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\DOI{10.5802/crchim.264}
\datereceived{2023-07-20}
\daterevised{2023-09-11}
\datererevised{2023-09-27}
\dateaccepted{2023-09-27}
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\dateposted{2024-01-23}
\begin{document}

\begin{noXML}

%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{French/Nordic Special Issue on Materials and Coordination Chemistry}
%%\def\cdr@specialtitle@french{Num\'ero sp\'ecial franco-nordique sur les mat\'eriaux et la chimie de coordination}
%\makeatother

\title{Rethinking gold(II) porphyrins: an inherent wave distortion}

\alttitle{Repenser les porphyrines d'or(II) : une distorsion intrins\`{e}que en forme de vague}

\author{\firstname{Abhik} \lastname{Ghosh}\CDRorcid{0000-0003-1161-6364}\IsCorresp}
\address{Department of Chemistry, University of Troms\o{}, N-9037 Troms\o{}, Norway}
\email[A. Ghosh]{abhik.ghosh@uit.no}

\author{\firstname{Jeanet} \lastname{Conradie}\CDRorcid{0000-0002-8120-6830}\IsCorresp}
\addressSameAs{1}{Department of Chemistry, University of Troms\o{}, N-9037 Troms\o{}, Norway}
\address{Department of Chemistry, University of the Free State, P.O.
Box 339, Bloemfontein 9300, Republic of South Africa}
\email[J. Conradie]{conradj@ufs.ac.za}

\keywords{\kwd{Gold}\kwd{Porphyrin}\kwd{Nonplanar
distortion}\kwd{Ligand noninnocence}\kwd{Relativistic effect}}

\altkeywords{\kwd{Or}\kwd{Porphyrine}\kwd{Distorsion non
plane}\kwd{Ligand non-innocent}\kwd{Effet relativiste}}

\thanks{Research Council of Norway (Grant agreement no. 324139)  and
South African National Research Foundation (Grant agreement nos. 129270
and 132504)}

\begin{abstract}
Relativistic DFT (OLYP-D3/ZORA-STO-TZ2P) calculations predict low
adiabatic ionization potentials for gold(II) porphyrins, from 4.60~eV
for Au[TPP] (TPP $=$\ tetraphenylporphyrin) to 5.34~eV for Au[TPFPP]
[TPFPP $=$\ tetrakis(pentafluorophenyl)porphyrin]. These values are
over 1~eV lower than those calculated for analogous silver(II)
porphyrins, reflecting much greater relativistic destabilization of the
Au 5d orbitals relative to Ag 4d orbitals. Interestingly, our
calculations also place the observed structural distortion of Au[TPP]
in an entirely new light. The electronic imperative of the Au(II)
center to assume a pseudo-d\tsup{10} configuration drives a wave
deformation of the porphyrin core that allows for 
{Au(d$_{x^{2}\hyphen y^{2}}$)}--porphyrin(${\uppi}$) 
mixing. The lateral
compression--elongation of the porphyrin (unequal pairs of Au--N bonds),
in contrast, appears to be a secondary effect, a \textit{consequence}
of the wave deformation. The wave distortion results in significant
${\uppi}$ spin populations on the porphyrin macrocycle, leaving behind
only about 20--25\% of the spin density on the gold. The effect is
specific to gold: silver(II) porphyrins exhibit strictly planar cores
with approximate $D_{4\mathrm{h}}$ local symmetry at the metal.
\looseness=-1
\end{abstract}

