Structural modulation of the dipolar-octupolar contributions to the NLO response in subphthalocyanines

Second order nonlinear optical properties of a series of trinitrosubphthalocyanine (SubPc) isomers were studied experimentally by electric field induced second harmonic (EFISH) generation and hyper Rayleigh scattering (HRS). These experimental values were compared to the ones obtained theoretically employing both sum over states (SOS) and finite field (FF) methods. From these studies, it was shown that the dipolar contributions to the beta tensor are very much dependent on the substitution pattern at the periphery of the subphthalocyanine macrocycle, whereas the octupolar contributions remain mostly unchanged. Consequently, it was deduced that SubPc is extremely well suited for the decoupling of octupolar and dipolar contribution to the NLO response.     

Heptametallic,Octupolar Nonlinear Optical Chromophores with Six Ferrocenyl Substituents

New complexes with six ferrocenyl (Fc) groups connected to Zn^II or Cd^II tris(2,2′‐bipyridyl) cores are described. A thorough characterisation of their BPh₄^? salts includes two single‐crystal X‐ray structures, highly unusual for such species with multiple, extended substituents. Intense, visible d(Fe^II)→π* metal‐to‐ligand charge‐transfer (MLCT) bands accompany the π→π* intraligand charge‐transfer absorptions in the near UV region. Each complex shows a single, fully reversible Fe^III/II wave when probed electrochemically. Molecular quadratic nonlinear optical (NLO) responses are determined by using hyper‐Rayleigh scattering and Stark spectroscopy. The latter gives static first hyperpolarisabilities β₀ reaching as high as approximately 10^?27 esu and generally increasing with π‐conjugation extension. Z‐scan cubic NLO measurements reveal high two‐photon absorption cross‐sections σ₂ of up to 5400 GM in one case. DFT calculations reproduce the π‐conjugation dependence of β₀, and TD‐DFT predicts three transitions close in energy contributing to the MLCT bands. The lowest energy transition has octupolar character, whereas the other two are degenerate and dipolar in nature.     

Theoretical Studies on the Electronic Structure of Nano-graphenes for Applications in Nonlinear Optics

In this work, azulene is introduced into nano-graphene with coronene center to enhance the second-order nonlinear optical (NLO) properties. The sum-over-states(SOS) model based calculations demonstrate that dipolar contributions are larger than octupolar contributions to the static first hyperpolarizability(〈β₀〉) in most nano-graphenes except those with high symmetry(e.g., a C_2v nano-graphene has octupolar contributions Φ^J=3 up to 59.0% of the 〈β₀〉). Nano-graphenes containing two parallel orientating azulenes (i.e., Out-P and Out-P_s) have large dipole moments, while their ground state is triplet. Introducing B/N/BN atoms into the positions with a high spin density transfers the ground state of Out-P and Out-P_s to closed-shell singlet, and the Out-P_s-2N has a large 〈β₀〉 of 1621.67×10⁻³⁰ esu. Further addition of an electron donor(NH₂) at the pentagon end enhances the 〈β₀〉 to 1906.22×10⁻³⁰ esu. The two-dimensional second-order NLO spectra predicted by using the SOS model find strong sum frequency generations and difference frequency generations, especially in the near-infrared and visible regions. The strategies to stabilize the electronic structure and improve the NLO properties of azulene-defect carbon nanomaterials are proposed, and those strategies to engineer nano-graphenes to be semiconducting while maintaining the π-framework are exten-dable to other similar systems.     

Nonlinear Optical Switching in Regioregular Porphyrin Covalent Organic Frameworks

Covalent organic frameworks (COFs) have garnered immense scientific interest among porous materials because of their structural tunability and diverse properties. However, the response of such materials toward laser‐induced nonlinear optical (NLO) applications is hardly understood and demands prompt attention. Three novel regioregular porphyrin (Por)‐based porous COFs—Por‐COF‐HH and its dual metalated congeners Por‐COF‐ZnCu and Por‐COF‐ZnNi—have been prepared and present excellent NLO properties. Notably, intensity‐dependent NLO switching behavior was observed for these Por‐COFs, which is highly desirable for optical switching and optical limiting devices. Moreover, the efficient π‐conjugation and charge‐transfer transition in ZnCu‐Por‐COF enabled a high nonlinear absorption coefficient (β=4470 cm/GW) and figure of merit (FOM=σ₁/σ_o, 3565) value compared to other state‐of‐the‐art materials, including molecular porphyrins (β≈100–400 cm/GW), metal–organic frameworks (MOFs; β≈0.3–0.5 cm/GW), and graphene (β=900 cm/GW).     

