The present Prefatory Review was prompted by the timely invitation of the Founder and Editor-in-Chief of Structural Chemistry, Professor Istvan Hargittai, on the occasion of the Journal’s 35th birthday and by the Chemical Science 2023 publication of the Perspective Essay entitled “Aromaticity – Quo Vadis”, authored by Gabriel Marino, et duodecim alia [1]. It is an attempt to present an additional analysis and a renewed insight. The phrase ‘Quo Vadis’ appears in the Vulgate, the Latin translation of the Bible, in John 13:36, the account of the last supper: when Jesus hints at his imminent detention and death Saint Peter inquires “Quo Vadis” [2]. However, the Christian tradition regarding Saint Peter’s first words to the risen Christ, during their encounter along the Appian Way outside Rome, late 2nd century AD [3] is perhaps better known. Furthermore, the Vulgate contains the ‘Quo Vadis’ phrase several times, e.g. in Genesis, 16:8, Genesis, 32:17. The ‘Quo Vadis’ phrase means idiomatically a reflection on someone’s purpose or direction in life. The essence of the “Quo Vadis” phrase is included in the opening Talmud saying attributed to Akabja Ben Mehalalel, ca. 100 AD:

“Know whence thou comest and whither thou goest and before whom thou art to give strict account” [4].

The point of the quote from the Talmud, which contains the element ‘whither thou goes’ of the ‘Quo Vadis’ phrase, preceded the Quo Vadis element. The two other elements of the Talmud saying, ’know whence thou comest’ and ‘before whom thou art to give strict account’, are also elements relevant to the Aromaticity: Quo Vadis Perspective. The authors discuss previous definitions and approaches to aromaticity and give account to the scientific community. I admire the authors’ choice of the phrase ‘Quo Vadis’ for the title of their Perspective. It provides a certain ‘multidisciplinary’ flavor. Likewise, introducing the Talmud quote.

I was introduced to the notion of aromaticity by my Vater Professor Ernst David Bergmann (1903–1975) at the outset of my Ph.D. research in the early 1960s. I advanced in my 1966 Ph.D. Thesis [5] the proposition that aromaticity is a theoretical notion, and as such, its meaning is theory dependent [6]. I claimed that any attempt to define explicitly the notion of aromaticity should take into consideration the following general statement made by the logician Ernst Nagel:

”In these cases in which a given theoretical notion is made to correspond to two or more experimental ideas, it would be absurd to maintain that the theoretical concept is explicitly defined by each of the two experimental ones in turn” [7].

The opening lecture at the Jerusalem Symposium on “Aromaticity, Pseudoaromaticity, Antiaromaticity“ [8] ended with the quotation of Nagel’s statement. The proposition that aromaticity is a theoretical notion was restated in the 1973 review on aromaticity in the series MTP International Review of Science entitled “Theoretical Aromatic Chemistry” [9] and in the Journal of Organic Chemistry 2007 article [10]. My Prefatory Review refers also to the Editorial [11], of the themed collection “Emerging Frontiers in Aromaticity”, guest edited by Gabriel Merino, Miquel Solà, and Israel Fernández [12] and to the Commentary entitled “A focus on aromaticity: fuzzier than ever before?” authored by Henrik Ottosson [13].

The Editorial [11], the Perspective [1], and the Commentary [13] of the collection were conspicuously silent on aromaticity as a theoretical notion, except for few brief statements: Harry thinks that “criteria for aromaticity should be grounded in parameters that can be measured experimentally and calculated theoretically” [1] (p. 5571). “Alternatively, if aromaticity becomes seen as primarily a theoretical quality, without experimental manifestations, it loses relevance” [1] (p. 5571). “It is not a matter of being theoretical or experimental” [1] (p. 5751). “Aromaticity is a phenomenon” [1] (p. 5571). The reviews on aromaticity [8, 9] and the 1976 review in International Review of Science, entitled “The Controversial Notion of Aromaticity” [14] were also overlooked. Consistently, an editor of a Nature (now Springer Nature) journal advised me a score years ago not to submit review chapters of edited books, because the majority of scientists will not read them and most libraries will not purchase such books.

