Atomic and molecular collisions: classical and quantum dynamics, chaos and fractals, periodic orbits, quantum mechanical resonances, gas-surface scattering, atomic and molecular clusters, atoms and molecules under confinement: a kaleidoscopic view

Narayanasami Sathyamurthy

Early days (1951–1972)

Born in a village (Agarasethur) in a French-occupied territory in India, I grew up in different places in Tamil Nadu, India, as my father (G. Narayanasami) was a surveyor and was transferred from place to place, often on short notice. My mother (Nagalatchoumi) was a strict disciplinarian and would not let us eat dinner until we finished our homework (under a kerosene lamp until grade 9). I topped the school in grade XI and joined a nearby Government Arts College in Cuddalore for the Pre-University Course (PUC). Although I wanted to study physics, the romantic subject of the 1960s, my chemistry teacher (C. Shanmugam) advised me to apply for BSc (Chemistry) at Annamalai University. I listened to him and applied there. While I was waiting for admission, I received a telegram (of yesteryears) announcing my selection for a Scholarship under the National Science Talent Search Scheme (NSTS) from the National Council of Educational Research and Training (NCERT), New Delhi. The scholarship was Rs. 100 (1 US$ = Rs. 8 at that time) per month during BSc and Rs. 250 per month during MSc studies. There was also a book grant. In addition, NSTS scholars attended a summer school for a month each year at a prestigious university.

Despite my excellent grades in PUC, I was not selected for admission to the BSc in Annamalai. When I met Professor V. Baliah, the Head of the Department of Chemistry and asked him for admission, he told me that he had not offered me admission because students with my kind of grades would not join chemistry but instead pursue engineering studies. Now that I have come and asked him, he would grant me admission. When I came out of the Head's office, I met a person (Dr T. Rangarajan (Dr TR)), full of energy and enthusiasm. He wanted to know what the matter was, and when I explained the situation, he went in and insisted that I be admitted. He remained my Godfather till he breathed his last in 2019.

Doctoral studies (1972–1975)

As an NSTS scholar, I could have pursued my doctoral studies at Annamalai University or in one of the other NCERT-approved academic institutions in India. But my mentor, Dr TR, advised me to go to the United States for my PhD. He recommended me to the Graduate School at Oklahoma State University (OSU) in Stillwater, Oklahoma, USA. However, I had no money to buy a plane ticket to go to the United States, and my father was in no mood to let me travel to a foreign country. Dr TR stepped in and convinced my father to let me go and gave me Rs. 10 000 to buy the air ticket!

After completing the visa formalities, I began my journey to Stillwater, Oklahoma, on August 15, 1972, with US$ 7 in my pocket (the only amount allowed by the Government of India at that time). Upon arrival, my former classmate Prakash allowed me to stay as his roommate in his apartment and helped me with the initial expenses.

Once in Stillwater, I cleared the diagnostic tests for graduate admission, except for instrumentation in analytical chemistry. Since I wanted to pursue theory, the department required me to take several theory courses, particularly in physics and mathematics, and an analytical chemistry course, to complete the course requirements. I took a course in mathematical physics, and the instructor, Herbert Pohl, instilled in us the idea of a spherical chicken for modelling. Bob Freeman taught us the value of the information-theoretic approach to thermodynamics. Gilbert Mains was the Chairman of the department, and he was a wonderful teacher for the course on chemical kinetics. More than that, he was a solid supporter for me even after I left Oklahoma State. The only faculty member conducting research closely related to my interest was Professor Lionel M. Raff. He was the best doctoral supervisor I could get. He gave me complete freedom and let me choose my thesis problem and work at my own pace.

I decided to investigate vibrational energy transfer in CO₂–H₂ collisions, as some shock tube results were available. I computed the interaction potential between CO₂ and H₂ in their equilibrium geometries as a function of the centre-of-mass separation (R) and the polar angles around CO₂ and H₂ and the dihedral angle between them. The resulting table of numbers in four dimensions had to be fitted analytically or numerically before the dynamics could be investigated. Lionel told me that it was a challenging problem and left for Los Alamos on his sabbatical! Once there, he learned about the work of Don Thompson and his collaborator, Suzukawa, on CO₂–He collisions. He also learned about using one-dimensional (1D) and two-dimensional (2D) splines to fit data and shared the available literature and FORTRAN subroutines.

Before reaching Stillwater, I had not seen a computer or a calculator for that matter. But OSU had an IBM System/360, perhaps one of the best computing facilities available at that time. All I had to do was to learn FORTRAN and numerical methods. I found that fitting the R-dependence of the CO₂–H₂ interaction by an analytic function was not difficult. However, fitting the angular dependence was a challenge. I decided to extend the 1D and 2D splines to three dimensions and it worked.¹

Based on Suzukawa's thesis on CO₂–He collisions, I wrote a computer program to investigate the CO₂–H₂ dynamics. What was remarkable was that the rate coefficient computed by me using the ab initio potential energy surface (PES) and classical trajectory calculations for the 5-atom system agreed with what was known experimentally.² In the meantime, an interesting paper by Kouri and Baer showed³ that the quantum probability for the reaction He + H₂⁺ → HeH⁺ + H in collinear geometry was oscillatory when plotted as a function of the relative translational energy of the reactants and there was no vibrational enhancement of the reaction found experimentally. A master's student, Radha Rangarajan and I fitted the available ab initio PES for collinear HeH₂⁺ using a 2D spline and showed that the dynamics were sensitive to the details of the PES.⁴ I would keep revisiting the problem of (He, H₂⁺) dynamics for the rest of my life.