Efficient,Reversible Redox‐Switching of Molecular First Hyperpolarizabilities in Ruthenium(II) Complexes Possessing Large Quadratic Optical Nonlinearities

Low‐energy metal‐to‐ligand charge‐transfer (MLCT) excitations are associated with the very large molecular nonlinear optical (NLO) coefficients, β, of the complexes [Ru^II(NH₃)₅(N‐R‐4,4′‐bipyridinium)]³⁺ (R=methyl, phenyl, or 4‐acetylphenyl). Chemical oxidation to the Ru^III forms causes bleaching of the MLCT absorptions and marked attenuation of the NLO responses. Both effects are completely reversed upon re‐reduction, and the extent of the β switching is about 10‐ to 20‐fold.     

Verbenone-based push–pull chromophores with giant first hyperpolarizabilities: A new structure–property correlation study

Novel chromophores Ch1–8 based verbenone bridge with various strong donors and acceptors were designed for applications in nonlinear optics, and the nonlinear optical (NLO) properties of those verbenone-type chromophores were systematically investigated using the bond length alteration (BLA) theory, two states model (TSM) and sum-over-states (SOS) model. The results show that several verbenone-based chromophores possess remarkably large molecular second-order hyperpolarizabilities, which is due to its electron distribution close to the cyanine limit, the appropriate strength of acceptor, rather large change in dipole moment and low excitation energy. Computed hyperpolarizability (β_tot) of Ch6 also approach an outstanding 2922 × 10⁻³⁰ esu in TFE. The hyperpolarizability density analyses and two states model (TSM) were carried out to make a further insight into the origination of molecular nonlinearity of this unique system, suggesting that tuning structure of acceptor and polarity of the medium have great influence on the second-order nonlinear optical properties. More importantly, chromophores Ch1–Ch8 exhibited distinct features in two-dimensional second order NLO responses, and the strong electro-optical Pockels effect and optical rectification responses. The excellent electronic sum frequency generations (SFG) and difference frequency generations (DFG) effect are observed in these verbenone-type chromophores. These chromophores have a possibility to be appealing second-order nonlinear optical (NLO) materials, data storage materials and DSSCs materials from the standpoint of large β values, high LHE, and excellent two-dimensional second order NLO responses.     

Theoretical Study of the Substituent Effects on the Nonlinear Optical Properties of a Room‐Temperature‐Stable Organic Electride

Excess‐electron compounds can be considered as novel candidates for nonlinear optical (NLO) materials because of their large static first hyperpolarizabilities (β₀). A room‐temperature‐stable, excess‐electron compound, that is, the organic electride Na@(TriPip222), was successfully synthesized by the Dye group (J. Am. Chem. Soc. 2005 , 127, 12416). In this work, the β₀ of this electride was first evaluated to be 1.13×10⁶ au, which revealed its potential as a high‐performance NLO material. In particular, the substituent effects of different substituents on the structure, electride character, and NLO response of this electride were systemically studied for the first time by density functional theory calculations. The results revealed that the β₀ of Na@(TriPip222) could be further increased to 8.30×10⁶ au by introducing a fluoro substituent, whereas its NLO response completely disappeared if one nitryl group was introduced because the nitro‐group substitution deprived the material of its electride identity. Moreover, herein the dependence of the NLO properties on the number of substituents and their relative positions was also detected in multifluoro‐substituted Na@(TriPip222) compounds.     

