Bonding, Reactivity, and Dynamics in Confined Systems - The Journal

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Bonding, Reactivity and Dynamics in Confined Systems Debdutta Chakraborty, and Pratim Kumar Chattaraj J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b00830 • Publication Date (Web): 22 Mar 2019 Downloaded from http://pubs.acs.org on March 22, 2019

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The Journal of Physical Chemistry

Manuscript id.: jp-2019-00830k

Bonding, Reactivity and Dynamics in Confined Systems Debdutta Chakraborty 1 and Pratim Kumar Chattaraj* 1, 2 Department of Chemistry and Centre for Theoretical Studies Indian Institute of Technology, Kharagpur 721302, West Bengal, India 1 Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India 2 *To

whom correspondence should be addressed. E-mail: [email protected], Telephone: +91 3222 283304, Fax: 91-3222-255303.

Abstract Confined systems often exhibit unusual behavior regarding their structure, stability, reactivity, bonding, interactions and dynamics. Quantization is a direct consequence of confinement. Confinement modifies the electronic energy levels, orbitals, electronic shell filling, etc. of a system thereby affecting its reactivity as well as various response properties as compared to the corresponding unconfined systems. Confinement may enforce two rare gas atoms to form a partly covalent bond. Gas storage is facilitated through confinement and unprecedented optoelectronic properties are observed in certain cases. Some slow reactions get highly accelerated in an appropriate confined environment. In the current feature article we analyze these aspects with a special emphasis on the work done by our research group.

1 ACS Paragon Plus Environment

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Introduction It is a well known fact that due to the effect of geometrical confinement, atoms and molecules exhibit fascinating changes in chemical reactivity vis-à-vis their corresponding free state counterparts. Confinement alters the electronic energy levels, electronic shell filling, orbitals, etc. of a system thereby affecting its reactivity as well as various response properties as compared to the corresponding unconfined systems consider the pedagogical model of a particle-in a-box problem

5

1-4.

One may

in order to understand

the salient features of the effect of confinement on the changes in electronic energy levels. The energy levels of a free particle appear in the continuum whereas upon introducing the ‘confining’ effects of the box, the energy levels become discrete. Therefore, confinement lies at the heart of quantization. It could also be noted that by varying the length of the box, the energy levels of the particle could be altered. It has been amply demonstrated by several research groups that confinement can have profound impact on physical as well as chemical properties of atoms and molecules 6-17. It is to be noted that atoms/molecules present within cavities, organic/inorganic host-guest complexes, etc. constitute ‘real life’ examples of confined systems. An analysis of the reactivity of atoms and molecules by utilizing various theoretical and computational methods can unravel numerous new paradigms vis-à-vis physicochemical properties of the systems under consideration. Therefore, confined quantum systems have been extensively analyzed from both epistemological as well as applied points of view

18-24.

The crucial point while analyzing quantum confined systems is to be able to construct an accurate theoretical model that takes into account the changes in the electronic wave function due to the effect of confinement. To this end, model theoretical calculations could be conceived by suitable choice of the boundary condition. On the other hand, while analyzing the various host-guest complexes, dispersion corrected density functional theory (DFT)

25-26

based calculations provide a cost effective and reasonably accurate

method. In this feature article, we would like to describe the research being carried out in our group concerning confined quantum systems vis-à-vis the corresponding results obtained by other research groups. The principal theoretical approach adopted by our research group while studying the effects of confinement on the reactivity of atoms and molecules in a dynamical context is 2 ACS Paragon Plus Environment

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the formulation and application of the quantum fluid density functional theory (QFDFT) 27-31.

The conceptual genesis of QFDFT lies at the hydrodynamic interpretation of

quantum mechanics pioneered by Madelung

32.

Later on, Bohm

33-34

postulated and

extended the hydrodynamic approach of quantum mechanics by demonstrating causal effects of various time-dependent phenomena. The crucial factor that emerged from these theories is the role played by the quantum potential 35 in dictating the dynamical outcome of a given quantum process. The hydrodynamic approach

36-40

to quantum mechanics

allows a simultaneous treatment of the wave and particle characters of the given physical system under consideration. Therefore, the time evolution of a system at the corresponding phase-space could be analyzed in an elegant manner thereby providing numerous physically relevant information. The usefulness of the Bohm-inspired quantum theory of motion (QTM)

35

has been amply demonstrated while analyzing several

dynamical phenomena like quantum equivalence of classical chaos, barrier scattering of a wave packet, etc

41-55.

Following these theoretical approaches, QFDFT was conceived as

an combination of quantum fluid dynamics (QFD) functional theory (TDDFT)

59-61.

56-58

and time dependent density

Within this approach, the time evolution of electron

density and current density are evaluated which provides a unique pathway to determine all the properties of the system. A critical reader might ask: why should one use the QFDFT or similar hydrodynamic formulations of quantum mechanics as opposed to the traditional routes? Apart from providing a ‘classical’ interpretation of the processes under consideration, QFDFT also intends to address a crucial computational bottleneck of the standard DFT

62-66.