Post-doctoral studies (1975–1978)

While I was exploring the possibility of working as a post-doctoral fellow with some of the leaders in the field, I received an offer from Professor J. C. Polanyi. I accepted it and applied for permanent residence in Canada. The papers were processed quickly, and I landed in Toronto in August 1975. On the very first day of meeting John, I showed him two potential energy contour plots for the collinear [He–H–H]⁺ system that were superimposable; however, one of them showed vibrational enhancement and the other one did not. He looked at the plots and then at me and told me that it was my first day and that I would soon learn how his research group approached problems. I was asked to share an office with Jerry L. Schreiber, a former graduate student of John and who was an expert in classical dynamics. I learned from Jerry the nuances of classical trajectories and how to extract quantum mechanical information from them. Together we published a paper, “Rotational energy transfer (theory) I. Comparison of quasiclassical and quantum mechanical results for elastic and rotationally inelastic HCl-Ar collisions”.⁵ Paul Brumer was a young assistant professor in the department and was always willing to discuss chemical dynamics and related topics with us. He had already examined the (in)stability of long-lived trajectories in alkali halide systems and was ready to read and explain René Thom's book on Catastrophe Theory to us. Jim Duff, a former student of Don Truhlar, was working as a post-doc with Paul. Along with Jim, I started investigating the detailed dynamics of collinear He + H₂⁺ collisions and wrote a paper, “On the origin of the dynamical differences on the diatomics-in-molecules and spline-fitted ab initio surfaces for the He + H₂⁺ reaction”.⁶ We saw the tell-tale signs of chaos and fractals in the system but did not recognise them at that stage because the field was not born yet. I had already started arguing with John about the non-unique means of connecting reactants and products through the transition state and the idea of “sudden” and “gradual” late-energy-barriers was born.⁷ During my second year at Toronto, Jerry secured a faculty position in the US and relocated. John was willing to let me continue for one more year, with the title of an assistant professor, which meant I had to teach the Freshman Chemistry course at the University of Toronto. It brought prestige and a bit more money. At the end of two years, I went home for a month but stayed on for two months and married Suguna. The third year went partly in teaching CHM150 and partly in completing the work started in the first two years of my stay at Toronto.

Here I must acknowledge the guidance of Professor Bob Davidson, who was spending a sabbatical year with John. He introduced me to the goodies in the Jewish market in Toronto and guided me in preparing for a faculty position. He showed an advertisement for a faculty position in chemistry from the Indian Institute of Technology (IIT) Kanpur and asked me to apply. When I told him that I was not interested in going to Kanpur, he said to me, “Go ahead and apply; let them offer; you can always turn it down; it feels great to reject an offer”. I applied and I did not get the position. However, the following year, the head of the department at IIT Kanpur changed, and he inquired about my continued interest in the job. If my answer was yes, he wanted me to submit an updated CV. Brooklyn Polytechnic had advertised for a laser spectroscopist. Bob convinced me to apply. Sure enough, I received an invitation from Brooklyn Poly. After my visit and seminar and interaction with the faculty, I was offered the job. When I returned to Toronto with the offer, Suguna showed me a cable from IIT Kanpur offering me a Lecturer position (salary: Rs. 1150 per month = US$ 1725 per year). The chairman of the chemistry department at Brooklyn had told me about the department and its track record. Flory had done his path-breaking work on polymers while at Brooklyn and received the Nobel Prize years later. Marcus had done his pioneering work on electron transfer processes while at Brooklyn. The Chair also told me that they were offering me the maximum possible salary (US$ 15 000 per year) and would support my application for permanent residence. It was not easy for me to turn down the offer from Brooklyn Poly and choose IIT Kanpur. But that was what I did.

Building a career in India (1978 onwards)

My wife and I watched the Dominion Day celebrations in Toronto on July 1, 1978 and travelled to Kanpur via New York and New Delhi. We were received at the railway station in Kanpur by Professor S. Ranganathan, Head of the Department of Chemistry at IIT Kanpur. After traveling in a jeep for about 16 km and reaching the campus, on July 5, I fell in love with that campus. Professor Ranganathan and his wife Darshan were extremely kind to us. Professors M. V. George and P. T. Narasimhan mentored us in different ways. On the professional side, I was delighted to have the opportunity to teach CHM 101, a foundational course in the first semester at IIT Kanpur. At the same time, I was crestfallen because the institute, which had the first IBM computer in India, lacked any computing facility. I had brought an HP-21 calculator with me from Canada and that would be my workhorse for the next year or so. On the personal side, my wife and I were blessed with our first daughter Aruna in May 1979.

I wrote a paper on exponential gap laws for rotational energy transfer⁸ with my first MSc project student (C. Gayatri) and a paper on negative activation energy⁹ with A. K. Menon. In a year's time, the new computing facility, DEC-1090, arrived, making it the first interactive computing system in the country. It also meant that the IBM punch cards became a thing of the past. Mercifully, the institute had set up a facility to read the existing cards (I had brought several boxes of them from Canada). My work on chemical dynamics started in all earnest. Since I was aware of the difficulties involved in computing potential energy surfaces using the configuration interaction (CI) method, I wondered if it was possible to compute the PES at the Hartree–Fock level and scale it to make it comparable to the one at the CI level. My paper on the subject was summarily rejected by the Editor of Chemical Physics as he thought it was ill-conceived. When I explained my idea to him in a letter, he agreed to reconsider my revised manuscript and the revised version¹⁰ was accepted without any difficulty.