Quantum chemical study of redox-switchable second-order optical nonlinearity in Keggin-type organoimido derivative [PW11O39(ReNC6H5)] n− (n = 2–4)

To analyze the effect of redox state changes on the second-order nonlinear optical (NLO) responses of organoimido-functionalized Keggin-type heteropolyanions, the excitation properties and static second-order polarizabilities of fully oxidized state, the first and second reduced states were calculated by means of the time-dependent density functional theory (TDDFT) method combined with the sum-over-states (SOS) formalism. The incorporation of extra electrons causes significant enhancement in the second-order NLO activity. The reduced complexes show more than three times the efficiency of fully oxidized state. Moreover, the NLO activities for PW₁₁Re^VNPh system can also be modified by controlling the spin multiplicity. The high spin state (³ 3) has twice larger β _vec value than the low spin state (¹ 3). The characteristic of the charge-transfer transition corresponding to the dominant contributions to the β _vec values indicates that metal-centered redox processes influence the intramolecular donor or acceptor character, which accordingly leads to the variations in the computed β values. Owing to the reversible and manipulable redox processes, these kinds of the POM-based hybrid complexes could comprise a promising family of three-state redox-switchable molecular device combining chromic, magnetic, and NLO output.     

LiMII(IO3)3 (MII=Zn and Cd): Two Promising Nonlinear Optical Crystals Derived from a Tunable Structure Model of α‐LiIO3

Excellent nonlinear optical materials simultaneously meet the requirements of large SHG response, phase‐matching capability, wide transparency windows, considerable energy band‐gap, good thermal stability and structure stability. Herein, two new promising nonlinear optical (NLO) crystals LiM^II(IO₃)₃ (M^II=Zn and Cd) are rationally designed by the aliovalent substitution strategy from the commercialized α‐LiIO₃ with the perfect parallel alignment of IO₃ groups. Compared with parent α‐LiIO₃ and related A^I₂M^IV(IO₃)₆, the title compounds exhibit more stable covalent 3D structure, and overcome the racemic twinning problem of A^I₂M^IV(IO₃)₆. More importantly, both compounds inherit NLO‐favorable structure merits of α‐LiIO₃ and show larger SHG response (≈14× and ≈12×KDP), shorter absorption edge (294 and 297 nm) with wider energy band‐gap (4.21 and 4.18 eV), good thermal stability (460 and 430 °C), phase‐matching behaviors, wider optical transparency window and good structure stability, achieving an excellent balance of NLO properties.     

A Promising Fluorooxoborate Framework with Flexibile Capability for Diverse Cations to Enhance the Second Harmonic Generation

Fluorooxoborates as potential deep ultraviolet (DUV) nonlinear optical (NLO) materials have exhibited diverse structures and NLO properties with metal cationic changes. Herein, the general mechanisms of metal cations on band gaps and optical properties in a series of typical fluorooxoborates have been clarified. It reveals that the framework of the emblematic 18-membered ring oxyfluorides has the flexibility of being able to contain different cations spanning from alkali to d¹⁰ metals by investigating the stability of the artificial CdB₅O₇F₃ structure. Besides, introducing d¹⁰ metal cations can enhance the second harmonic generation (3.1×KH₂PO₄ (KDP), d₃₆=0.39 pm V⁻¹) and also keep a DUV spectral transparency (E_g>6.2 eV). Thus, the d¹⁰-containing fluorooxoborate exhibits a great potential to be a new DUV optical material for nonlinear light-matter interactions.     

Energetic of molecular interface at metal-organic heterojunction: the case of thiophenethiolate chemisorbed on Au(111)

To probe the cooperativity of charge transfer between organoimido and hexamolybdate, and enhance the second-order nonlinear optical (NLO) response of organoimido derivatives of hexamolybdates, electronic structures and second-order NLO properties of a series of charge-transfer covalently bonded organoimido derived hexamolybdate complexes with donor-(π conjugated bridge)-acceptor-(π conjugated bridge)-donor or acceptor-(π conjugated bridge)-donor-(π conjugated bridge)-acceptor structures were studied by density functional theory. Studies show that different combinations of the donor, acceptor, heterocycle, –C≡C– and –N=N– moieties, and orientation of heterocycle remarkably affect the second-order NLO responses. The complexes containing electronic acceptor matched with the direction of charge transfer possess remarkable large molecular second-order polarizabilities. Electronic transitions to crucial excited states show that x-polarized transition, contributed to the off-diagonal second-order polarizabiliy tensor (β_zxx), possesses lower excited energy compared with z-polarized transition which accounted for the diagonal second-order polarizabiliy tensor (β_zzz) and thus led to the large in-plane nonlinear anisotropy (u = β_zxx/β_zzz) value, as well as good two-dimensional (2-D) second-order NLO properties. These complexes can be used as excellent 2-D second-order NLO materials from the standpoint of both large β and u values.     

