PHYSICAL REVIEW MATERIALS 5, 094409 (2021)

Hydrogen-bonded single-component organic ferroelectrics revisited by van der Waalsdensity-functional theory calculations

Shoji IshibashiResearch Center for Computational Design of Advanced Functional Materials (CD-FMat), National Institute of Advanced Industrial

Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan

Sachio HoriuchiResearch Institute for Advanced Electronics and Photonics (RIAEP), National Institute of Advanced Industrial

Science and Technology (AIST), Tsukuba, Ibaraki 305-8565, Japan

Reiji KumaiPhoton Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba,

Ibaraki 305-0801, Japan

(Received 21 June 2021; accepted 13 September 2021; published 22 September 2021)

We apply van der Waals density-functional theory (vdW-DFT) calculations to predict crystal structureparameters and spontaneous polarization values for seven hydrogen-bonded single-component organic ferro-electrics. The results show good agreement with experimental results, implying that an important step for thecomputational materials design of organic ferroelectrics has been achieved. This approach also enables thesimulation of electromechanical responses. Calculations using the vdW-DFT method are performed for croconicacid (CRCA), 2-phenylmalondialdehyde (PhMDA), and 5,6-dichloro-2-methylbenzimidazole (DC-MBI) underuniaxial stresses or electric fields. Direct piezoelectric d33 constants are evaluated from the polarization changeas a function of stress, whereas converse piezoelectric d33 constants are evaluated from the change in latticeparameter as a function of electric field. The obtained values show acceptable agreement with the experimentalvalues if possible objective factors are considered. The stress-induced or electric-field-induced variation ofpolarization is analyzed considering two types of contributions. One is from proton transfer as a classical pointcharge motion and the other residual part corresponds to the redistribution of π electrons.

DOI: 10.1103/PhysRevMaterials.5.094409

I. INTRODUCTION

Organic ferroelectrics and piezoelectrics are attracting in-creasing attention, mainly because they contain neither toxicnor rare elements, making them environmentally friendly.They offer additional advantages of being lightweight andworkable. Organic ferroelectrics include a class of com-pounds known as “hydrogen-bonded systems,” in whichproton transfer induces π -bond dipole switching [1]. Forsuch hydrogen-bonded systems, we recently reported thattheoretical calculations based on the generalized gradient ap-proximation (GGA) of the Perdew-Burke-Ernzerhof (PBE)form [2] can well predict their spontaneous polarization val-ues using experimentally obtained crystal structures with onlyhydrogen positions computationally optimized [3–7]. Hydro-gen positions are well known to be difficult to accuratelydetermine by x-ray diffraction analysis. In some cases, such

Published by the American Physical Society under the terms of theCreative Commons Attribution 4.0 International license. Furtherdistribution of this work must maintain attribution to the author(s)and the published article’s title, journal citation, and DOI.

calculated polarization values have been utilized as the targetfor process optimization [3,6]. Of course, spontaneous polar-ization is one of the most important factors in describing theperformance of ferroelectrics. Nonetheless, accurate experi-mental structural data are not always available. Computationaloptimizations for all of the crystal structure parameters arenecessary in such cases. For organic ferroelectrics, the vander Waals (vdW) interaction is often important for binding.Neither the local density approximation (LDA) [8,9] nor theGGA [2] can describe the vdW interaction accurately. To over-come this problem, the vdW density-functional theory (DFT)method [10] is expected to be a good solution. Accurate infor-mation about crystal structures is crucial in predicting not onlyground-state properties but also excited-state properties [11].