The Quo Vadis Perspective [1] contains the following sentences that are pointing at a scenario of incompatibility of aromaticity criteria with one another, a scenario, which is somewhat relevant to aromaticity as a theoretical notion. “Thus ‘aromaticity’ would be something that can be measured via some proper yardstick. Several long established ‘quantifiers’ of different kinds are available – energetic, geometrical, magnetic, electronic, topological, etc. – sometimes incompatible with one another” [1] (p. 5571). “If we rely on magnetic properties as a probe of aromaticity, we might list some molecules as aromatic, which might not be considered as aromatic if we chose intrinsic criteria of aromaticity, i.e., energetic, structural, and electronic criteria” [1] (p. 5572).

On the other hand, the Quo Vadis Perspective quotes the following viewpoint that is in contrast with aromaticity as a theoretical notion: “we can call a molecule aromatic if it does satisfy all criteria of aromaticity, i.e., structural, energetic, electronic, and magnetic, at the same time. This involves that if a molecule satisfies the magnetic criterion of aromaticity but fails in energetic test, we should not call the system aromatic and vice versa” [1] (p. 5574), referring to Cuyacot, et al. [15]. : “Considering the conflicts between magnetic response and ground-state aromaticity criteria (energetic, structural, and electronic criteria), we propose that the term aromatic be used for labeling a molecule if and only if all criteria confirm aromaticity. In other words, neither magnetic nor ground-state criteria [are necessary and sufficient conditions for labeling a molecule aromatic” [15].

The JOC article [10] included a response to Cyrañski, et al., who in 2002 raised the old question “to what extent can aromaticity be defined uniquely?” [16]. These authors adopted a statistical analysis of quantitative criteria of aromaticity, concluding that “the various manifestations of aromaticity are related” and that aromaticity “… from a philosophical point of view … can be regarded as a one-dimensional phenomenon.” The authors qualified this conclusion: “in practical applications energetic, geometric and magnetic descriptors of aromaticity … do not speak with the same voice. Thus, in this sense the phenomenon of aromaticity can be regarded essentially as being statistically multidimensional” [16]. The statistical approach is in contrast to aromaticity being a theoretical notion. The 2002 Cyrañski, et al., article [16], is reminiscent of the plot of the Japanese film Rashomon, where the audience is left with the buffing feeling of the relativity of truth [14, 17]. In this context, the Quo Vadis Perspective [1] quotes “the suggestive idea of aromaticity as a “multidimensional property”, which is a sort of conundrum including several different qualities challenging to assemble and reconcile within a comprehensive frame” [1], yet it also quotes critical arguments against this idea. V. I. Minkin, et al., stated in the authoritative book on Aromaticity and Antiaromaticity that “It is impossible to define aromaticity in a completely exhaustive manner” [18].

The Preface of the 2022 book Aromaticity and Antiaromaticity: Basics and Applications [19] authored by M. Sola, et al., and the Foreword of this book by G. Frenking [20], contained the following related sentences: “With the advent of quantum theory and its application in chemistry, the models were partially modified and they received a quantum chemical basis that allowed a theoretical understanding and an extension of the rules associated with the model. A prominent example is aromaticity” [19] (pp. xi-xii) “Aromaticity is a not well-defined property that cannot be measured experimentally” [20] (pp. xiii-xv).

In the spirit of the “Aromaticity: Quo Vadis” Perspective [1], it should be noted that the proposition “aromaticity is a theoretical notion and as such, its meaning is theory dependent”, submitted by a fox, not by a hedgehog [21], is an addition to the range of viewpoints on the essence of aromaticity, not a substitute. However, it is not a guise of aromaticity [22]. Paraphrasing Ernst Nagel [7], in the case of the theoretical notion aromaticity, which is made to correspond to two or more experimental ideas, it would be absurd to maintain that aromaticity is explicitly defined by each of the two (or more) experimental ones in turn. This emphasized message was not claimed in the Quo Vadis “disclosure”. On the contrary, the Quo Vadis Perspective ‘teaches away’ from this message not only by omitting it, but also by devoting long sections on “Are there criteria for aromaticity that are superior (or more desirable) to the others?” [1]. A reference may be said to ‘teach away’ when a person skilled in the art, upon reading the reference, would be discouraged from following the path set out in the reference or would be led in a direction divergent from the path that was taken by the applicant [23].