Substituent Effects on the Structural Features and Nonlinear Optical Properties of the Organic Alkalide Li+(calix[4]pyrrole)Li−

The effects of substituents on the structure, character, and nonlinear optical (NLO) properties of the organic alkalide Li⁺(calix[4]pyrrole)Li^? were studied by density functional theory. Natural bond orbital analysis and vertical ionization energies reveal that electron‐donating substituents strengthen the alkalide character of Li⁺(calix[4]pyrrole)Li^? and that they are beneficial for a larger first hyperpolarizability (β₀) value. However, electron‐withdrawing substituents have the opposite effect. The dependence of the NLO properties on the number of substituents and their relative position was detected in multisubstituted Li⁺(calix[4]pyrrole)Li^? compounds. For both the amino‐ and methyl‐substituted derivatives, the polarizabilities and the first hyperpolarizabilities increase as more pyrrole β‐H atoms are substituted. Moreover, distribution of the substituents so that they are as far away from each other as possible resulted in an increase in the β₀ value. The new knowledge obtained in this study may provide an effective approach to enhance the NLO responses of alkalides by employing pyrrole derivatives as complexants.     

A High-Performance Nonlinear Optical Crystal with a Building Block Containing Expanded π-Delocalization

Common nonlinear optical (NLO) crystals consist of traditional functional building blocks with inherent optical limitation. Herein, inspired by traditional (B₃O₆)³⁻ inorganic building block, we theoretically identified a new type of organic functional building blocks and then successfully synthesized the first cyamelurate NLO crystal, Ba(H₂C₆N₇O₃)₂ ⋅ 8 H₂O. To our surprise, the constituent (H₂C₆N₇O₃)⁻ building block is not in structurally optimal arrangement, but Ba(H₂C₆N₇O₃)₂ ⋅ 8 H₂O exhibits excellent optical properties including wide band gap of 4.10 eV, very large birefringence of 0.24@550 nm, and exceptionally strong second-harmonic generation (SHG) response of about 12×KH₂PO₄. Both the SHG response and birefringence are much larger than those of commercial NLO crystal β-BaB₂O₄ with optimally aligned (B₃O₆)³⁻ building block. Theoretical calculations suggest that the expanded π-conjugation delocalization within (H₂C₆N₇O₃)⁻ vs (B₃O₆)³⁻ should be responsible to the enhanced performance. This work implies that there is still much room to develop new NLO crystals with excellent functional building blocks that may be longly neglected.     

Tailoring the donor moieties in TPA-based organic dyes for efficient photovoltaic,optical and nonlinear optical response properties

The current study reports tailoring the electronic donor structures of organic dyes to modify their optical and nonlinear optical (NLO) response properties. Five (5) tri-phenyl amine (TPA) based Donor-π-Acceptor (D-π-A) organic dyes with the codes ICAA1 , ICAA2 , ICAA3 , ICAA4 , and ICAA5 were designed and investigated for their optical and NLO properties using quantum chemical methods. Optical and NLO properties of these dyes were studied by CAM-B3LYP method and 6-311G* basis set. The focus has been on the impact of adding secondary donors and shifting their substitutions at ortho (o), meta (m) and para (p) positions. Among all designed compounds, ICAA4 showed the highest amplitude of average third-order NLO polarizability <γ>, which is calculated to be 1316 × 10⁻³⁶ esu. Time-dependent Density Functional Theory (TD-DFT) method was used to determine how a change in the position of the donor affected the excitation energy (E_g) and NLO response properties. The findings showed that changing the position of the secondary donor results in a red shift among absorption spectra as well as the increase in their NLO responses. Complete process of intramolecular charge transfer (ICT) has been investigated in terms of different optical parameters such as frontier molecular orbitals (FMOs), molecular electrostatic potentials (MEPs), transition density matrix (TDMs), density of states (DOS), electron density difference (EDD), and natural bond orbital (NBO) analysis. Our calculations for study of ICT process indicate that p-position of methoxy group performs better among all other positions and even it has better NLO response properties than the compound with three collective methoxy groups. The calculated V_oc values of all designed molecules range from 1.09 to 1.30, all of them are positive while their ΔG_inject is found to be in the range of −0.87 to −1.79 eV indicating their decent potential for photovoltaic applications. The studied optical, NLO and photovoltaic parameters illustrated that ICAA1 to ICAA5 are appropriate molecules not only for NLO applications but also for efficient photovoltaic purposes.     