I received my first professional recognition in the form of the Young Scientist Medal from the Indian National Science Academy, New Delhi. It was presented by the Prime Minister of India, Indira Gandhi (Fig. 1).

Fig. 1 The author receiving the Young Scientist Medal from the Prime Minister of India (1981).

While I was at Toronto, John's lab had interesting experimental results on the effect of reagent rotation on the rate of alkali + hydrogen halide exchange reactions. Therefore, I suggested to my first PhD student NoorBatcha to fit the ab initio PES for the (Li, FH) system published by Gabriel Balint-Kurti and investigate the dynamics. He showed that the reaction cross section decreased initially with an increase in the initial rotational state (j) of FH and increased on further increase in j. The results were communicated to the Journal of American Chemical Society.¹¹

Noor initiated an investigation on the dynamics of six-centre exchange reactions by computing the potential energy values and the derivatives on the fly within the diatomics-in-molecules framework. It took some time for Sukarma Thareja to complete the work to make the results publishable.¹² By the time Tomi Joseph joined my research group, McLaughlin and Thompson had published the ab initio PES for HeH₂⁺ in three dimensions. After making sure that Don Thompson was not planning to pursue dynamical studies on the system, Tomi undertook the task of fitting the ab initio PES and investigating the dynamics of the system. The results were exciting and in agreement with the available experimental results on the system. We could publish a communication in J. Chem. Phys.¹³

I took a sabbatical for a semester with John at Toronto, where I taught a course on Chemical Dynamics and assisted him with the studies on the transition state spectroscopy. On my return, Mohan and I started working on a time-dependent quantum mechanical (TDQM) approach to reactive scattering and an interesting paper followed.¹⁴ In addition to computing classical trajectories, Tomi computed state-to-state reaction probabilities for the collinear (He, H₂⁺) system on the McLaughlin–Thompson–Joseph–Sathyamurthy (MTJS) PES and found several oscillations that required explanation.¹⁵ Raghavan worked on the information theoretic analysis and synthesis for rotational energy transfer in HF–Li collisions.¹⁶

I was keen on spreading the knowledge of molecular reaction dynamics in India and the Department of Science and Technology, New Delhi, had a program to support summer/winter schools for such purposes. We organized two winter schools, one in 1984 and another in 1988. With financial support from the government, we published an edited volume, “Reaction dynamics: recent advances”.¹⁷ In the meantime, I was made a Professor at IIT Kanpur in 1985 and our second daughter Anjana was born around the same time!

Sabbatical at the Max Planck Institute (1986–1987)

When I participated in the Gas Kinetics Conference at Göttingen in 1983, I visited Professor Peter Toennies at the Max-Planck-Institut für Strömungsforschung. A couple of years later, when I wanted to take a sabbatical from IIT Kanpur, Peter agreed to host me, and the Alexander von Humboldt (AvH) Foundation awarded me a Fellowship. By that time, Tomi had joined the research group of Jörn Manz at Würzburg and was doing well. I got an invitation to visit Würzburg. I discussed the problem of resonances in collinear (He, H₂⁺) collisions with Manz and he suggested that I work in hyperspherical coordinates to identify the Feshbach resonances. Upon arrival at Göttingen, I was shown a desk in the Gästezimmer and I was delighted to see Franco Gianturco and Michael Baer already sitting in that office. With Michael, I discussed the oscillations in the reaction probability curves for the collinear HeH₂⁺ system and the possibility of interpreting them in terms of Feshbach resonances that could be related to the quasi-bound states in hyperspherical coordinates. The results were published in Chem. Phys.¹⁸ Little did I realize at that time that this sharing of an office would lead to collaborations with Franco and Michael in the years to come.

Peter hosted several visitors at any time and each one was invariably associated with one of the ongoing projects in the lab. I was asked to interact with H.-G. Rubahn, who was investigating Li₂–Na inelastic collisions. Although we could not explain the experimentally observed results, we investigated the vibrational energy transfer in Li₂–He, Kr systems up to very high vibrational states of Li₂ using the quasi-classical trajectory method.¹⁹ Bratislav Friedrich was also a Humboldt Fellow in the lab. With travel support assured by Peter and the Humboldt Fellowship, I started spending subsequent summers in Göttingen. I remember arriving at the Max-Planck-Institute on a Friday afternoon and Friedrich and Rubahn confronting me with some exciting new results on the forward scattering of Ar with ICl in a pendular state. While both went away for the weekend, I worked on the problem and by Monday, I could explain the observed results in terms of rotational energy transfer in ICl–Ar collisions. The results were published in Phys. Rev. Lett.²⁰

Collaborative efforts at IIT Kanpur (1987–2007)

Before going on a sabbatical to Germany, I was initiated into an Indo-US collaborative effort in chemical dynamics, with Bill Gadzuk at the National Bureau of Standards (which got renamed to National Institute of Standards and Technology), in Gaithersburg, USA, as my partner. For the next several years, I was collaborating with Bill on gas–surface scattering. We published perhaps the first paper on chaos and fractals in gas-surface scattering²¹ and a paper on channel control involving TDQM wave packet dynamics.²²