The descriptor ‘theoretical’ in this Prefatory Review does not mean ‘computational’. The Review is addressed to experimentalists as well as to theoreticians and “is not a matter of being theoretical or experimental” [1] (p. 5575). Charles Coulson’s seminal statement “we want insight, not numbers” summarizes what we should strive for, and what separates theory from computations. The statement is attributed to Coulson’s “after dinner speech” at the Banquet of the Conference on Molecular Quantum Mechanics on June 26, 1959 in Boulder, Colorado. Coulson published his speech in 1960 in Reviews of Modern Physics [24]. Surprisingly, Coulson’s statement, verbatim, was absent in this published article. In 2019, F. Neese, et al., modified Coulson’s statement: “Give us insight and numbers” [25]. A case in point, illustrating that ‘theoretical’ is often interpreted as ‘computational’ (contrary to my statement), is the following statement in the Quo Vadis Perspective: “Harry (Harry L. Anderson) thinks that “criteria for aromaticity should be grounded in parameters that can be measured experimentally and calculated theoretically. Alternatively, if aromaticity becomes seen as primarily a theoretical quality, without experimental manifestations, it loses relevance” [1] (p. 5571). This Prefatory Review is an opportunity to stress the difference between theory and computations. Interestingly, the authors of “Aromaticity: Quo Vadis?” stated: “we need to strive for a better qualitative insight, not just numbers from various computational tools, for (anti)aromaticity assessments (ultimately machine learning)” [1] (p. 5573). The similarity of this statement to Coulson’s statement is striking. The authors of the Quo Vadis Perspective used the words “insight and numbers”, but omitted a reference to Coulson’s statement. In a related 2020 tripartite Essay on “Simulation vs. Understanding: A Tension in Quantum Chemistry and Beyond”, the authors offer a “triangle, with experiment, especially in chemistry, impelling interaction between theory, numerical simulation and understanding” [26].

The Prefatory Review is an opportunity to commemorate the contributions by the late theoretical chemist Professor David P. Craig (1919–2015) [27], who introduced in his seminal papers on Aromatic Character [28] and Aromaticity [29] the notion of pseudoaromaticity, Craig’s rules of aromaticity and a second type of aromaticity based on delocalization in πp-dπ bonds [9, 30, 31]. The Quo Vadis Perspective [1] did not refer to Craig’s rules. Craig’s rules are theoretical rules, criteria of aromaticity based on symmetry, distinguishing between ‘aromatic’ and ‘pseudoaromatic’ cyclic conjugated hydrocarbons. In the broad sense, pseudoaromaticity referred to all nonbenzenoid aromatic compounds, for which the problem of the presence or the absence of an aromatic character arises [4]. Thus, the descriptor ‘pseudoaromatic’ in the general sense was first replaced by ‘nonbenzenoid’ (e.g., the 1959 book “Non-Benzenoid Aromatic Compounds”, see reference [29]) and later by the descriptor ‘novel’, (e.g., the series “International Symposia on the Chemistry of Novel Aromatic Compounds (ISNA)”) [32]. More specifically, pseudoaromaticity is associated with Craig’s rules of aromaticity. Craig’s rules are guidelines for the classification of cyclic conjugated hydrocarbons. They relate aromatic character to high resonance energy, which they attempt to predict on the basis of certain symmetry features whether the resonance energy between the canonical structures representing the ground state of a conjugated hydrocarbon is high or low. Craig’s rules distinguish between molecules with a valence bond wave function totally symmetrical, (e.g., benzene) and not totally symmetrical in the ground state (e.g., pentalene, heptalene). The former are designated aromatic, whereas the latter are designated pseudoaromatic. “The necessary element of symmetry for the application of Craig’s rules is a symmetry axis of order two passing through two or more π centres and transforming one Kekulé structure into another Kekulé structure” [9]. In Craig’s words [27]: “We discovered that whereas the ground state of the normal aromatics was totally symmetrical in the symmetry group, the other ones were not. So, if you could find a rule for saying which would go this way and which would go that, you would enable people to say straight off, without trying, ‘Well, this is a pseudo-aromatic. It won’t be easy to make.’ We did put out some rules, which worked quite well for a few years, but then an exception was found and that was that. We had the pleasant experience later on of people successfully making these molecules and finding they really were very unstable – decomposing very quickly” [27]. Craig’s rules have been criticized and occasionally led to ambiguous or faulty predictions (e.g., cyclopent[ef]heptalene) [9, 33].