Chiral crystal of a C2v‐symmetric 1,3‐diazaaulene derivative showing efficient optical second harmonic generation

Achiral nonlinear optical (NLO) chromophores 1,3‐diazaazulene derivatives, 2‐(4′‐aminophenyl)‐6‐nitro‐1,3‐diazaazulene (APNA) and 2‐(4′‐N,N‐diphenylaminophenyl)‐6‐nitro‐1,3‐diazaazulene (DPAPNA), were synthesized with high yield. Despite the moderate static first hyperpolarizabilities (β₀) for both APNA [(136 ± 5) × 10^?30 esu] and DPAPNA [(263 ± 20) × 10^?30 esu], only APNA crystal shows a powder efficiency of second harmonic generation (SHG) of 23 times that of urea. It is shown that the APNA crystallization driven cooperatively by the strong H‐bonding network and the dipolar electrostatic interactions falls into the noncentrosymmetric P2₁2₁2₁ space group, and that the helical supramolecular assembly is solely responsible for the efficient SHG response. To the contrary, the DPAPNA crystal with centrosymmetric P‐1 space group is packed with antiparalleling dimmers, and is therefore completely SHG‐inactive. 1,3‐Diazaazulene derivatives are suggested to be potent building blocks for SHG‐active chiral crystals, which are advantageous in high thermal stability, excellent near‐infrared transparency and high degree of designing flexibility. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Synthesis and characterization of NLO chromophore with benzo [1,2-b:4,5-b′]dithiophene unit as π-electron bridge

A novel chromophore BDT–TCF with benzo[1,2-b:4,5-b′]dithiophene (BDT) unit as electron bridge was synthesized and characterized by UV–vis, NMR spectroscopy, and thermal analysis. It is the first time that BDT unit was introduced into NLO materials. The chromophore showed excellent solubility in most common solvents, and good thermal stability for practical applications. The second order nonlinear optical effect was measured by hyper Rayleigh scattering method. The diagonal hyperpolarizability β_zzz of BDT–TCF was 8.2 × 10^?28 and 9.3 × 10^?29 esu in THF solvent and in PMMA polymer matrices, respectively. The potential NLO response indicates that BDT unit is a promising π-electron bridge and an excellent candidate for nonlinear optical devices.     

Stability and Nonlinear Optical Response of Alkalides that Contain a Completely Encapsulated Superalkali Cluster

Guided by density functional theory (DFT) computations, a new series of superalkali‐based alkalides, namely FLi₂⁺(aza222)K^?, OLi₃⁺(aza222)K^?, NLi₄⁺(aza222)K^?, and Li₃⁺(aza222)K^? were designed with various superalkali clusters embedded into an aza222 cage‐complexant. These species possess diverse isomeric structures in which the encapsulated superalkalis preserve their identities and behave as alkali metal atoms. The results show that these novel alkalides possess larger complexation energies and enhanced hyperpolarizabilities (β₀) compared with alkali‐metal‐based and previous superalkali‐based clusters. Especially, a prominent structural dependence of β₀ is observed for these studied compounds. Hence, the geometric factors that affect the nonlinear optical (NLO) response of such alkalides is elucidated in detail in this work. This study not only provides novel candidates for alkalides, it also offers an effective way to enhance the NLO response and stability of alkalides.     

A New Copper(I) Complex Based on Imidazole and Triphenylphosphine Ligands: Synthesis,Structure, Third‐Order NLO,and Fluorescence Properties

A new candidate [Cu(PPh₃)₂Him]Br ( 1 , PPh₃=triphenylphosphine, Him=1‐H‐imidazole) for nonlinear optical (NLO) materials has been synthesized and characterized crystallographically. The third‐order NLO optical properties were measured by the Z‐scan technique with an 8 ns pulsed laser at 532 nm. Compound 1 exhibits strong NLO absorptive abilities [α₂=(61±5)×10^?12] and effective self‐focusing performance [n₂=(15±3)×10^?18 m²·W^?1] in 1.01×10^?4 mol·dm^?3 DMF solution. The compound also exhibits luminescence in DMF solution at room temperature and shows narrow emission with maximum at 382 nm. The electronic structure and photoluminescent process were investigated by means of TD‐DFT calculations. The results suggest that the contribution to the frontier orbitals from the Cu? Br δ bond plays a crucial role in its linear optical properties, and the origin of luminescence is attributable to the π??→n transitions.     