Chaos and fractals were hot topics, and the (He, H₂⁺) dynamics were full of them.²³ With Sanjay Kumar as a PhD scholar, we extended our earlier studies on (He, H₂⁺) collisions to higher energies and investigated collision-induced dissociation for which Guyon in France had published new experimental results.²⁴ Balakrishnan started investigating quantum mechanical wave packet dynamics for the same system on the MTJS PES, initially in collinear geometries²⁵ and later in three dimensions.²⁶ While Susanta Mahapatra undertook a detailed three-dimensional wave packet dynamics study of the system,²⁷ Pankaj Bhatia and Biswajit Maiti investigated the (in)stability of quasiperiodic orbits and the bifurcation route to chaos.²⁸ With Ram Ramaswamy, we could establish the connection between classical chaos and quantum mechanical resonances.²⁹

In the meantime, Franco came up with the idea of submitting a proposal along with Lutz Zuelicke of the Univ. Potsdam on “Ion–molecule reactions” for funding from the European Union. I had met Lutz in Göttingen in 1983, well before the Berlin Wall came down.

With the introduction of the fast Fourier transform algorithm for obtaining the Laplacian of the wave function, and the split-operator method and Chebyshev polynomial route for its time evolution, the TDQM wave packet approach started yielding state-to-state reaction probabilities and reaction cross sections that were comparable in accuracy to the time-independent (close-coupling) quantum mechanical results.³⁰ In addition, we could compute bound states and quasibound states for triatomic systems³¹ and Raman excitation profiles for diatomic systems.³² The use of Jacobi coordinates and absorbing potentials introduced by Baer and his research group enabled us to study the dynamics in three dimensions. It also helped Sujitha Kolakkandy and Kousik Giri in investigating collision-induced dissociation using the TDQM wave packet approach,³³ which was (and is) not possible in the time-independent framework. Here, it is important to mention the work of Aditya Narayan Panda on (He, H₂⁺)³⁴ and (H⁻, H₂)³⁵ dynamics and the contribution of Ashwani Tiwari and Sujitha in investigating the role of Coriolis coupling in the three-dimensional dynamics of (He, HD⁺) collisions.³⁶

The Director, DMSRDE, Kanpur, wanted us to collaborate on a study of atoms and molecules under confinement, particularly inside fullerene (C₆₀) and was willing to provide the necessary financial support. Kalidas Sen at the University of Hyderabad had told me about the pioneering work of D. S. Kothari and others on the subject under astrophysical conditions in earlier years. Kankan Bhattacharyya at the Indian Association for the Cultivation of Science (IACS), Jadavpur, Kolkata, was experimentally investigating the behaviour of water molecules in the pockets of protein folds. Shameema and Ramachandran showed for the first time that confinement could lead to blue shifts in stretching frequencies of molecules like H₂O, NH₃ and CH₄.³⁷ Ramachandran also examined the possibility of packing more than one water molecule inside a fullerene cage and showed that confinement could result in breaking of hydrogen bonds.³⁸ Pradeep Kumar and others in the lab undertook detailed investigations of host–guest interactions.³⁹ Under an Indo-Italian collaboration with Enzo Aquilanti of the University of Perugia, Italy, we could pursue some studies on atoms and molecules in confined environments such as carbon nanotubes.

At the suggestion of Dr T. Ramasami, Director, Central Leather Research Institute, we got a collaborative project with Dr V. Subramanian of the same institute funded by the Council of Scientific Industrial Research, New Delhi.

What started off as a classroom project evolved into a research project in the hands of Shruti Maheshwary, who investigated the structure and stability of water clusters. Although J. Chem. Phys. rejected our manuscript, its publication⁴⁰ in J. Phys. Chem. became one of our most cited papers. With Subbu and his students, we undertook a detailed quantum chemical study of protonated water clusters⁴¹ and related topics. Particularly satisfying work was the formation of bowls, balls, and sheets of boric acid clusters.⁴² With Shridhar Gadre, we could extend our studies to nanotubes using his molecular tailoring approach.⁴³ With Subbu and his student Parthasarathi, we wrote a classic paper on “Hydrogen Bonding without Borders”, which related the strength of hydrogen bonds and van der Waals interactions to the electron density at the bond critical points.⁴⁴ It continues to be cited extensively. With Brijesh Mishra as a final year master's student, we started investigating the π–π interaction in pyridine.⁴⁵ After joining the PhD programme, Brijesh extended his studies to stacking and spreading interactions in a variety of N-heteroaromatic systems⁴⁶ and could provide an insight into the role of π–π stacking and hydrogen bonds in the double helical structure of DNA.⁴⁷ In an Indo-Portugal collaborative project with Antonio Varandas, Saurabh Srivastava and I discovered how challenging it was to investigate a simple diatomic system like H₂⁻.⁴⁸ In collaboration with Helene Lefebvre-Brion, Moumita Majumder and I started investigating the nuances of photoexcitaion in CO.⁴⁹

Institution building (2007–2017)

While the decade of 1996–2006 was perhaps my most active period of research, I participated in National Chemistry Olympiad activities culminating in India hosting the International Chemistry Olympiad in 2001. I became the Founder President of the Association of Chemistry Teachers. I also participated in designing the curriculum for the 5-year BS–MS dual degree programme of the to-be established Indian Institutes of Science Education and Research (IISERs). I was pleasantly surprised when I was invited to head the proposed IISER in Mohali in 2007. The secret to success in building an academic institute is in recruiting the best possible faculty members and providing them the necessary technical and financial support. I went about building IISER Mohali for the next 10 years. The details of the trajectory of IISER Mohali's growth and that of other IISERs are provided in a book edited by my colleague and me.⁵⁰

Working with undergraduates

While the students left behind at IIT Kanpur in 2007 continued their PhD programme with long-distance guidance from me, I started working with undergraduates at IISER Mohali. The advantage of working with undergraduates is that you can get them to explore new ideas, which a graduate student may be reluctant.