In the present paper, we demonstrate that vdW-DFT calcu-lations can predict, with good accuracy, the crystal structureparameters and spontaneous polarization values for sevenhydrogen-bonded single-component organic ferroelectrics—croconic acid (CRCA), 2-phenylmalondialdehyde(PhMDA), 3-hydroxyphenalenone (HPLN), cyclobutene-1,2-dicarboxylic acid (CBDC), 2-methylbenzimidazole(MBI), 5,6-dichloro-2-methylbenzimidazole (DC-MBI), and3-anilinoacrolein anil (ALAA)—whose structural parametersand spontaneous polarization values have been experimentally

2475-9953/2021/5(9)/094409(8) 094409-1 Published by the American Physical Society

ISHIBASHI, HORIUCHI, AND KUMAI PHYSICAL REVIEW MATERIALS 5, 094409 (2021)

FIG. 1. Chemical structural formulas and hydrogen-bonded network views of (a) CRCA, (b) PhMDA, (c) HPLN, (d) CBDC, (e) MBI, (f)DC-MBI, and (g) ALAA. For CRCA, PhMDA, and DC-MBI, whose piezoelectric effects are simulated, unit cells and polarization vectorsalso are shown.

determined with good quality [6]. For the vdW-DFT method,we used two forms: the van der Waals density-functionalconsistent-exchange (cx) method [12] and the revisedVydrov–van Voorhis (rVV10) method [13,14]. These twoforms show good performance both for hydrogen-bondingand dispersion-bonding cases [15–18]. This is importantbecause both types of bonding exist in the above-mentionedcompounds. In fact, we have successfully reproduced thecrystal structure parameters of squaric acid using these twoforms [19]. Once the lattice parameters are successfullyreproduced, we expect that electromechanical responses toan external stress or electric field can be simulated. Directand converse piezoelectric effects are investigated for CRCA,PhMDA, and DC-MBI to evaluate the piezoelectric d33

constants, and the obtained values are compared with theexperimental results [20]. Since the ferroelectric switching isaccomplished by the proton motion in the hydrogen bond andthe induced redistribution of π electrons for these compounds,the ferroelectric and piezoelectric mechanisms are analyzedby dividing the total polarization as well as its variation understress or under electric field into the contribution from theproton motion as a classical charged particle and the residualcontribution.

II. COMPUTATIONAL METHODS

Calculations were performed using the QMAS code [21]based on the projector augmented-wave method [22] and aplane-wave basis set. The cx and rVV10 functionals were im-plemented according to the Wu-Gygi algorithm [23,24] basedon the efficient algorithm proposed by Román-Pérez andSoler [25]. Starting from the experimental room-temperature

structures (CRCA [26], PhMDA, HPLN, CBDC [27], MBI,DC-MBI [28], and ALAA [6]), structural optimization calcu-lations were performed with the cx and rVV10 functionals aswell as with the LDA and PBE functionals for comparison.Figure 1 shows the hydrogen-bonded network of the sevencompounds, together with their chemical structural formulas.The atomic positions were optimized using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [29]. For somecalculations under an electric field, where ferroelectric switch-ing is apt to occur, the fast inertial relaxation engine (FIRE)algorithm [30] was used. The FIRE algorithm was also usedfor calculating the lattice vectors. The convergence criteriawere 5 × 10−5 Ha/bohr for the maximum force and 5 ×10−7 Ha/bohr3 for the square root of the sum of the squares ofthe stress components. The finite basis set correction [31] wasapplied to evaluate the stress components. The plane-wavecutoff energy was set to 20 Ha. The number of k pointsin the full Brillouin zone was 8 × 12 × 8, 6 × 2 × 12, 4 ×2 × 4, 16 × 6 × 10, 4 × 6 × 4, 4 × 8 × 8, or 2 × 2 × 4 forCRCA, PhMDA, HPLN, CBDC, MBI, DC-MBI, or ALAA,respectively.

The electric polarization was evaluated using the Berryphase approach [32,33]. Calculations under a static electricfield were carried out according to the method proposed bySouza et al. [34].