The Role of Ion Pairs in the Second‐Order NLO Response of 4‐X‐1‐Methylpiridinium Salts

A series of 4‐X‐1‐methylpyridinium cationic nonlinear optical (NLO) chromophores (X=(E)‐CH?CHC₆H₅; (E)‐CH?CHC₆H₄‐4′‐C(CH₃)₃; (E)‐CH?CHC₆H₄‐4′‐N(CH₃)₂; (E)‐CH?CHC₆H₄‐4′‐N(C₄H₉)₂; (E,E)‐(CH?CH)₂C₆H₄‐4′‐N(CH₃)₂) with various organic (CF₃SO₃^?, p‐CH₃C₆H₄SO₃^?), inorganic (I^?, ClO₄^?, SCN^?, [Hg₂I₆]^2?) and organometallic (cis‐[Ir(CO)₂I₂]^?) counter anions are studied with the aim of investigating the role of ion pairing and of ionic dissociation or aggregation of ion pairs in controlling their second‐order NLO response in anhydrous chloroform solution. The combined use of electronic absorption spectra, conductimetric measurements and pulsed field gradient spin echo (PGSE) NMR experiments show that the second‐order NLO response, investigated by the electric‐field‐induced second harmonic generation (EFISH) technique, of the salts of the cationic NLO chromophores strongly depends upon the nature of the counter anion and concentration. The ion pairs are the major species at concentration around 10^?3 M , and their dipole moments were determined. Generally, below 5×10^?4 M , ion pairs start to dissociate into ions with parallel increase of the second‐order NLO response, due to the increased concentration of purely cationic NLO chromophores with improved NLO response. At concentration higher than 10^?3 M , some multipolar aggregates, probably of H type, are formed, with parallel slight decrease of the second‐order NLO response. Ion pairing is dependent upon the nature of the counter anion and on the electronic structure of the cationic NLO chromophore. It is very strong for the thiocyanate anion in particular and, albeit to a lesser extent, for the sulfonated anions. The latter show increased tendency to self‐aggregate.     

Enhanced third‐order nonlinear optical properties determined in thin films using the Z‐scan technique: bis(μ‐4,4′‐oxydibenzoato)bis[(4′‐phenyl‐2,2′:6′,2′′‐terpyridine)cobalt(II)]

π‐Conjugated organic materials exhibit high and tunable nonlinear optical (NLO) properties, and fast response times. 4′‐Phenyl‐2,2′:6′,2′′‐terpyridine (PTP) is an important N‐heterocyclic ligand involving π‐conjugated systems, however, studies concerning the third‐order NLO properties of terpyridine transition metal complexes are limited. The title binuclear terpyridine Co^II complex, bis(μ‐4,4′‐oxydibenzoato)‐κ³O,O′:O′′;κ³O′′:O,O′‐bis[(4′‐phenyl‐2,2′:6′,2′′‐terpyridine‐κ³N,N′,N′′)cobalt(II)], [Co₂(C₁₄H₈O₅)₂(C₂₁H₁₅N₃)₂], (1), has been synthesized under hydrothermal conditions. In the crystal structure, each Co^II cation is surrounded by three N atoms of a PTP ligand and three O atoms, two from a bidentate and one from a symmetry‐related monodentate 4,4′‐oxydibenzoate (ODA²⁻) ligand, completing a distorted octahedral coordination geometry. Neighbouring [Co(PTP)]²⁺ units are bridged by ODA²⁻ ligands to form a ring‐like structure. The third‐order nonlinear optical (NLO) properties of (1) and PTP were determined in thin films using the Z‐scan technique. The title compound shows a strong third‐order NLO saturable absorption (SA), while PTP exhibits a third‐order NLO reverse saturable absorption (RSA). The absorptive coefficient β of (1) is −37.3 × 10⁻⁷ m W⁻¹, which is larger than that (8.96 × 10⁻⁷ m W⁻¹) of PTP. The third‐order NLO susceptibility χ⁽³⁾ values are calculated as 6.01 × 10⁻⁸ e.s.u. for (1) and 1.44 × 10⁻⁸ e.s.u. for PTP.