\begin{altabstract}
Les calculs de la th\'{e}orie de la fonctionnelle de la densit\'{e}
relativiste (OLYP-D3/ZORA-STO-TZ2P) pr\'{e}voient des potentiels
d'ionisation adiabatiques faibles pour les porphyrines d'or(II), de
4,60~eV pour Au[TPP] (TPP $=$\ t\'{e}traph\'{e}nylporphyrine) \`{a}
5,34~eV pour Au[TPFPP] [TPFPP $=$\
 t\'{e}trakis(pentafluoroph\'{e}nyl)porphyrine]. Ces valeurs sont
inf\'{e}rieures de plus de 1~eV \`{a} celles calcul\'{e}es pour des
porphyrines d'argent(II) analogues, ce qui refl\`{e}te une
d\'{e}stabilisation relativiste beaucoup plus importante des orbitales
Au 5d par rapport aux orbitales Ag 4d. Il est int\'{e}ressant de noter
que nos calculs placent \'{e}galement la distorsion structurelle
observ\'{e}e de Au[TPP] sous un tout nouveau jour. L'imp\'{e}ratif
\'{e}lectronique du centre Au(II) d'adopter une configuration
pseudo-d$^{10}$ entra\^{i}ne une d\'{e}formation en forme de vague du
noyau de la porphyrine qui permet le m\'{e}lange Au(d$_{x^{2}\mbox{-}
y^{2}}$)--porphyrine(${\pi}$). La compression--allongement lat\'{e}rale
de la porphyrine (paires in\'{e}gales de liaisons Au--N), en revanche,
semble correspondre \`{a} un effet secondaire, une cons\'{e}quence de
la d\'{e}formation en vague. La distorsion en vague entra\^{i}ne des
populations de spin p significatives sur le macrocycle de la
porphyrine, ne laissant qu'environ 20 \`{a} 25~\% de la densit\'{e} de
spin sur l'or. L'effet est sp\'{e}cifique \`{a} l'or : les porphyrines
d'argent(II) pr\'{e}sentent des coeurs strictement plans avec une
sym\'{e}trie locale $D_{4\mathrm{h}}$ approximative au niveau du
m\'{e}tal.
\end{altabstract}
\begin{DefTralics}
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\section{Introduction}\label{sec1}

The consequences of Einstei{n'}s special theory of
relativity~\cite{1,2} manifest themselves in virtually every aspect of
the chemistry of gold~\cite{3,4,5,6,7,8,9}. Relativistic
destabilization of the 5d orbitals allows for the existence and
stability of such pentavalent Au species as the AuF\tsub{6}$^{-}$\
anion~\cite{10,11} and Au\tsub{2}F\tsub{10}~\cite{12}. Relativistic
stabilization of the 6s orbitals on the other hand \mbox{allows} for the
existence and stability of the auride anion, a unique metal-based
pseudohalide~\cite{13,14,15}. The latter effect is also responsible for
gold having the highest electronegativity among all nonradioactive
metals, essentially the same as carbon. It is worth mentioning in
passing that even more dramatic relativistic effects have been
postulated for roentgenium, gold's superheavy congener, notably a
6d\tsup{9}7s\tsup{2} atomic ground state and a heptavalent
$D_{5\mathrm{h}}$-symmetric fluoride, RgF\tsub{7}~\cite{16}. 

Relativistic effects also explain why stable, structurally
characterized Au(II) porphyrins have long \mbox{remained} elusive, in
sharp contrast to Cu(II) and Ag(II) porphyrins~\cite{17}. The Au(III)
center in porphyrins was long thought to be electrochemically
inert~\cite{18,19} and only in 2002 was the one-electron reduction of
Au(III) porphyrins identified as metal-centered~\cite{20,21}. Only in
2017 was Au[TPP] reported as the first structurally characterized
Au(II) porphyrin~\cite{22}. The structure turned out to be more than a
synthetic feat: the metalloporphyrin core was found to exhibit a unique
lateral distortion (Figure~\ref{fig1}), in contrast to the usual
$D_{4\mathrm{h}}$ geometry. The distortion, whereby the Au--N bonds in
one direction are longer than those in the other direction, was also
attributed to a second-order Jahn--Teller effect involving the
relativistically destabilized 5d$_{x^{2}\hyphen y^{2}}$ orbital and the
relativistically stabilized 6s orbital. A mild wave distortion of the
porphyrin was also noted, but was assumed to be incidental to the
lateral distortion~\cite{22}.

\begin{figure*}
{\vspace*{1pt}}
\includegraphics{fig01}
{\vspace*{1pt}}
\caption{\label{fig1}Top left: crystal structure of Au[TPP] (CSD:
TEHZOY). Bottom left: view of porphyrin core exhibiting wave
distortion. Right: selected bond distances (black) and out-of-plane
deformations (red) in~\AA{}.}
{\vspace*{1pt}}
\end{figure*}

In this study, we have critically examined two key aspects of Au(II)
porphyrins---their ionization potentials and the putative second-order
Jahn--Teller distortion. Relativity was found to downshift the
ionization potentials of Au(II) porphyrins by ${\sim}$0.6~eV, which is
severalfold that calculated for Ag(II) porphyrins. Significantly, the
present study also places the unusual geometrical distortions of
Au[TPP] in an entirely new light. On account of a heretofore
unsuspected orbital interaction, ultimately attributable to relativity,
it is the wave distortion that emerges as the preeminent
stereoelectronic effect in Au(II) porphyrins; the lateral distortion
appears merely incidental to the wave distortion.