III. RESULTS AND DISCUSSION

A. Crystal structures

The lattice and hydrogen-bond parameters calculated usingvarious exchange-correlation functionals are listed in Table Ifor the O−H · · · O systems and in Table II for the N−H · · · N

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TABLE I. Lattice and O−H · · · O bond parameters obtained using various exchange-correlation functionals.

a (Å) b (Å) c (Å) β (deg) V (Å3) dO–H (Å) dO···O (Å)

CRCAcx 8.804 5.066 10.816 482.4 1.062, 1.060 2.523, 2.520rVV10 8.609 5.016 10.869 469.4 1.044, 1.042 2.557, 2.549LDA 8.384 4.857 10.587 431.1 1.212, 1.204 2.414, 2.408PBE 9.109 5.629 10.908 559.2 1.045, 1.042 2.559, 2.567EXP 8.711 5.169 10.962 493.6 2.617, 2.629PhMDAcx 7.481 17.488 5.479 716.9 1.073 2.499rVV10 7.405 16.835 5.520 688.1 1.052 2.524LDA 7.109 16.855 5.405 647.6 1.193 2.401PBE 8.190 18.874 5.376 831.0 1.043 2.569EXP 7.683 17.160 5.553 732.1 2.604HPLNcx 9.190 17.471 11.441 1832.4 1.098, 1.077, 1.077, 1.092 2.471, 2.495, 2.496, 2.478rVV10 8.935 17.244 11.410 1754.7 1.062, 1.047, 1.047, 1.054 2.524, 2.549, 2.557, 2.544LDA 8.898 16.876 11.127 1668.2 1.243, 1.173, 1.188, 1.227 2.415, 2.415, 2.414, 2.414PBE 9.417 19.364 12.623 2300.5 1.073, 1.060, 1.057, 1.074 2.495, 2.518, 2.522, 2.492EXP 9.088 17.707 11.604 1863.3 2.545, 2.580, 2.586, 2.566CBDCcx 5.482 13.641 8.572 99.196 632.8 1.051, 1.048 2.554, 2.553rVV10 5.449 13.214 8.455 101.298 597.0 1.033, 1.029 2.596, 2.603LDA 5.327 12.925 8.203 100.980 554.5 1.124, 1.114 2.437, 2.446PBE 5.858 13.743 9.365 90.383 754.0 1.041, 1.040 2.582, 2.560EXP 5.551 13.509 8.690 98.916 643.8 2.632, 2.614

systems, together with the experimentally determined values.In cases where plural sites are crystallographically indepen-dent, the averaged values are compared. The experimentalC–H or O–H bond lengths are omitted because hydrogen posi-tions cannot be accurately determined by the x-ray diffractionmethod, as previously mentioned.

Figure 2(a) shows the deviations of the calculated struc-tural parameters (lattice parameters a, b, and c, and hydrogen-bond length d , namely, the O · · · O or N · · · N distance) from

the room-temperature experimental results. The results showthat the LDA generally underestimates these parameters. Bycontrast, the GGA greatly overestimates lattice parametersalong specific directions but well describes the hydrogen-bond lengths. In the case of the lattice parameters of CRCA,a similar tendency has been reported in a previous study[35]. The results in Fig. 2 show that, in most cases ofthe well-reproduced lattice parameters, there are hydrogen-bonded networks along the directions corresponding to the

TABLE II. Lattice and N–H · · · N bond parameters obtained using various exchange-correlation functionals.

a (Å) b (Å) c (Å) β (deg) V (Å3) dN–H (Å) dN···N (Å)

