Context This research focuses on the theoretical study of six push–pull molecules composed of conjugated bridges based on porphyrin and metalloporphyrins where the metals used are Fe(II), Co(II), Ni(II), Cu(II), and Zn(II); these bridges are linked at their ends by acceptor groups (–NO2) and donors (–N(CH3)2) at the meso positions of the cycles mentioned before. The CAM–B3LYP, M08HX, and MN15 functionals tend to describe well the systems studied in non-linear optics NLO in addition to the use of the basis set 6–31 + + G(d,p) which is considered to be the adequate and least expensive basis set. The highest values of the first static hyperpolarizabilities (βtot) are assigned to the two molecules 2A and 3A; the corresponding values are as follows: βtot (2A) = 46.43 * 10−30 esu and βtot (3A) = 46.30 * 10−30 esu. The highest value of the second static hyperpolarizability (γav) is assigned to the molecule 1A5 with a value of 9.49 * 10−35 esu. The highest values of the first dynamic hyperpolarizabilities (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="894_2025_6326_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="110" /> </InlineMediaObject> <EquationSource Format="TEX">${\beta }_||^{\lambda }(-2\omega ;\omega ,\omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>β</mi> <mo stretchy="false">|</mo> </msub> <msup> <mrow> <mo stretchy="false">|</mo> </mrow> <mi>λ</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>2</mn> <mi>ω</mi> <mo>;</mo> <mi>ω</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>) and second dynamics hyperpolarizabilities (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="894_2025_6326_Article_IEq2.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="124" /> </InlineMediaObject> <EquationSource Format="TEX">${\gamma }_||^{\lambda }(-2\omega ;\omega ,\omega ,0)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>γ</mi> <mo stretchy="false">|</mo> </msub> <msup> <mrow> <mo stretchy="false">|</mo> </mrow> <mi>λ</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>2</mn> <mi>ω</mi> <mo>;</mo> <mi>ω</mi> <mo>,</mo> <mi>ω</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>) are attributed to the molecule 2A; the corresponding values are as follows:<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="894_2025_6326_Article_IEq3.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="110" /> </InlineMediaObject> <EquationSource Format="TEX">${\beta }_||^{\lambda }(-2\omega ;\omega ,\omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>β</mi> <mo stretchy="false">|</mo> </msub> <msup> <mrow> <mo stretchy="false">|</mo> </mrow> <mi>λ</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>2</mn> <mi>ω</mi> <mo>;</mo> <mi>ω</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>) (2A) = 8229.88 * 10−30 esu and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="894_2025_6326_Article_IEq4.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="124" /> </InlineMediaObject> <EquationSource Format="TEX">${\gamma }_||^{\lambda }(-2\omega ;\omega ,\omega ,0)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>γ</mi> <mo stretchy="false">|</mo> </msub> <msup> <mrow> <mo stretchy="false">|</mo> </mrow> <mi>λ</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>2</mn> <mi>ω</mi> <mo>;</mo> <mi>ω</mi> <mo>,</mo> <mi>ω</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> (2A) = − 10,943.10 * 10−35 esu. The molecules 1A2 and 1A5 based on the metals Co(II) and Zn(II), respectively, are the most profitable in second- and third-order dynamic NLOs. The specific solvents for the six molecules are acetone, acetonitrile, and dichloromethane. The maximum wavelengths recorded for all molecules in vacuum and in combination with all solvents are in the range 355.75 to 397.15 nm and absorb in the UV transparency. Method All calculations were performed with the Gaussian 16 program. The dispersion functional B3LYP–D3 is used for optimizations. Electronic parameters were calculated using the following functionals: CAM-B3LYP, LC-wPBE, LC-BLYP, M11, wB97X, M08-HX, M06-2X, MN12SX, and MN15. The basis set studied for the whole manuscript is 6–31 + + G(d,p) for non-metallic atoms and LanL2DZ for transition metals. Other basis sets studied include 6–31G(d,p), 6–31 + + G(d,p), cc–pVDZ, AUG–cc–pVDZ, 6–311G(d,p), 6–311 + + G(d,p), cc–pVTZ, and AUG–cc–pVTZ. The natural bond orbital (NBO) method was also considered. The implicit solvation models studied are solvation models based on density (SMD) and conductor polarizable continuum model (C–PCM). The time-dependent density functional (TD-DFT) approach was also studied. Graphical Abstract