\section{Results and discussion}\label{sec2}

In this study, we have critically examined the role of relativity in
determining two key aspects of Au{(II)} porphyrins, their ionization
potentials and the putative Jahn--Teller distortion. Three Au(II)
porphyrins were studied in this work---Au[P], Au[TPP], and
Au[TPFPP]---where P, TPP, and TPFPP denote porphine,
tetraphenylporphyrin, and tetrakis(pentafluorophenyl)porphyrin,
respectively. For comparison purposes, the analogous Ag porphyrins were
also studied. Each molecule and its corresponding cation were optimized
with scalar-relativistic and two-component spin--orbit DFT as described
in the \textit{Computational methods} section.

The relativistic calculations revealed unusually low adiabatic IPs for
the Au(II) porphyrins (Table~\ref{tab1}), which are about 1~eV lower
than those of Ag(II) porphyrins and a little under 2~eV lower than
those of Zn(II) porphyrins~\cite{23} (DFT has long excelled at
predicting ionization potentials and photoelectron spectra of
porphyrins~\cite{24,25,26,27}). Both scalar-relativistic and spin--orbit
calculations yielded very similar IPs, to within 0.05~eV. For Au, the
relativistic effects are large, some 0.7~eV, compared with only
0.05--0.2~eV for Ag, in line with analogous findings from our
laboratory on other pairs of 4d and 5d transition metal
complexes~\cite{28,29,30,31,32,33}. Substituent effects were also found
to be important~\cite{25,34}: both for the Ag and Au series, the IP of
the TPFPP complex is some three-quarters of an~eV higher than that of
the TPP complex. Electron-deficient porphyrins thus appear clearly
poised to deliver more oxidatively robust Au(II) derivatives.

%tab1
\begin{table}
\caption{\label{tab1}Adiabatic OLYP ionization potentials obtained with
nonrelativistic (NR), scalar-relativistic (SR), and two-component
spin--orbit (SO) ZORA calculations$^{\mathrm{a}}$}
\begin{tabular}{cccc}
\thead
Molecule & NR & SR & SO \\ 
\endthead
Ag[P]     & 6.13 & 5.93 (6.17) & 5.93 \\ 
Au[P]     & 5.55 & 4.90 (4.96) & 4.87 \\ 
Ag[TPP]   & 5.64 & 5.57 (5.88) & 5.59 \\ 
Au[TPP]   & 5.14 & 4.60 (4.57) & 4.60 \\ 
Ag[TPFPP] & 6.50 & 6.34 (6.67) & --  \\ 
Au[TPFPP] & 5.91 & 5.36 (5.48) & 5.34 
\botline
\end{tabular}
\tabnote{$^{\mathrm{a}}$The values shown in parentheses are based on
single-point B3LYP$^{*}$ calculations on OLYP geometries.}
\end{table}

Turning now to the question of geometry, the Ag(II) complexes all
optimized to their expected point groups: $D_{4\mathrm{h}}$ for Ag[P]
and $D_{\mathrm{2d}}$ for Ag[TPP] and Ag[TPFPP] (Figures~\ref{fig2}
and~\ref{fig3})~\cite{35,36}. In contrast, for the Au analogues of the
three molecules, both scalar and spin--orbit relativistic calculations
revealed a lateral compression--elongation, much as observed
experimentally. Furthermore, like the experimental~\cite{22} structure,
and DFT-optimized structures evinced a distinct wave distortion. The
optimized equilibrium geometries of all the Au(II) structures,
accordingly, were found to conform to only $C_{2\mathrm{h}}$ symmetry,
with the $C_{2}$ axis passing through a pair of opposite nitrogen
atoms.

\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig02}
{\vspace*{2pt}}
\caption{\label{fig2}Top: selected OLYP-D3 optimized distances (black),
out-of-plane distortions (red), and Mulliken spin populations (blue)
for Au[P] (left) and Ag[P] (right). Middle row: HOMOs (SOMOs). Bottom:
spin densities.}
{\vspace*{1pt}}
\end{figure*}

\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig03}
{\vspace*{4pt}}
\caption{\label{fig3}Selected OLYP-D3 optimized distances (black),
out-of-plane distortions (red), and Mulliken spin populations (blue)
for M[TPP] and M[TPFPP], where M $=$\ Ag, Au. All distances are
in~\AA{}. \textit{Note}: HOMOs (SOMOs) and spin density plots are
omitted for these complexes as these are visually almost
indistinguishable from those shown in Figure~\ref{fig2} (in spite of
quantitative differences).}
{\vspace*{2pt}}
\end{figure*}

