

H

O

NOt-Ht-1a J= -1832.25 cm-1


N

N

N

NOt-Ht-1b(1c) J= -1933.03 cm-1

HN

N

HN

H

N

HN

NH

N

N

N

NH

N

H

HN

N


HN

N

N

N

NH

N

NH

N

N

N

NOt-Hc-1b J= -1368.47 cm-1 O


HN

N

H

NOt-Ht-2a J= -1486.84 cm-1

O

H

N

N

NOc-Hc-2c J= 712.68 cm-1

H

NOt-Hc-1a J= -1037.46 cm-1

NH

O

NOt-Ht-1d J= -2125.85 cm-1

HN

H

O

H

O

H

N

O

N

NH


N

O

N

HN

O

NH

O

N

N

H

H

N


NOt-Hc-1c J= -996.63 cm-1 H

O

N

O

NH

NOc-Ht-1b J= 703.71 cm-1


NOc-Hc-2a J= 570.45 cm-1

N

O

H

N

N

O

H

N

H

N

NH

NOc-Hc-2b J= 401.47 cm-1

O

H O

N


N

H

N

NH

H

O

N

NH

HN

H

H

NOc-Hc-1c J= -661.59 cm-1

N

O

N

O N

NH

N

H

H

N


N

H

H

O

H

N

NH

O

N

NH

NOc-Hc-1a J= -321.46 cm-1

N

O

H

N


O

O

H O

N

N

N

NH

N

HN

N

O

H

NOt-Ht-2b(2c) J= -1563.58 cm-1

N

O

H

NOt-Ht-2d J= -1704.36 cm-1

Scheme 2. Design scheme and schematic structures of the porphycene diradicals for the radical group orientation isomers. NOc/NOt denote the two NO in the cis/trans form with respect to the parallel two C=C units, while Hc/Ht denote the two H in the porphycene core in the cis/trans form. For the suffixes, 1 and 2 denote the numberings of the corresponding isomers, while a, b, and c denote the orientation isomers of the nitroxide radical groups.

29



647.5 590.7

500

712.7 728.9

703.7

Antiferromagnetic (AFM) Ferromagnetic (FM)

570.5 401.5

NOc-Hc-1 b a c

0

J values (cm-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-43.9

Page 30 of 36

c a b b a c a NOc-Ht-1 NOc-Hc-2NOc-Ht-2

NOt-Ht-1 a b/c d

NOt-Hc-1 c a db

NOt-Ht-2 a b/c d

-321.4

-500

-661.6

-1000

-996.6 -1037.5 -1364.9 -1368.5

-1500

-1486.8 -1563.6 -1704.4

-1832.3 -1933.0

-2000

-2125.8

Figure 1. Histogram of the calculated coupling constants (J, cm-1) for all designed porphycene diradicals. 0.461 O

H

O

0.275

N

-0.161 -0.041 0.056

0.110

-0.011

-0.005 0.068

-0.038 0.048

-0.002 NH0.073 N -0.026

-0.025 0.045

0.123

O

NH

N

0.108 0.009

NH

N

0.082

0.112 0.068

O

H

0.478 O

N

0.022

0.051

-0.022 0.060

-0.005 -0.045

0.072

N

HN

0.155

-0.021 -0.152

O

0.465

N

HN

-0.054 -0.010

N

HN

-0.038 -0.050

N

O

0.010

0.046-0.033

NH

O

N

0.157

0.045

N

NH

0.040-0.043

N

N

0.016 0.032

0.273 N

H

NH

N

NH

N

0.037

0.093 -0.180

-0.015

N

H

H

O

O 0.445

NOt-Hc-1a

NOc-Hc-2a

Figure 2.

HN

H

H

N-0.255

-0.112

0.196

H

O

-0.425 O

H

N

0.030 -0.094

N 0.294

N

-0.167 0.183 0.112 0.023 -0.016 -0.115

-0.053

HN

-0.0460.052

0.052 -0.064

N

NOc-Ht-1a

O H

0.088

HN

NH

H

spin alternation analysis

0.234 -0.173 -0.102 0.003 0.046 0.169 0.062

N

0.066 -0.003 -0.103 -0.177 0.246 O N 0.294 0.462

N

H

N 0.301

-0.0560.048

N

0.190

0.028

NOc-Hc-1a

H

O H

N 0.289

0.235 -0.177 -0.111 -0.027 0.019 0.159 -0.040 N NH 0.087 0.015 -0.031 0.080 -0.035

-0.120

-0.094 N -0.267

-0.435

O 0.467 H

N

-0.098 -0.032

N

NH

0.016

H

Spin density distributions (the left column) and derived spin alternation scheme

(the right column) for NOc-Hc-1a, NOc-Ht-1a, NOc-Hc-2a and NOt-Hc-1a.

The red numbers

and arrows donate α spin, while the purple numbers and arrows denote β spin where the pink and blue bonds show the spin coupling channels. 30


Page 31 of 36

2

Porphycene diradicals

Ferromagnetic (FM)

ST SS

0 S-T Gap (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Antiferromagnetic (AFM)

-2

-4

-6 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

SOMO-SOMO (eV)

Figure 3. The linear correlation between the SOMO-SOMO energy gaps (ΔESS) of triplet states and the singlet-triplet energy gaps (ΔEST) for all porphycene diradicals.