Craig made the “distinction between two types of aromaticity; this distinction depends on symmetry” [30]. Craig presented an outline of the theory of a second type of aromaticity and illustrated its application by reference to the monocyclic phosphonitrilic chlorides (NPCl2)n, which, certainly for n = 3 and n = 4 and possibly higher, display aromatic character without special preference “for a group of six electrons” [30] and for Hückel’s rule of 4n + 2 versus 4n π electrons [28, 30, 31]. Craig’s “novel type of aromaticity” [30], a kind of Möbius topology, has recently been highlighted as ‘Craig-Type Möbius aromaticity’ (in dimetalla[10]annulenes) [34]. “Craig demonstrated the introduction of the essential 180° half-twist into a cyclic array of atomic orbitals and analyzed the influence of the presence of main group d orbitals in an alternating cyclic array of p-d π interaction” [34]. Craig concluded in 1959 that “In plane systems of alternating atoms A and B each providing one π-electron, there are only two symmetry distinguishable types of delocalization, represented as examples by neighbour pπ-pπ interactions and pπ-dxz, the former being the type familiar in aromatic hydrocarbons and the latter not hitherto recognized” and “In pπ-dxz delocalization the dominance of the sextet is lost. The delocalization energy per electron increases steadily with the number of π-electrons, leading to the expectation that on the basis of π-electrons alone an eight-membered ring would be more stable than a sixth-membered ring” [31]. “aromaticity is in fact of two types, the phosphonitrilic halides being the first recognized examples of the second type” [30].

According to Dewar, “Craig [31] has pointed out that the replacement of one p-AOs in a cyclic conjugated system by a d-AO, leads to a dislocation such that at least one pair of adjacent orbitals overlap out of phase” [35, 36]. “David Craig’s Möbius transition state ideas, while not glaringly visible, were nonetheless a precedent for the aromaticity/anti-aromaticity transition state model of Dewar” [36]. Craig’s ‘Möbius aromaticity’ [30], which Craig introduced in 1958 as a novel type of aromaticity, should be distinguished from Heilbronner’s ‘Möbius aromaticity’ [37]: “Feature of a monocyclic array of π orbitals in which there is a single out-of-phase overlap (or, more generally, an odd number of out-of-phase overlaps), whereby the pattern of aromatic character is opposite to Hückel systems; with 4n π electrons it is stabilized (aromatic), whereas with 4n + 2, it is destabilized (antiaromatic)” [38].

The present Prefatory Review serves as a platform for briefly stating my view point which theoretical framework of aromaticity to prefer, which theoretical framework I advocate. We mark as aromaticity several phenomena with different theoretical cornerstones. The following quotes from recent articles support this statement: “The different aspects of triplet state Baird-aromaticity are nothing but different” [39]. “Our findings support the view that one should speak of aromaticity as two phenomena, one response aromaticity represented by the magnetic aspect and one intrinsic aromaticity represented by the electronic, energetic and geometric aspects” [39]. “Since aromaticity is synonymous for a particular stability of cyclic delocalized systems, it may be stated that calculation or measurement of magnetic indices, i.e., NICS or current density, is not a reliable method to ascertain the aromatic character of a molecule” [40]. My preferred aromaticity criterion is the energetic criterion. It may be applied by both experimentalists and practitioners of computations. The application of the energetic criterion requires a reference molecule. The applicant may select a preferred reference or a number of references (e.g., homodesmotic reactions).

The aromaticity community should recall A. T. Balaban’s 1980 call: “So instead of trying to turn our thumbs down on a frequently used term, we should better make use of it” [41].

Conclusions

Aromaticity is a theoretical notion and as such its meaning is theory dependent! Therefore, when aromaticity is made to correspond to two or more ‘experimental’ ideas, e.g., energetic, structural, electronic, magnetic, it would be absurd to maintain that aromaticity is explicitly defined by each of these ideas in turn. Consistently, aromaticity is considered as several phenomena with different theoretical frameworks. The notion of aromaticity will survive [22], in spite of the many viewpoints and the hype of the scientists. Craig’s application of symmetry considerations in constructing aromaticity criteria is highlighted. The Prefatory Review stresses the difference between theory and computations. The meaning of the descriptor ‘theoretical’ is not ‘computational’, is not a synonym and is not a metonym to ‘computational’, in the context of aromaticity and in general.

Finally,

“A clash of doctrines is not a disaster–it is an opportunity” [42] (Alfred North Whitehead).

Reference is made to the eighteen-hundred-year-old Talmud teaching “Whoever reports a saying in the name of the one who said it brings redemption to the world” [43]. This virtue (in Hebrew “middah”) is the ethical obligation of quoting one’s sources! Credit should be given for another’s ideas and for previous related work. The Sages have identified such an act as a cause for redemption” [44].