As of now, the unusual core geometry of Au[TPP] has been ascribed to a
second-order Jahn--Teller distortion involving the Au 5d$_{x^{2}\hyphen
y^{2}}$ and 6s orbitals~\cite{22}. An examination of the
scalar-relativistic frontier MOs of each of the three Au(II) porphyrins
studied indeed revealed varying degrees of mixing of the d$_{z^{2}}$,
d$_{x^{2}\hyphen y^{2}}$, and 6s orbitals. Unlike in a simple
Jahn--Teller system (but not uncommonly for second-order Jahn--Teller
systems~\cite{37,38}), however, the OLYP-D3 Kohn--Sham MOs with major
contributions from the three atomic orbitals were found to exhibit a
remarkable 8-eV span of orbital energies in these systems. For Au[P],
the orbital energies for the ${\upalpha}$ or majority-spin orbitals
were ${-}$7.63~eV for the primarily d$_{z^{2}}$-based HOMO-18, ${-}$3.27~eV
for the primarily d$_{x^{2}\hyphen y^{2}}$-based HOMO, and 0.56~eV for
the primarily 6s-based LUMO$+$27.
Of the three MOs, it was the
lower-energy, primarily d$_{z^{2}}$-based HOMO-18, not the
d$_{x^{2}\hyphen y^{2}}$-based HOMO, that was found to exhibit the
greatest degree of d$_{x^{2}\hyphen y^{2}}$ and 6s admixture. The HOMO,
it turned out, engages in a very different orbital interaction, namely
one with the porphyrin's $\uppi$-HOMO. Thus, both the HOMOs and spin
density profiles of the complexes exhibit surprisingly significant
$\uppi$-amplitudes at the \textit{meso} positions of porphyrin
(Figure~\ref{fig2}). The Au(II) centers, as a result, carry
correspondingly smaller spin populations than the Ag(II) centers in the
{analogous} complexes (Figures~\ref{fig2} and~\ref{fig3}). The latter
finding greatly intrigued us, as it seemed to indicate an electronic
imperative underlying the porphyrin's wave distortion: the Au(II)
center appears to exploit the nonplanar wave geometry to suck electron
density from the porphyrin's $\uppi$-HOMO into its 5d$_{x^{2}\hyphen
y^{2}}$ orbital.

To gauge the relative importance of the lateral compression--elongation
and the wave distortion, we next optimized Au[P] with
scalar-relativistic OLYP-D3 calculations under three different symmetry
constraints, $D_{4\mathrm{h}}$, $D_{2\mathrm{h}}$, and
$C_{2\mathrm{h}}$, with all MO irreps worked out by hand. Both the
$D_{4\mathrm{h}}$ and $D_{2\mathrm{h}}$ calculations led to non-aufbau
orbital occupations (i.e., where LUMO is below the HOMO), an indication
of the instability of the molecule under those symmetry constraints.
Most interestingly, the $D_{2\mathrm{h}}$ optimized geometry did not
exhibit the expected lateral distortion and proved essentially
identical to the $D_{4\mathrm{h}}$ geometry. In other words, the
lateral distortion does not occur in the absence of the wave
distortion. We are thus led to conclude that \textit{it is the wave
distortion that is fundamental and drives the lateral distortion}, and
not the other way around.

The above findings lend an entirely new complexion to the electron
structure of Au(II) porphyrins. The tendency of the Au(II) center to
increase its effective d-electron count parallels a recent study in
which a variety of formally Au(III) complexes have been described as
quasi-d\tsup{10}, based on theoretical analyses of their bonding
interactions~\cite{39}. These complexes nevertheless exhibit distinct
2p$\rightarrow$5d XANES features, indicative of a 5d hole. Like many
d\tsup{10} complexes, on the other hand, they also exhibit weak,
low-energy MLCT transitions in the near-infrared~\cite{22}. In this
study, TDDFT calculations, which do a rather good job of reproducing
the visible absorption spectrum of Au[TPP] (details of which are not
particularly \mbox{relevant}), also predict two infrared absorptions with
almost vanishingly small oscillator strengths. The wavelengths of the
two absorptions vary considerably with details of the computational
method, such as the choice of the exchange--correlation functional and
basis set, but the assignment of the two features seems stable with
respect to such details. With the well-calibrated range-separated
CAMY-B3LYP functional~\cite{40} and the COSMO solvation
model~\cite{41}, the two absorptions in dichloromethane are at 0.55~eV
(2215~nm) and 0.66~eV (1863~nm, Figure~\ref{fig4}).
Given their low energies and
intensities, these two features have not been experimentally detected
so far, but may be viewed as computational signatures of Au[TPP].
Comfortingly, the electrochemical HOMO-LUMO gaps (defined as the
algebraic difference between the oxidation and reduction potentials) of
Au(II) porphyrins of ${\sim}$0.6~eV, which may be inferred from the
literature~\cite{20,21} are in almost perfect agreement with the
CAMY-B3LYP excitation energy.