In-depth theoretical study on the impact of transition metals incorporation into the cavities of porphyrins considered conjugated bridges in NLO-active push–pull molecules: analysis by DFT, NBO, and TD–DFT

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发表日期：

2025年2月28日

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Assia Laib,
Abdelkader M. Elhorri,
Madani Hedidi,
Mourad Zouaoui–Rabah,
Hicham Mahdjoub–Araibi,
Mahammed Zenati

摘要

Context

This research focuses on the theoretical study of six push–pull molecules composed of conjugated bridges based on porphyrin and metalloporphyrins where the metals used are Fe(II), Co(II), Ni(II), Cu(II), and Zn(II); these bridges are linked at their ends by acceptor groups (–NO₂) and donors (–N(CH₃)₂) at the meso positions of the cycles mentioned before. The CAM–B3LYP, M08HX, and MN15 functionals tend to describe well the systems studied in non-linear optics NLO in addition to the use of the basis set 6–31 + + G(d,p) which is considered to be the adequate and least expensive basis set. The highest values of the first static hyperpolarizabilities (β_tot) are assigned to the two molecules 2A and 3A; the corresponding values are as follows: β_tot (2A) = 46.43 * 10⁻³⁰ esu and β_tot (3A) = 46.30 * 10⁻³⁰ esu. The highest value of the second static hyperpolarizability (γ_av) is assigned to the molecule 1A5 with a value of 9.49 * 10⁻³⁵ esu. The highest values of the first dynamic hyperpolarizabilities ( ${\beta }_||^{\lambda }(-2\omega ;\omega ,\omega )$ $β_{|} |^{λ} (- 2 ω; ω, ω)$ ) and second dynamics hyperpolarizabilities ( ${\gamma }_||^{\lambda }(-2\omega ;\omega ,\omega ,0)$ $γ_{|} |^{λ} (- 2 ω; ω, ω, 0)$ ) are attributed to the molecule 2A; the corresponding values are as follows: ${\beta }_||^{\lambda }(-2\omega ;\omega ,\omega )$ $β_{|} |^{λ} (- 2 ω; ω, ω)$ ) (2A) = 8229.88 * 10⁻³⁰ esu and ${\gamma }_||^{\lambda }(-2\omega ;\omega ,\omega ,0)$ $γ_{|} |^{λ} (- 2 ω; ω, ω, 0)$ (2A) = − 10,943.10 * 10⁻³⁵ esu. The molecules 1A2 and 1A5 based on the metals Co(II) and Zn(II), respectively, are the most profitable in second- and third-order dynamic NLOs. The specific solvents for the six molecules are acetone, acetonitrile, and dichloromethane. The maximum wavelengths recorded for all molecules in vacuum and in combination with all solvents are in the range 355.75 to 397.15 nm and absorb in the UV transparency.

Method

All calculations were performed with the Gaussian 16 program. The dispersion functional B3LYP–D3 is used for optimizations. Electronic parameters were calculated using the following functionals: CAM-B3LYP, LC-wPBE, LC-BLYP, M11, wB97X, M08-HX, M06-2X, MN12SX, and MN15. The basis set studied for the whole manuscript is 6–31 + + G(d,p) for non-metallic atoms and LanL2DZ for transition metals. Other basis sets studied include 6–31G(d,p), 6–31 + + G(d,p), cc–pVDZ, AUG–cc–pVDZ, 6–311G(d,p), 6–311 + + G(d,p), cc–pVTZ, and AUG–cc–pVTZ. The natural bond orbital (NBO) method was also considered. The implicit solvation models studied are solvation models based on density (SMD) and conductor polarizable continuum model (C–PCM). The time-dependent density functional (TD-DFT) approach was also studied.

Graphical Abstract