MBIcx 13.991 6.967 13.993 89.928 1364.0 1.057, 1.064, 1.057, 1.064 2.918, 2.818, 2.920, 2.817rVV10 13.831 6.757 13.823 89.918 1291.9 1.053, 1.058, 1.052, 1.058 2.872, 2.794, 2.872, 2.795LDA 13.546 6.555 13.541 89.953 1202.5 1.091, 1.099, 1.090, 1.099 2.750, 2.690, 2.751, 2.689PBE 13.893 8.603 14.214 89.674 1698.9 1.049, 1.053, 1.047, 1.052 2.949, 2.883, 2.972, 2.885EXP 13.964 7.211 13.964 90.000 1406.0 2.960, 2.861, 2.965, 2.859DC-MBIcx 14.289 5.734 10.322 845.7 1.043 2.920rVV10 13.639 5.562 10.313 782.3 1.033 2.936LDA 13.366 5.664 9.928 751.6 1.072 2.740PBE 16.870 6.774 9.961 1138.2 1.056 2.819EXP 14.238 5.687 10.398 841.9 2.977ALAAcx 19.838 15.757 7.813 2442.3 1.063 2.868rVV10 19.222 15.241 7.745 2269.0 1.052 2.903LDA 18.549 15.197 7.593 2140.4 1.095 2.743PBE 21.105 19.855 7.694 3224.0 1.057 2.880EXP 20.165 16.110 7.696 2500.2 2.965

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FIG. 2. Deviations of calculated structural parameters using various exchange-correlation functionals (a) from room-temperature (RT)experimental results and (b) from 0-K extrapolated values, as well as (c) their averages and bounds with respect to each functional. Parameters a,b, c, and d represent the three lattice parameters and the hydrogen-bond length, respectively. The zero point (solid horizontal line) correspondsto each experimental value of a, b, c, or d .

lattice parameters. The two vdW-DFT functionals reproducethe structural parameters well; however, a tendency towardunderestimation is observed. Notably, the experimental struc-tures are at room temperature, whereas the calculation resultscorrespond to 0 K. Unfortunately, only a limited numberof low-temperature structures have been reported (CRCA at20 K [36], PhMDA at 111 K [37], and CBDC at 50 K [27]).From the room-temperature and low-temperature structuralparameters, 0-K values were extrapolated for a, b, c, and d .Deviations of the calculated structural parameters from the0-K extrapolated values for CRCA, PhMDA, and CBCD areplotted in Fig. 2(b). In Fig. 2(c), averages and bounds ofthe deviations are shown for each functional. The agreementsbetween the two types of vdW-DF values and the experimentalvalues are clearly improved when the 0-K extrapolated valuesare used, especially in the cx case.

B. Spontaneous polarization

The space groups and general positions of CRCA, Ph-MDA, HPLN, CBDC, MBI, DC-MBI, and ALAA are listed inTable III. According to this symmetry information, for CRCA,PhMDA, DC-MBI, and ALAA, the polarization vector shouldbe parallel to the c axis of the orthorhombic lattice, while forHPLN, CBDC, and MBI, the polarization vector should beparallel to the ca plane of the monoclinic lattice. Needlessto say, the obtained results in the present work meet theseconditions. Figure 3 shows a comparison between the calcu-lated spontaneous polarization values and the experimentalvalues. For the O−H · · · O systems, except for CBDC, thespontaneous polarization obtained by LDA almost vanishes.In Table I, for these cases, the O–H bond length is approx-imately one-half of the hydrogen-bond length, implying thathydrogen atoms in the hydrogen bonds are located close to

TABLE III. Space groups and general points of CRCA, PhMDA, HPLN, CBDC, MBI, DC-MBI, and ALAA.

Space group General points

CRCA, DC-MBI Pca21 (No. 29) (x, y, z), (−x, −y, 1/2 + z), (1/2 + x, −y, z), (1/2 − x, y, 1/2 + z)PhMDA Pna21 (No. 33) (x, y, z), (−x, −y, 1/2 + z), (1/2 + x, 1/2 − y, z), (1/2 − x, 1/2 + y, 1/2 + z)HPLN, MBI P1n1 (No. 7) (x, y, z), (1/2 + x, −y, 1/2 + z)CBDC C1c1 (No. 9) (x, y, z), (x, −y, 1/2 + z), (1/2 + x, 1/2 + y, z), (1/2 + x, 1/2 − y, 1/2 + z)ALAA Iba2 (No. 45) (x, y, z), (−x, −y, z), (1/2 + x, 1/2 − y, z), (1/2 − x, 1/2 + y, z),