With the help of my colleague N. G. Prasad, I began to appreciate the symmetry of various flowers. I was struck by the beauty of a passionflower (Fig. 2) in our garden. Out of curiosity, I started counting the number of flowers on the plant every day. Soon, we discovered temporal oscillations in flowering in passionflowers. On the advice of my colleague Professor T. R. Rao, we continued counting the number of flowers the following year. Unfortunately, the plant died. Fortunately for me, my wife got four more plants planted in the garden. With the help of an undergraduate student, the counting continued even after my term as the Director ended and I left the campus. Finally, after a few years, we had enough data to analyse and publish the results. The critical reviewer helped us in discovering a rare phenomenon: synchronous pulsed flowering in passionflower (Passiflora incarnata).⁵¹ While we could explain the temporal oscillations in flowering using the prey-predator model, we needed to use a diffusion-based activator-inhibitor model to explain the concentric rings in the passionflower.⁵² My colleagues at IISER Mohali helped us identify the flavones and anthocyanins responsible for the violet colour of the flower using mass spectrometry and UV-vis absorption spectroscopy.⁵³

Fig. 2 The breathtakingly beautiful passionflower.

When I met Michael Baer after a gap of about two decades in Kolkata, he surprised me by expressing his willingness to come to IISER Mohali and teach a course on Beyond Born–Oppenheimer Approximation for a semester. The beauty of that course was that almost everyone who enrolled in it ended up publishing a research paper with Michael and me as coauthors.

Post-retirement from IIT Kanpur and IISER Mohali (2017–)

I retired as an Institute Chair Professor from IIT Kanpur in 2016 and as the Director from IISER Mohali in 2017. I agreed to become the President of the Chemical Research Society of India and that gave me an opportunity to interact with colleagues across the Nation and beyond. When Michael turned 80, there was a symposium in his honour at the Hebrew University, Jerusalem, in 2018, and I was invited. After my presentation, Michael expressed interest in continuing our collaboration. Satrajit Adhikari at IACS, Kolkata, joined hands and together with his graduate students and post-docs, we published a set of papers relating to HeH₂⁺ and non-adiabatic interactions in the system.^54–56 It is important to point out specifically that the most recent paper⁵⁶ relates to the TDQM wave packet dynamics on 2-state diabatic PESs that includes the nonadiabatic interactions and yields results that agree by far the most with the experimental results.

The following year (2019), Franco Gianturco turned 80 and there was a symposium in his honour at the University of Innsbruck, Austria, and I was invited. After that, Franco expressed interest in another round of collaboration on scattering dynamics of ions and molecules of interest in interstellar media. To start with, the inelastic scattering of HeH⁺ with He was investigated.⁵⁷ When we started discussing (HeH⁺, H₂) collisions, I was visiting my daughter in Kansas City, and we visited my former thesis supervisor Lionel Raff at Oklahoma State. We talked about his pioneering work on using artificial neural networks (ANNs) in fitting ab initio PESs. When I was the Editor of Resonance – Journal of Science Education published by the Indian Academy of Sciences, Bangalore, we published an issue highlighting Artificial Intelligence and Machine Learning.⁵⁸ I had invited U. Lourderaj, a former student of mine at IITK and presently a Professor at the National Institute of Science Education and Research (NISER) Bhubaneswar, to contribute an article. Thanks to my friend Sankar Bhattacharyya gifting me a copy of his book, “Soft-Computing in Physical and Chemical Sciences: A Shift in Computing Paradigm”, I learned how to use ANNs for fitting large data. With the possibility of using ANNs for fitting ab initio PESs, Raj and I started a collaboration that continues to date. Typically, a good quality multi-dimensional ab initio PES gets generated in Turkey or Poland and gets fitted in Bhubaneswar, and the scattering dynamics is investigated in the Central University of Punjab by Kousik Giri and/or by Lola González-Sánchez and her team in Spain. This collaboration has led to several publications in journals such as the Astrophysical Journal,⁵⁹ Monthly Notices of the Royal Astronomical Society,⁶⁰ etc., in which I had not published previously.

We realized recently that adding the (1/R) coulombic repulsion term to the electronic energy to compute the PES for a molecular system makes the subsequent fitting unnecessarily difficult. The exact (1/R) term can be added after fitting the electronic energy via the ANN route, for example. Such a route has been shown to yield accurate fits of the ab initio PES.⁶¹

During the COVID-19 pandemic, when personal interaction was difficult, V. Ramamurthy of the University of Miami initiated a Saturday Seminar Series on photochemistry. Researchers from different parts of the world started participating. I also gave some talks and started attending the lectures given by others. In the process, Brijesh and I joined Murthy and his collaborators in examining the possibility of non-covalent dimers facilitating photodimerization in aqueous media.⁶²

Concluding remarks

It has been an enjoyable academic journey for me for the last 50+ years. Thanks to the undergraduate and graduate students who have worked with me, I have gained a deep understanding of potential energy curves and surfaces, as well as chemical dynamics. This has been facilitated by the wonderful collaboration we have had with several researchers across the globe.