\begin{figure*}
{\vspace*{-2pt}}
\includegraphics{fig04}
{\vspace*{-2pt}}
\caption{\label{fig4}CAMY-B3LYP/STO-TZ2P-derived infrared transitions
and their MO composition for Au[TPP].}
{\vspace*{-2pt}}
\end{figure*}

The inherent, electronically driven wave distortion of Au(II)
porphyrins is reminiscent of the inherent saddling of copper
corroles~\cite{42,43,44,45}, {which is driven by the electronic
imperative of the formally empty Cu(3d}$_{x^{2}\hyphen y^{2}}${)
orbital to accept electron density from the corrole's $\uppi$-HOMO. A
similar orbital interaction is less important for silver
corroles~\cite{46,47} and not at all important for gold
corroles~\cite{48,49,50,51,52}. The reason for the latter has to do
with both relativistic destabilization of the Au(5d}$_{x^{2}\hyphen
y^{2}}$) orbital and the exceptionally strong $\upsigma$-ligand field
of the corrole~\cite{53}. Charge-neutral gold porphyrins and copper
corroles provide rare examples where metal(d)--porphyrinoid($\uppi$)
interactions alone suffice to engender nonplanar distortions of the
macrocyclix ligands, even in the absence of sterically hindered,
peripheral substituents~\cite{54}.

\section{Computational methods}\label{sec3}

Each Au(II) porphyrin and its corresponding cation were optimized with
scalar-relativistic and two-component spin--orbit DFT 
(OLYP~\cite{55,56}-D3~\cite{57}) calculations with the ZORA~\cite{58}
Hamiltonian and ZORA STO-TZ2P basis sets, as well as with
nonrelativistic calculations with the same basis sets, all as
implemented in the ADF program system~\cite{59}. Single-point
scalar-relativistic energies were also calculated using the
B3LYP$^{*}$~\cite{60,61} functional and found to be in excellent
agreement with the OLYP-D3 results. Carefully tested, fine integration
grids and tight SCF and geometry optimization criteria were used in all
calculations.

\section{Conclusion}\label{sec4}

The present study, in our view, has significantly deepened our
electronic-structural understanding of Au(II) porphyrins.

First, the first IPs of Au(II) porphyrins have been found to be
unusually low, ${>}$1~eV lower than those calculated for Ag(II)
porphyrins; this difference is largely attributable to scalar
relativistic effects, which are much stronger for gold than for silver.
Electron-withdrawing substituents, however, are predicted to yield
Au(II) derivatives such as Au[TPFPP] with higher oxidative stability.

Second, our calculations have put a whole new complexion on the
experimentally observed structural distortions of Au[TPP]. The primary
\mbox{stereoelectronic} effect appears to be a wave distortion driven by an
Au(5d$_{x^{2}\hyphen y^{2}}$)--porphyrin(${\uppi}$) orbital interaction,
which allows the formal Au(II) center to assume a pseudo-d\tsup{10}
configuration. The lateral distortion allowing for Au 5d$_{x^{2}\hyphen
y^{2}}$-5d$_{z^{2}}$-6s mixing appears to be a secondary effect,
a consequence of the wave deformation. Tellingly, in computational
experiments, absent a wave formation, Au(II) porphyrins do not undergo
an in-plane lateral distortion.

\section*{Declaration of interests}

The authors do not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and have
declared no affiliations other than their research organizations.

\section*{Data availability statement}

All data generated or {analyzed in} this study are included in this
published article and its supplementary information.

\section*{Funding}

This work was supported in part by grant no. 324139 of the Research
Council of Norway (AG) and grant nos. 129270 and 132504 of South
African National Research Foundation (JC).

\CDRGrant[RCN]{324139}
\CDRGrant[NRF]{129270}
\CDRGrant[NRF]{132504}

\back{}

\section*{Supplementary data}

Supporting information for this article is available on the journal's
website under \printDOI\ or from the author.

\CDRsupplementaryTwotypes{supplementary-material}{\cdrattach{crchim-264-suppl.pdf}}

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