Electrochemistry is a natural science. Any natural science requires a balanced interaction of physical experiments and theoretical modelling, as its basic operational methods. A purely “experimental” natural science does not exist. But for the last seven decades or so, a third operational method, computer experiments, has come into play as well. Apart from this, the appearance of computers has offered unprecedented possibilities for automating, intensifying, and improving the reliability of diverse research practices. This gave rise to new research areas, usually called “computational physics,” “computational chemistry,” etc. As a result, we witness a methodological revolution that some call “a second metamorphosis of science” [1].

The new research areas (“computational physics,” “computational chemistry,” etc.) are, in part, counterparts of the traditional “experimental physics,” “theoretical physics,” “experimental chemistry,” “theoretical chemistry,” etc., focused on computer experimenting, although they are not entirely separable from “theoretical physics,” theoretical chemistry,” etc. However, they are also perceived as interdisciplinary fields (involving physics, chemistry, etc., together with elements of mathematics and computer science), which jointly form what is now called “computational science,” according to the emerging definition (see, for example, [2,3,4]).

I have devoted most of the 42 years of my professional life to the efforts to introduce modern computational (and more generally computer-aided) methods to the practices of electroanalytical chemistry. My intention is to contribute to the creation of computational electrochemistry as a full-fledged area of study, understood as a part of computational science related to electrochemistry, and consistent with the aforementioned definition of computational science [2,3,4]. Hence, in my work, and in the present note, I perceive computational electrochemistry as an interdisciplinary field, involving not merely simple uses of computers, computer programs, and/or computational methods in electrochemistry, but also an active development of computer-aided methods, algorithms, programs, or other tools, aimed at solving diverse problems occurring in the electrochemical research [5]. I also argue [6] that computational electrochemistry should unify all kinds of computations occurring in electrochemistry: quantum computations, molecular computations, as well as those based on the assumption of continuity of matter—the latter are typical for formal electrochemical kinetics, in which I am particularly interested.

When 20 years ago I published my research program for (such understood) computational electrochemistry, with a focus on electroanalytical chemistry [5], the perspectives seemed bright. There were plenty of computer-based methods and approaches available in the non-electrochemical literature. One could be optimistic about applying them to (or adjusting them to the needs of) electroanalytical chemistry, thereby pulling out the methodology of electroanalytical chemistry from the misery of pre-computer times. One could also expect an outburst of publications dealing with an interdisciplinary development of new, computer-based approaches to studying electrochemical phenomena. Now, when the end of the first quarter of the twenty-first century is approached, one can ask if these hopes have become a reality and how the present situation in this respect might be related to the education of electrochemists.

Some answers to this question should be obtainable by comparing the temporal changes in the numbers of publications dealing with the theories and computer simulations or other computational activities in electrochemistry and remaining natural sciences. Modern literature databases, such as Scopus [7], offer some tools that can help obtaining such information. The tools are not perfect—their main disadvantage is that they “don’t understand” the intentions of their users (a true artificial intelligence still does not exist). Any database search based on the occurrences of certain keywords will obviously not find a publication that does not contain the keywords, even if the subject of the publication is closely related. Therefore, the results of such searches are likely to be incomplete or biased. Nevertheless, I have performed several Scopus searches, in the hope of obtaining at least some guidance. The searches were for the following keywords or keyword combinations: DISCIPLINE, DISCIPLINE AND THEORY, DISCIPLINE AND SIMULATION, and for the phrase “COMPUTATIONAL DISCIPLINE,” where DISCIPLINE stands for PHYSICS, CHEMISTRY, BIOLOGY, or ELECTROCHEMISTRY. These keywords or phrases were searched within publication titles, abstracts, and author-declared keywords. I assumed that the papers containing the keyword DISCIPLINE form a representative sample of the papers published in a given discipline and that the number of such papers is proportional to the total number of papers in a given discipline, with a proportionality coefficient identical for all disciplines. In the further text, these two sets of papers are assumed to be equivalent, for simplicity. Additional keywords (such as THEORY or SIMULATION) then allow one to identify theoretical papers or papers dealing with simulations in a given discipline. Such assumptions might be criticized, but I often observe that research areas to which some Scopus tools automatically attribute publications are completely wrong. Of course, one has to be aware of the multiplicity of meanings the words such as THEORY or SIMULATION may have. In particular, THEORY may not necessarily mean a “hard” theory (or model) based on rigorous, mathematically formulated laws of nature; it may also mean a “soft” theory (or model) based on heuristic concepts. But such “soft” theories or models are often useful and should not be deprecated or ignored (see, for example, [8, 9]). The word SIMULATION also possesses numerous meanings and definitions (see, for example, [10, 11]).