(1/2 + x, 1/2 + y, 1/2 + z), (1/2 − x, 1/2 − y, 1/2 + z), (x,−y, 1/2 + z), (−x, y, 1/2 + z)

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FIG. 3. Comparison of spontaneous polarization values calcu-lated using various exchange-correlation functionals with experi-mental results. The right panel is a partial enlargement of the leftpanel.

their midpoints. For such a case, the polarizations switchingeffect is expected to be very small. The hydrogen-bondlengths for these compounds are underestimated to be about2.4 Å by LDA. It is experimentally confirmed that a hydrogenatom is centered in the short hydrogen bond (2.393 Å) [38].For the other compounds also, the calculated spontaneouspolarization values tend toward underestimation. The slightlysmaller values in the case of the PBE are attributable to thesubstantial overestimation in volume. The results correspond-ing to the two vdW-DF functionals show good agreement withthe experimental results.

The calculated spontaneous polarization values are plottedas a function of the hydrogen-bond length in Fig. 4 (leftpanel). For the O−H · · · O systems (<2.65 Å), a positive cor-relation is observed. To clarify the origin of this correlation,we plotted the O–H or N–H bond lengths as a function of thehydrogen-bond length in Fig. 4 (right panel). A much clearer(negative) correlation is observed than in the polarizationcase. The longer the hydrogen bond, the shorter the O–H orN–H bond. This result is reasonable because the interactionof H with one O or N becomes stronger, whereas that withthe other O or N becomes weaker, when the hydrogen-bondlength increases. As previously mentioned, the π -bond dipoleswitching is important for the ferroelectricity in the hydrogen-bonded systems. The shorter the O–H or N–H bond, themore strongly is the π bond affected. However, the extent

FIG. 4. Spontaneous polarization (left) and (average) O–H or N–H bond length (right) calculated using various exchange-correlationfunctionals as a function of the (average) hydrogen-bond length.

FIG. 5. Calculated spontaneous polarization vector componentPc as a function of uniaxial stress σ (‖c).

of the effect depends on the compound, which is why thecorrelation between the hydrogen-bond length and the spon-taneous polarization is slightly weaker than that between thehydrogen-bond length and O–H or N–H bond lengths.

C. Piezoelectric effects

The success in reproducing the crystal structures enablessimulations of the direct and converse piezoelectric effects.Here, we focus on three compounds: CRCA, PhMDA, andDC-MBI. Their polarization vectors are all parallel to c, asmentioned above and shown in Fig. 1, and the piezoelectrictensors are simply described because their structures are or-thorhombic. In addition, experimental values of direct and/orconverse d33 constants are available for these compounds [20].

Figure 5 shows the calculated polarization vector compo-nent Pc as a function of uniaxial stress σ (‖c). For DC-MBI,the sign of Pc has been changed to be positive because the po-larization vector is antiparallel to c for the given experimentalstructure of DC-MBI [28], as shown in Fig. 1. Positive valuesof σ correspond to tensile stresses. For CRCA and DC-MBI,(a part of) hydrogen-bonded networks are parallel to c. Thevariations of the c lattice constants are predominantly broughtby the variations of the corresponding hydrogen-bond lengths.By contrast, for PhMDA, the hydrogen-bonded networks areparallel to 2c ± a. The dihedral angle between the two typesof the networks is ∼70◦ and, when a uniaxial stress is appliedalong c, this angle varies. While at the same time, the variationof |2c ± a| is consistent with the variation of the hydrogen-bond length.

Using these results, we evaluated the “proper” direct piezo-electric d33 constants for each compound. This approachfollows the procedure used to evaluate the piezoelectric e-form constant in a previous study [39]. First, the Berry phaseφ for the total polarization P = (0, 0, Pc) was calculated as afunction of σ ,

φ = �

2eGcPc, (1)

where � and Gc are the unit-cell volume and one of thereciprocal lattice vectors as a function of σ , respectively, ande is the elementary charge. We then evaluated d33 as

d33 = 1

π

e

�0

dφ

dσc0, (2)

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TABLE IV. Piezoelectric d33 constants and Young’s modulus EY3 obtained using vdW-DFT functionals.