Computational chemistry has grown along with advances in computer hardware in speed and memory size: from ab initio calculations at the Hartree–Fock/STO-3G/4-31G level for small molecules in the 1970's, to computing at the coupled cluster singles, doubles and perturbative triples level of theory for large molecules and for many geometries for tri-/tetra-/penta-atomic systems in the complete basis set limit; from fitting Morse or Buckingham-exp-6 type functions to diatomic potentials, to ANN fitting of ab initio PESs for several thousand geometries in several dimensions; from quasi-classical trajectory calculations, to converged close-coupling or TDQM scattering calculations to compute state-to-state differential and integral reaction cross sections and rate coefficients and investigating photochemical processes and gas-surface dynamics. Yet, dealing with more than one potential energy surface and conical intersections for more than three atoms remains a challenge. Computing scattering data at ultracold temperatures of astrophysical interest is still not a matter of routine!

Acknowledgements

I am grateful to PCCP and the guest editors Ashwani, Bala, Swathi, and Neelanjana for putting together this Festschrift and giving me an opportunity to look back at my own life, from an academic point of view. I am grateful to all the contributors to this collection. I take this opportunity to express my gratitude to my parents, Dr TR, Lionel Raff, John Polanyi, Jerry Schreiber, Bob Davidson, S. Ranganathan, P. T. Narasimhan, M. V. George, P. K. Ghosh, K. Swami, and many others for their guidance and support at various stages of my life. I would like to place on record my appreciation of my wife Suguna for her unstinted support since 1977. I was fortunate to have received adequate funding from the Department of Science and Technology, New Delhi, the Council of Scientific and Industrial Research, New Delhi, USAID, Indo-CEC and DMSRDE, Kanpur, over the years. I am grateful to the Indian National Science Academy (INSA) for its support as an INSA Distinguished Professor.