Tables 1, 2, 3, and 4 contain absolute numbers of papers containing the above keywords or phrases, published in successive years between 1970 and 2021. As the tables reveal, all these absolute numbers of papers tend to grow from year to year (on average), because of the overall growth of the number of scientific publications. Therefore, instead of comparing absolute numbers of papers containing particular keywords, it is more informative to compare relative numbers, obtained by normalizing the absolute numbers with the total numbers of papers published in a given year in a given scientific discipline. Figures 1, 2, and 3 present such relative numbers of papers.

Table 1 Absolute numbers of papers containing the keywords or keyword combinations: PHYSICS, PHYSICS AND THEORY, PHYSICS AND SIMULATION, COMPUTATIONAL PHYSICS, published between 1970 and 2021
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Table 2 Absolute numbers of papers containing the keywords or keyword combinations: CHEMISTRY, CHEMISTRY AND THEORY, CHEMISTRY AND SIMULATION, COMPUTATIONAL CHEMISTRY, published between 1970 and 2021
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Table 3 Absolute numbers of papers containing the keywords or keyword combinations: BIOLOGY, BIOLOGY AND THEORY, BIOLOGY AND SIMULATION, COMPUTATIONAL BIOLOGY, published between 1970 and 2021
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Table 4 Absolute numbers of papers containing the keywords or keyword combinations: ELECTROCHEMISTRY, ELECTROCHEMISTRY AND THEORY, ELECTROCHEMISTRY AND SIMULATION, COMPUTATIONAL ELECTROCHEMISTRY, published between 1970 and 2021
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Fig. 1
figure 1

Relative numbers of papers containing the keyword combinations: PHYSICS AND THEORY (black squares), CHEMISTRY AND THEORY (black circles), BIOLOGY AND THEORY (black triangles), and ELECTROCHEMISTRY AND THEORY (white circles), published between 1970 and 2021

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Fig. 2
figure 2

Relative numbers of papers containing the keyword combinations: PHYSICS AND SIMULATION (black squares), CHEMISTRY AND SIMULATION (black circles), BIOLOGY AND SIMULATION (black triangles), and ELECTROCHEMISTRY AND SIMULATION (white circles), published between 1970 and 2021

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Fig. 3
figure 3

Relative numbers of papers containing the phrase: “COMPUTATIONAL PHYSICS” (black squares), “COMPUTATIONAL CHEMISTRY” (black circles), “COMPUTATIONAL BIOLOGY” (black triangles), and “COMPUTATIONAL ELECTROCHEMISTRY” (white circles), published between 1970 and 2021

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As can be seen in Fig. 1, the relative numbers of papers containing ELECTROCHEMISTRY AND THEORY are comparable to the relative numbers of papers containing CHEMISTRY AND THEORY and BIOLOGY AND THEORY but are about three times smaller than the relative numbers of papers containing PHYSICS AND THEORY. Furthermore, the relative numbers of theoretical electrochemical papers seem to have increased somewhat over the past 10 years or so, whereas other theoretical disciplines do not exhibit such a trend. This is surprising for me, as my subjective impression resulting from the inspection of basic electrochemical journals is that theoretical papers have been recently rather rare, at least in the domain of the theory of electroanalytical methods. But from Fig. 1, one might conclude that there is no reason to worry about theoretical electrochemistry, which performs comparably to theoretical chemistry and theoretical biology. The dominant position of theoretical physics can be attributed to the fact that this is an old and mature field, in which theorizing is of particular value with consequences for all sciences.