Direct (pC/N) Converse (pm/V) EY3 (GPa)

cx rVV10 EXP cx rVV10 EXP cx rVV10

CRCA 13.8 10.8 15.1 13.6 10.9 7.6 102.3 103.3PhMDA 17.2 12.5 10.4 11.5 8.3 4.3 13.1 14.4DC-MBI 15.3 7.8 12.2 13.2 6.8 24.2 38.7

where �0 and c0 represent � and c values at zero stress,respectively. These equations are simplified forms for the casewhere the system has an orthorhombic unit cell and the polar-ization as well as the uniaxial stress is parallel to c. We hereconsider the spin degeneracy. The dφ/dσ term is evaluatedby linear regression using 11 points for each compound andfunctional. The obtained direct d33 constant values are listedin Table IV, together with the experimental results [20]. TheYoung’s modulus EY

3 values are also evaluated by linear re-gression between σ and c and are listed in Table IV.

For each compound, the d33 value obtained using cx islarger than that obtained using rVV10. The difference ismost prominent in the DC-MBI case. By contrast, for eachcompound, the EY

3 value obtained using cx is significantlylower than that obtained using rVV10. Again, the differenceis largest for DC-MBI. These results are reasonably explainedby a uniaxial stress causing a larger strain and, therefore, alarger polarization change in the case of cx than in the caseof rVV10. For solids, various forms of the vdW-DFT areoften assessed in terms of the lattice constants as well asthe cohesive energy. It is thought that the Young’s modulusreflects a different aspect of the exchange-correlation func-tional. In fact, as mentioned above, there is a large differencein the calculated EY

3 values between cx and rvv10 for DC-MBIalthough these two functional forms give similar c (and alsod) values to each other as shown in Fig. 2 and Table II. In addi-tion to this, the Young’s modulus is experimentally obtainablewithout severe difficulty. Thus, this physical property valuewould be useful in assessments of functionals. As for d33, theagreement with the experimental results is not excellent but isacceptable if the temperature effect and possible experimentaldifficulties are considered. The calculations were conductedimplicitly assuming a temperature of 0 K. Experimentally,d33 would be underestimated unless the crystals are perfectlypoled.

Figure 6 shows the calculated lattice parameter c as a func-tion of electronic field E (‖c). For CRCA and for PhMDA,polarization switching occurs at −5 and −4 MV/cm, respec-tively, in the calculation results obtained using cx. Such pointsare not included in Fig. 6. In the neighboring region of E , thelinear behavior appears to be lost. Given these situations, wecarried out linear regression analyses from −3 to +5 MV/cmfor CRCA, from −2 to +5 MV/cm for PhMDA, and with allthe points for DC-MBI to evaluate the converse piezoelectricd33 constants. The results are listed in Table IV, togetherwith the experimental results [20]. The difference betweenthe calculated and experimental results is larger than in thedirect piezoelectric case. Notably, the temperature effect andexperimental difficulties are also encountered in this case.Again, the difference between the cx and rVV10 results is

prominent for DC-MBI. The N−H · · · N bond appears to bemore sensitive to the choice of functional than the O−H · · · Obond.

The ferroelectricity in these compounds is characterizedby the proton transfer and the induced redistribution of π

electrons. We therefore try to divide the total polarization intotwo types of contributions. One is described as the protonmotion as a classical point charge of +|e|. Before and afterthe ferroelectric transitions, the relative positions of the O or Natoms at the ends of the hydrogen bond are unchanged. Settingthe position of the one end atom as the origin and representingthe proton displacement as �rH, this point-charge (pc)-likecontribution to the total polarization is evaluated to be

Ppcc = 1

2

|e|�rH

�. (3)

The factor 1/2 exists because the polarization amplitude isa half of the polarization difference before and after theferroelectric switching. By subtracting Ppc

c from the total po-larization, the residual (res) contribution, which is thoughtto correspond to the π -electron redistribution as discussedin Refs. [1,6], is obtained. In Fig. 7 (top), the results areshown for each vdW-DFT form and compound. Regardlessof the vdW-DFT form, the ‘res” contribution is predominant.It is over 80% for CRCA and PhMDA, while it is 64% forDC-MBI. Thus, the π -electron redistribution is the key factorfor the ferroelectricity in these compounds.