References

1. N. Sathyamurthy and L. M. Raff, Quasiclassical trajectory studies using 3D spline interpolation of ab initio surfaces, J. Chem. Phys., 1975, 63, 464–473.
2. N. Sathyamurthy and L. M. Raff, Inelastic scattering calculations in polyatomic systems using an ab initio intermolecular potential-energy surface: The CO₂(0,0,1,0) + H₂(D₂) → CO₂(0,0,0,0) + H₂(D₂) system, J. Chem. Phys., 1977, 66, 2191–2211.
3. D. J. Kouri and M. Baer, Collinear quantum mechanical calculations of the He + H₂⁺ proton transfer reactions, Chem. Phys. Lett., 1974, 24, 37.
4. N. Sathyamurthy, R. Rangarajan and L. M. Raff, Reactive scattering calculations on a spline-fitted ab initio surface: He + H₂⁺(v = 0, 1, 2) → HeH⁺ + H reaction, J. Chem. Phys., 1976, 64, 4606–4611.
5. J. C. Polanyi, N. Sathyamurthy and J. L. Schreiber, Rotational energy transfer (theory) I. Comparison of quasiclassical and quantum mechanical results for elastic and rotationally inelastic HCl-Ar collisions, Chem. Phys., 1977, 24, 105–110.
6. N. Sathyamurthy, J. W. Duff, C. Stroud and L. M. Raff, On the origin of the dynamical differences on the diatomics-in-molecules and spline-fitted ab initio surfaces for the He + H₂⁺ reaction, J. Chem. Phys., 1977, 67, 3563–3569.
7. J. C. Polanyi and N. Sathyamurthy, Location of energy barriers. VII. Sudden and gradual late-energy-barriers, Chem. Phys., 1978, 33, 287–303.
8. C. Gayatri and N. Sathyamurthy, Exponential gap relation and the rotational inelasticity of H₂-M systems, Chem. Phys., 1980, 48, 227–235.
9. A. Menon and N. Sathyamurthy, Negative activation energy for the Cl(Br)O + NO → Cl(Br) + NO₂ reactions, J. Phys. Chem., 1981, 85, 1021–1023.
10. N. Sathyamurthy, Importance of correlation energy in collision dynamics: Quasiclassical trajectory study of collinear He + H₂⁺(v′) → HeH⁺ + H using HF and CI potential-energy surfaces, Chem. Phys., 1981, 62, 1–19.
11. I. NoorBatcha and N. Sathyamurthy, Effect of reagent rotation on cross section for the reaction Li + FH → LiF + H, J. Am. Chem. Soc., 1982, 104, 1766–1767.
12. I. NoorBatcha, S. Thareja and N. Sathyamurthy, Dynamics of a model six-center exchange reaction, J. Phys. Chem., 1987, 91, 2171–2173.
13. T. Joseph and N. Sathyamurthy, Three dimensional quasiclassical trajectory study of the reaction He + H₂⁺ → HeH⁺ + H on an accurate ab initio potential-energy surface, J. Chem. Phys., 1984, 80, 5332–5333.
14. P. M. Agrawal, V. Mohan and N. Sathyamurthy, Time-dependent wave mechanical study of the wings to the Lyman-α line in H + H₂ reactive collisions, Chem. Phys. Lett., 1985, 114, 343–347.
15. T. Joseph and N. Sathyamurthy, Quantum mechanical study of the collinear reaction He + H₂⁺ → HeH⁺ + H, J. Indian Chem. Soc., 1985, 62, 874–877.
16. K. Raghavan, S. K. Upadhyay, N. Sathyamurthy and R. Ramaswamy, Rotational energy transfer in HF–Li collisions, J. Chem. Phys., 1985, 83, 1573–1577.
17. Reaction Dynamics: Recent Advances, ed. N. Sathyamurthy, Narosa (New Delhi) and Springer-Verlag (Berlin), 1991.
18. N. Sathyamurthy, M. Baer and T. Joseph, Resonances in collinear He + H₂⁺ collisions, Chem. Phys., 1987, 114, 73–83.
19. H.-G. Rubahn and N. Sathyamurthy, Quasiclassical trajectory calculations of integral cross sections for highly vibrationally excited Li₂-He, Kr systems, Chem. Phys. Lett., 1990, 171, 506–512.
20. B. Friedrich, H.-G. Rubahn and N. Sathyamurthy, State-resolved scattering of molecules in pendular states: ICl + Ar, Phys. Rev. Lett., 1992, 69, 2487–2490.
21. V. Balasubramanian, N. Sathyamurthy and J. W. Gadzuk, Fractals in molecule-surface collisions, Surf. Sci. Lett., 1989, 221, L741–L749.
22. N. Chakrabarti, N. Sathyamurthy and J. W. Gadzuk, Photoinduced desorption of molecules from metal surfaces using femtosecond pulses: A model dynamical study, J. Phys. Chem. A, 1998, 102, 4154.
23. V. Balasubramanian, B. K. Mishra, A. Bahel, S. Kumar and N. Sathyamurthy, Fractals and resonances in collinear (He + H₂⁺) collisions, J. Chem. Phys., 1991, 95, 4160–4167.
24. S. Kumar and N. Sathyamurthy, Competition between exchange and dissociation processes in He + H₂⁺ collisions, Chem. Phys., 1989, 137, 25–32.
25. N. Balakrishnan and N. Sathyamurthy, Resonances in collinear (He, H₂⁺) collisions: A time-dependent quantum mechanical study, Chem. Phys. Lett., 1993, 201, 294–300.
26. N. Balakrishnan and N. Sathyamurthy, Three-dimensional time-dependent quantum mechanical study of the reaction He + H₂⁺ → HeH⁺ + H, Proc. – Indian Acad. Sci., Chem. Sci., 1994, 106, 531–538.
27. S. Mahapatra and N. Sathyamurthy, Resonances in He + H₂⁺ → HeH⁺ + H reaction in three dimensions: Energy resolved reaction probabilities by the time-dependent wave packet method, J. Chem. Phys., 1997, 107, 6621.
28. P. Bhatia, B. Maiti, N. Sathyamurthy, S. Stamatiadis and S. C. Farantos, Exploring molecular motions in collinear HeH₂⁺ and its isotopic variants using periodic orbits, Phys. Chem. Chem. Phys., 1999, 1, 1105–1113.
29. S. Mahapatra, R. Ramaswamy and N. Sathyamurthy, Quantum chaos in collinear (He, H₂⁺) collisions, J. Chem. Phys., 1996, 104, 3989.
30. B. Maiti, S. Mahapatra and N. Sathyamurthy, A time-dependent quantum mechanical investigation of dynamical resonances in three dimensional HeH₂⁺ and HeHD⁺ systems, J. Chem. Phys., 2000, 113, 59–66.
31. B. Maiti and N. Sathyamurthy, Bound and quasibound states of HeH₂⁺ and its isotopomers, Chem. Phys. Lett., 2001, 345, 461–470.
32. N. Chakrabarti and N. Sathyamurthy, An interesting isotope effect in the Raman excitation profile for HI, J. Phys. Chem. A, 1998, 102, 7089–7092.
33. S. Kolakkandy, K. Giri and N. Sathyamurthy, Collision-Induced Dissociation in (He, H₂⁺ (v = 0–2; j = 0–3)) System: A Time-Dependent Quantum Mechanical Investigation, J. Chem. Phys., 2012, 136, 244312.