To a less positive conclusion leads an analogous comparison of the relative numbers of papers containing DISCIPLINE AND SIMULATION (cf. Figure 2). One can see a distinct reduction of the relative number of papers containing ELECTROCHEMISTRY AND SIMULATION over the recent decade, placing electrochemistry in the last position among the scientific disciplines considered. In all remaining disciplines an opposite, systematic growth of the relative number of simulation papers is observed. This finding agrees with my subjective impression (but again referring mostly to the modelling of electroanalytical methods) that the population of electrochemists willing to engage in the development of computer simulation approaches has decreased in recent years and currently involves only a few research groups and individuals. In addition, those who remained are often already retired or likely to retire soon.

The comparison of relative numbers of papers containing the phrase “COMPUTATIONAL DISCIPLINE,” presented in Fig. 3, puts electrochemistry in an even worse position. The use of the phrase “COMPUTATIONAL ELECTROCHEMISTRY” is currently marginal, compared to “COMPUTATIONAL PHYSICS” and “COMPUTATIONAL CHEMISTRY,” and about two orders of magnitude less frequent (in electrochemistry) than the use of the phrase “COMPUTATIONAL BIOLOGY” (in biology), which exhibits an extraordinary systematic growth of popularity from year to year. The number of papers thematically related to computational electrochemistry is surely bigger than the number of those containing the phrase “COMPUTATIONAL ELECTROCHEMISTRY.” But apparently, their authors do not consider it important to label them with the phrase. This suggests that the authors do not view computational electrochemistry as a distinct area of research, with which they can identify themselves. It is also pertinent to notice that out of the electrochemical journals, only one (Electrochemistry Communications) officially declares publishing papers related to computational electrochemistry and that according to Scopus, during the entire period of existence of Electrochemistry Communications, the journal published merely 5 papers containing the phrase “COMPUTATIONAL ELECTROCHEMISTRY,” between 1999 and 2007.

In my opinion, the above findings indicate that among the scientific disciplines considered, electrochemistry is the least advanced one, in the process of adopting computational and computer-aided research practices. Computational electrochemistry, in its present state, has not yet been integrated with the mainstream of computational science. The electrochemical community shows also a considerable inability, to accept changes in this respect. Even if the numbers of papers obtained by Scopus are not exact, they are surely meaningful in illustrating the “cultural” differences between electrochemistry and other natural science disciplines, in dealing with the computer revolution.

One can provide other arguments to support my opinion. As in my youth I studied physics, I always felt uncomfortable when confronted with some customary practices in electrochemistry. Every student of physics learns (usually in the first semester of the studies) that physical experiments should always be repeated many times, and their results averaged and/or subject to some other statistical analysis. Statistical methods serving for such purposes are currently available in numerous computer programs, and they were even built into some computer languages, such as Python or R. However, typical electroanalytical experiments (such as cyclic voltammetry and chronoamperometry) are rarely (if ever) repeated more than once. Furthermore, the analysis of experimental responses is often limited to selected data points on the recorded responses (for example, one only analyzes a cyclic voltammetric peak height or potential), the rest of the collected data, together with its information content, being ignored. Ironically, such a practice seems to be considered by some electrochemical experts as a standard or most desirable way of analyzing the experimental data. Reviewers of my papers dealing with the theory and computational aspects of electroanalytical experiments regularly urge me to provide “diagnostic criteria” serving for theoretical model discriminations or parameter determinations. But the concept of the “diagnostic criteria” dates back to the pre-computer era, when the storage and analysis of experimental results were technically difficult, and some “quick and dirty” methods of obtaining conclusions were needed. For example, plotting a voltammetric peak height as a function of the potential sweep rate was a diagnostic criterion enabling an identification of reversible charge transfers. Today, using such “quick and dirty” data analysis methods makes little sense, as the experimental data is normally obtained in digital form, and a plethora of robust computer-aided data analysis methods applicable to digital data are available, such as (for example) multiparameter/multiresponse fitting, possibly supported by sensitivity analysis [12,13,14], Bayesian inference [14], bootstrap resampling [15], or (recently extremely fashionable in the computer science world) model identification based on machine learning [14, 16]. Although such modern techniques are addressed sometimes in the electrochemical literature, as the above references prove, their use is still rather sporadic.