31



0.472 O

-0.088

0.050

-0.009

-0.007 0.067

-0.026 0.026

-0.107

NH

-0.050

0.035

0.129

0.009

N

0.027

0.088 0.149

-0.066 0.037

0.065 -0.063

HN

0.183

0.021

-0.100

0.073

0.038 0.052

N

-0.022 0.100

-0.097

H

0.480

0.213

N 0.299

NH

-0.037 -0.116

0.007

0.223

H

NOc-Ht-2a

NOc-Hc-2a

NOc-Ht-1a

-0.061

N

N 0.278

O

0.438

O

0.084

-0.014 0.095

-0.053 0.154 -0.178

0.036

0.084 -0.067

-0.073 0.035

0.006 -0.047

-0.099

HN

N

0.056 0.146

HN

-0.167

0.265

0.191

0.006

0.161

0.000

0.249

0.478 O

NOc-Hc-1a

HN

N

-0.038 0.052

0.061

0.072

-0.047

0.073

0.025

0.036

77.9

N 0.300

-0.169

-0.100

0.161

0.061

N 0.297

H

O

-0.472

-0.050

-0.170

-0.111 N -0.283

H

-0.026 0.083

N

0.057

-0.037

N

NH

0.087

0.000

0.012

H

0.213

-0.167

-0.114

0.479 O

77.9

N 0.299

H

0.227

0.154

0.001

0.107

0.007 -0.067

-0.009

-0.031

0.480 O

75.1

N 0.285

-0.180 -0.027

N

NH

0.009

H

0.111

-0.149 -0.035

O

0.466

75.5

N 0.283

H

Page 32 of 36

comparison O

-0.425

H

N

-0.054 -0.010 -0.038 -0.050 0.010

H

NH

0.045

N

0.040 -0.043 0.046 -0.033

NH

-0.016

N

0.037 0.016 0.032

-0.112 0.093 -0.180

0.157 0.273

N

-0.015

0.046 -0.061 0.032 -0.085

0.139

-0.110

N

NH

0.046

0.024 -0.049

0.085

-0.032 -0.016

-0.068 -0.024

-0.032 0.061

-0.045

HN

0.110 -0.207

-0.001

NOt-Hc-1a

0.015

0.001

0.180 0.233

N

-0.037

-0.047

0.016

0.112

-0.093

N

N

0.050

HN

-0.112

0.038 0.010 0.054

0.115 -0.183

O 0.425

NOt-Ht-1a

-0.010

HN

0.033 -0.046 0.045 -0.040

NOt-Hc-2a

O

-0.023

H

0.004

0.194

HN

N

0.070 -0.016

-0.042

-0.122

0.129

0.037

0.069

69.9

N 0.262

-0.194

0.255 N

O0.390

H

-0.158

0.167

H

0.429

71.9

N -0.273

0.180

-0.140

O 0.445

H

-0.180

N

H

O -0.446

62.3

N -0.233 0.207

0.112

-0.115

O

-0.390

-0.167

0.183 0.023

68.0

-0.255

-0.069

-0.061 0.033

0.016 -0.070

-0.033 0.061

NH

-0.037

N

-0.128

0.122 -0.194

0.042

-0.004

0.194

-0.262 N

O-0.429

H

NOt-Ht-2a

Figure 4. Analysis of the spin density distribution and comparison of spin polarization for the matching porphycene diradicals, where the upper panel donates the NOc-structured molecules and the lower panel donates the NOt-structured molecules. The red and purple circles donate the degree of spin polarization.

32


Page 33 of 36


1 2 3 4 5 comparision comparision comparision 6 7 8 9 10 11 NOt-Ht-1a NOc-Hc-1a NOc-Hc-1c NOc-Hc-1b 12 -1 -1 -1 AFM= -43.95 cm AFM= -1832.25 cm-1 AF AFM= -321.30 cm AFM= -661.30 cm 13 14 15 16 comparision comparision comparision 17 18 19 20 21 NOt-Ht-2a NOc-Hc-2b NOc-Hc-2a NOc-Hc-2c 22 -1 -1 -1 AFM= -1486.84 cm-1 AF AFM= 407.47 cm AFM= 712.68 cm AFM= 570.45 cm 23 24 25 26 comparision comparision omparision 27 28 29 30 31 32 NOt-Ht-1b/c NOt-Ht-1a NOt-Ht-1d NOc-Hc-1c -1 -1 33 AFM= -1933.03 cm AFM= -2125.85 cm-1 AFM= -661.30 cm-1 AFM= -1832.25 cm 34 35 36 37 comparision comparision mparision 38 39 40 41 42 NOt-Ht-2a NOt-Ht-1d NOt-Ht-2b/c NOc-Hc-2c 43 -1 -1 -1 AFM= -1486.84 cm AFM= -1704.36 cm-1 AFM= -1563.58 cm AFM= 712.68 cm 44 45 Figure 5. Schematic diagram for nitroxide radical orientations and corresponding magnetic 46 47 coupling constant variations and the optimized geometries with possible intramolecular 48 49 hydrogen bonds marked by red-dot-square boxes for NOc-Hc-1, NOc-Hc-2, NOt-Ht-1 and 50 51 NOt-Ht-2. 52 53 54 55 56 57 58 59 60 33



-1249.640 -1249.645 -1249.650

Energies (au)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

BS state energies T state energies BS state energy line T state energy line

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Antiferromagnetic Coupling Ferromagnetic Coupling

EBS-T>0

-1249.655 -1249.660

EBS-T

EBS-T

EBS-T

Proton-Transfer Regulated Magnetic Spin Couplings in Nitroxide

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