34. B. Maiti, C. Kalyanaraman, A. N. Panda and N. Sathyamurthy, Reaction probabilities and reaction cross sections for three dimensional He + H₂⁺(v) collisions: A time-dependent quantum mechanical study, J. Chem. Phys., 2002, 117, 9719–9726.
35. A. N. Panda and N. Sathyamurthy, Dynamics of (H⁻, H₂) collisions: A Time-dependent quantum mechanical investigation on a new ab initio potential-energy surface, J. Chem. Phys., 2004, 121, 9343–9351.
36. A. K. Tiwari, S. Kolakkandy and N. Sathyamurthy, Importance of Coriolis coupling in isotopic branching in (He, HD⁺) collisions, J. Phys. Chem. A, 2009, 113, 9568–9574.
37. O. Shameema, C. N. Ramachandran and N. Sathyamurthy, Blue shift in X-H stretching frequency of molecules due to confinement, J. Phys. Chem. A, 2006, 110, 2–4.
38. C. N. Ramachandran and N. Sathyamurthy, Water clusters in a confined nonpolar environment, Chem. Phys. Lett., 2005, 410, 348–351.
39. P. Kumar and N. Sathyamurthy, Theoretical studies of host-guest interaction in gas hydrates, J. Phys. Chem. A, 2011, 115, 14276–14281.
40. S. Maheshwary, N. Patel, N. Sathyamurthy, A. D. Kulkarni and S. R. Gadre, Structure and stability of water clusters (H₂O)_n, n = 8–20: An ab initio investigation, J. Phys. Chem. A, 2001, 105, 10525–10537.
41. R. Parthasarathi, V. Subramanian and N. Sathyamurthy, Hydrogen bonding in protonated water clusters: An atoms-in-molecules perspective, J. Phys. Chem. A, 2007, 111, 13287–13290.
42. M. Elango, R. Parthasarathi, V. Subramanian and N. Sathyamurthy, Bowls, balls and sheets of boric acid clusters: The role of pentagon and hexagon motifs, J. Phys. Chem. A, 2005, 109, 8587–8593.
43. M. Elango, V. Subramanian, A. P. Rahalkar, S. R. Gadre and N. Sathyamurthy, Structure, Energetics, and Reactivity of Boric Acid Nanotubes: A Molecular Tailoring Approach, J. Phys. Chem. A, 2008, 112, 7699–7704.
44. R. Parthasarathi, V. Subramanian and N. Sathyamurthy, Hydrogen Bonding without Borders:  An Atoms-in-Molecules Perspective, J. Phys. Chem. A, 2006, 110, 3349–3351.
45. B. K. Mishra and N. Sathyamurthy, π–π interaction in pyridine, J. Phys. Chem. A, 2005, 109, 6–8.
46. B. K. Mishra, J. S. Arey and N. Sathyamurthy, Stacking and spreading interaction in N-heteroaromatic systems, J. Phys. Chem. A, 2010, 114, 9606–9616.
47. S. Mittal, B. K. Mishra and N. Sathyamurthy, The influence of sugar-phosphate backbone on the stacking interaction in B-DNA helix formation, Curr. Sci., 2015, 108, 1126–1131.
48. S. Srivastava, N. Sathyamurthy and A. J. C. Varandas, An accurate ab initio potential energy curve and vibrational bound states for the X²Σ_u⁺ state of H₂⁻, Chem. Phys., 2012, 398, 160–167.
49. M. Majumder, N. Sathyamurthy, G. J. Vazquez and H. Lefebvre-Brion, Interpretation of the accidental predissociation of the E¹Π state of CO, J. Chem. Phys., 2014, 140, 164303.
50. R. Bandyopadhyay and N. Sathyamurthy, Institution Building: The Story of IISERs, Indian Academy of Sciences, Bengaluru, 2018.
51. S. Goyal, R. Reji, S. S. Tripathi and N. Sathyamurthy, Synchronous pulsed flowering in passionflower (Passiflora incarnata), Curr. Sci., 2019, 117, 1211–1216.
52. A. P. Bhati, S. Goyal, R. Yadav and N. Sathyamurthy, Pattern formation in Passiflora incarnata: An activator-inhibitor model, J. Biosci., 2021, 46, 84.
53. Y. Silori, S. Chawla, A. K. De, R. P. Shirke, J. Grover, S. S. V. Ramasastry and N. Sathyamurthy, Spectral characteristics of the flavones and anthocyanins present in passionflower (Passiflora incarnata), Photochem. Photobiol., 2024, 100, 923–935.
54. A. K. Gupta, V. Dhindhwal, M. Baer, N. Sathyamurthy, S. Ravi, S. Mukherjee, B. Mukherjee and S. Adhikari, Non-adiabatic coupling and conical intersection(s) between potential energy surfaces for HeH₂⁺, Mol. Phys., 2020, 118, e1683243.
55. S. Ravi, S. Mukherjee, B. Mukherjee, S. Adhikari, N. Sathyamurthy and M. Baer, Non-adiabatic coupling as a frictional force in (He, H, H)⁺ dynamics and the formation of HeH₂⁺, Mol. Phys., 2021, 119, e1811907.
56. K. Naskar, S. Ghosh, S. Adhikari, M. Baer and N. Sathyamurthy, Coupled three-dimensional quantum mechanical wave packet study of proton transfer in H₂⁺ + He collisions on accurate ab initio two-state diabatic potential energy surfaces, J. Chem. Phys., 2023, 159, 034302.
57. F. A. Gianturco, K. Giri, L. González-Sánchez, E. Yurtsever, N. Sathyamurthy and R. Wester, Energy-transfer quantum dynamics of HeH⁺ with He atoms: rotationally inelastic cross sections and rate coefficients, J. Chem. Phys., 2021, 154, 054311.
58. Reson. J. Sci. Educ., 2020, 25, 1–155.
59. L. González-Sánchez, A. Veselinova, A. Martin Santa Daria, E. Yurtsever, R. Biswas, K. Giri, N. Sathyamurthy, U. Lourderaj, R. Wester and F. A. Gianturco, Computed Rotational collision rate coefficients for recently detected anionic cyanopolyynes, Astrophys. J., 2024, 960, 40.
60. K. Giri, L. Gonzàlez-Sànchez, F. A. Gianturco, U. Lourderaj, A. Martín Santa María, S. Rana, N. Sathyamurthy, E. Yurtsever and R. Wester, Collision rate coefficients for C₇N⁻ and C₁₀H⁻ with H₂, Mon. Not. R. Astron. Soc., 2024, 534, 1950–1962.
61. S. Rana, U. S. Manoj, U. Lourderaj and N. Sathyamurthy, Artificial neural networks fitting of potential energy curves and surfaces: the 1/R conundrum, J. Comput. Chem., 2025, 46, e70220.
62. V. Jeyapalan, B. K. Mishra, S. Moorkkannur, R. Prabhakar, N. Sathyamurthy and V. Ramamurthy, Consequences of heterogeneity of organic molecules in water: Enhanced photodimerization of olefins, Langmuir, 2025, 41, 27781–27793.

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