Similar analyses are made for the variations when a uniax-ial stress of +0.5 GPa is applied or when an electric field of+5 MV/cm is applied along c. The results are shown in Fig. 7(middle) and (bottom), respectively. For the stress-inducedvariation of polarization, the relative percentage of the“res” contribution is lowered and furthermore, for DC-MBI,

FIG. 6. Calculated lattice parameter c as a function of electronicfield E (‖c).

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FIG. 7. Analysis of contributions to total polarization (top) aswell as its variation under stress (middle) or under electric field(bottom). ‘pc” represents the contribution from the motion of hydro-gen as a point charge in the hydrogen bond, while ‘res” representsthe residual contribution. For each case, the ratio of the residualcontribution is expressed in percentage.

the “pc” contribution is larger than the “res” contribution.The functional dependence of the relative percentage becomessignificant. It is thought that the stress-induced change of thehydrogen bond plays a role. In contrast with the stress-inducedcase, for the electric-field-induced variation, the “res” con-tribution becomes even larger, implying that the π -electronredistribution is a major response to the induced electric field.

IV. CONCLUSIONS

Using vdW-DFT calculations, we successfully reproducedthe crystal structure parameters and spontaneous polarizationvalues for seven hydrogen-bonded single-component organicferroelectrics: CRCA, PhMDA, HPLN, CBDC, MBI, DC-MBI, and ALAA. This achievement is an important step for

the computational materials design of organic ferroelectricsand piezoelectrics. Our success in reproducing the latticeparameters, which is not possible by LDA or PBE, enablessimulations of electromechanical responses such as directand converse piezoelectric effects. The corresponding piezo-electric d33 constants were evaluated for CRCA, PhMDA,and DC-MBI. The agreement with the experimental resultswas not excellent but is acceptable given the temperatureeffect and possible experimental difficulties. Particularly inthe case of DC-MBI with the N−H · · · N type bond, theamplitudes of the direct and converse piezoelectric responsesare different between the two vdW-DFT functionals in spiteof the similar predicted lattice constant c and hydrogen-bond d values at zero stress and electric field. The Young’smodulus is thought to be closely related to these piezoelec-tric responses and expected to be useful in assessments ofexchange-correlation functionals. The ferroelectricity in thecompounds investigated in this study is characterized by twotypes of contributions from a hydrogen motion as a classicalpoint charge and π -electron redistribution (described as ‘pc”and ‘res” in the main text). The direct and converse piezo-electric responses are analyzed from this perspective. For thedirect piezoelectric response, although both the contributionsare significant, the relative magnitude of the ‘pc” contributionincreases. By contrast, for the converse piezoelectric response,the ‘res” contribution corresponding to the π -electron redis-tribution plays a predominant role. The present approach canbe applied not only to hydrogen-bonded single-componentferroelectrics but also to those consisting of multiple com-ponents with different ferroelectric switching mechanisms.Furthermore, a similar way is expected to be applicable for awide variety of molecular solids in predicting their physicalproperties. This is an important step toward computationalmaterials design as well as materials informatics.

ACKNOWLEDGMENTS

This work was partially supported by JST CREST GrantNo. JPMJCR18J2 and JSPS KAKENHI Grant No. 21H04679,Japan. Part of the computation in this work was carried outusing the facilities of the Supercomputer Center, the Institutefor Solid State Physics, the University of Tokyo.

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