In the nineties of the past century, there were some efforts to create simulation environments for electroanalytical chemistry, some of which were supplied with data analysis algorithms. I would mention here, in particular, EASIEST [17], ELSIM [18], and DigiSim [19]. There were a few more, but out of all these programs, only DigiSim (currently called DigiElch) remained at the battlefield until today, having a fairly large number of users, and it has also been used for teaching [20]. The users of DigiSim/DigiElch benefit from automatic parameter estimation routines. However, one may not be so sure whether the users understand these routines [21]. A worrying aspect also is that in spite of the enormous progress in the scientific software technology, that occurred since those times, the present activity in the area of the development of this type of programs appears rather minor. This situation contrasts with the fact that the development of “problem-solving environments for computational science” is formulated to be a crucial research goal for computational science [22].

In addition, there exist spectacular computer-based research technologies, invented outside electrochemistry, and apparently not ever applied in electrochemistry. One of them are “robot scientists” [23] capable of automatically proposing research hypotheses and performing relevant experiments. The robot scientists have proven effective in drug design investigations, which in some aspects resemble typical electrochemical investigations. In both scientific areas, there often occurs a recursive sequence of experiments and theoretical model adjustments, which may well be dedicated to a robot, thereby releasing human investigators from tedious routine actions.

Summing up, I would argue that the present status of computational electrochemistry is far from satisfactory. There is a question what could be done to improve this situation. In my opinion, young generations of electrochemists should be more comprehensively (than thus far) educated in this area. They should also be prepared for (and encouraged in) undertaking interdisciplinary investigations between electrochemistry and widely understood computational science. It is illusory to expect (as some may do) that experts from other scientific disciplines (such as mathematics or computer science) will produce relevant algorithms and tools to be used by electrochemists. From my experience, such externals experts are uninterested in electrochemistry and its problems. Even scientific journals devoted to mathematics, numerical methods, computational science, and computer science are not willing to consider and publish papers related to electrochemical applications, as they perceive such papers as too specialized or incorrectly classify them as related to engineering areas. However, mathematical problems pertinent to electroanalytical chemistry are unique in many aspects; for example, they often involve reaction–diffusion systems with complicated boundary conditions not encountered in any other areas of science. Hence, they should be of interest to mathematicians and computational scientists, who need challenging examples for their studies of various methods and algorithms. But the currently marginal intellectual transfer between electrochemistry, mathematics, and computational science leaves such problems largely unknown outside electrochemistry, so that mathematicians keep using old and much less interesting examples from the more commonly known areas, such as e.g. heat transfer studies.

Hence, I believe a considerable effort must be undertaken by the electrochemical community, and this calls for adequate educational curricula. All those who intend to work in the area of traditional electrochemical experiments and investigations should be better educated about the existing computer-aided methods and techniques and about benefits of computer experiments or simulations. This postulate is consistent with the earlier observation [24] of shortcomings in these aspects of the education of electrochemists. But in the first place, I would suggest creating new kinds of interdisciplinary studies, with the aim of educating interdisciplinary specialists. It should be noted that interdisciplinary university studies combining a number of traditional natural sciences and computer science have been advocated for a long time and have become quite frequent in recent decades (see, for example, [25, 26]). Sadly, I am not aware of similar studies combining electrochemistry and computer science, but there is no reason for not opening such studies. This might even be a useful trick attracting young people to electrochemistry, as nowadays most of the ambitious youngsters think it is only computer science that offers the most attractive careers for them, which deprives traditional natural science disciplines of new talented adepts.

Of course, education of young electrochemists is not the only issue that awaits improvements. Another painful problem is the deficiency of quality journals in which interdisciplinary computational electrochemists can publish. Yet another problem is the deficiency of initiatives aimed at creating publicly available databases of electrochemical experimental results. Databases of this sort exist in other scientific areas (for example, in biomedicine), and they are fundamental for stimulating the development of data analysis algorithms (cf., for example, [27]). But these, and other problems, are probably topics for a different Special Volume.