Within the formalism of QFDFT, a single orbital is obtained as a

solution to a generalized nonlinear Schrödinger equation which in turn provides the time dependent density and current density. Therefore, the contribution arising from the kinetic energy part could be evaluated by taking a functional derivative. This approach substantially reduces the computational cost associated with the numerical solution of the pertinent integro-differential equations as compared to the traditional time dependent Kohn-Sham approach to DFT. Therefore, in principle, QFDFT and related ‘orbital free’ approaches

67-71

could be employed to study larger systems which are not amenable to

traditional DFT. The crucial point, however, is the accurate construction of a suitable kinetic energy functional

72

exhibiting the correct local and global behavior. Kinetic



energy functionals suitable

30, 73

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for analyzing reactivity and dynamics of atoms and

molecules have been developed and applied to study various dynamical processes such as interaction of an external electric or magnetic field with atoms/molecules, collision processes between various atoms and molecules, etc. To this end, the impact of confinement on the reactivity of the concerned systems has also been analyzed by employing conceptual DFT (CDFT)

74-92

based reactivity descriptors such as hardness,

polarizability, electrophilicity, etc. Detailed results will be presented in the subsequent sections of this article. It is to be noted that ‘click chemistry’ 93 pioneered by Sharpless constitutes a very useful synthetic methodology as far as organic chemistry is concerned. It has been demonstrated that by introducing copper in the reaction medium, cycloaddition reaction such as Huisgen 1, 3 dipolar reaction between alkyne and azide could be catalyzed

94, 95.

Apart

from catalyzing a given cycloaddition reaction, Click chemistry can enhance the product conversion as well as the regioselectivity. Despite its usefulness, presence of copper in the reaction medium limits the applicability of Click chemistry in biological medium 96. Therefore, the quest for finding a copper-free route towards catalyzing cycloaddition reactions constitutes a well-studied research topic

97.

In this context, the effect of

geometrical confinement can have profound impact on the kinetic outcome of a given chemical reaction. Mock and co-workers

98, 99

were able to demonstrate (experimentally)

that a 1, 3 dipolar cycloaddition reaction between 2-azidoethylamine and propargylamine yielding

1-(2-aminoethyl)-4-aminomethyl-1,2,3-triazole,

could

be

accelerated

substantially in the presence of an organic host, cucurbit[6]uril (CB[6]). Later on, several experimental studies reported similar findings in the cases of several organic supramolecular hosts

100-105.

Despite these interesting developments, there seems to be

only a few computational studies which have been executed pertaining to detailed mechanistic insights until very recently

106-114.

Crucial question that emerges from these

recent developments is whether the presence of any organic or inorganic supramolecular host can promote any given reaction from a thermodynamic as well as kinetic points of view

109.

Given the fact that catalyzing a chemical reaction has immense importance as

far as various applications are concerned, obtaining an a priori guess about the plausible hosts that might facilitate a chemical reaction can be very useful. Therefore, detailed 4 ACS Paragon Plus Environment

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computational investigations using state-of the-art dispersion corrected DFT can unravel numerous insights as far as the underlying reaction mechanism is concerned. Our research group has utilized organic macrocyclic moieties (such as cucurbit[6,7,8]uril, ExBox+4) as ‘confining’ hosts and we have tried to understand whether due to the effect of confinement imposed by these hosts, one can promote model Diels-Alder reactions. Impact of confinement can bring about interesting changes in the nature of chemical bonding 4. Our group has particularly focused on analyzing the change in the nature of bonding in between rare gas atoms, due to the effect of confinement. It is a well known fact that rare gas atoms are less reactive as compared to other elements in the periodic table owing to their completely filled valence orbitals 115-116. Therefore, it is expected that two rare gas atoms would interact with each other in a weak manner (non-covalent interaction). Successful experimental characterization of species such as He@C60 has proven the fact that it might be possible to encapsulate rare gas atoms inside various cavities 117-124. Therefore, we have tried to understand whether the strength of interaction between two rare gas atoms could be enhanced due to encapsulation inside various cavitands. To this end, moieties such as carbon nanotube, B12N12, B16N16, B40 , etc. 125-127 have been utilized as hosts for encapsulating rare gas atoms. We note that encapsulation processes involving organic hosts are significant for various applications as they provide a suitable pathway for sequestering gas molecules. In these host-guest complexes, quantum confinement effects play a crucial role thereby affecting the interaction between the host and the guest. The electron density distribution of the guest gets substantially altered as a result of the geometrical constraint imposed by the host. As a result of this, various response properties

128-135

gets tuned. For example, the polarizability and

hyperpolarizability of the guest can be significantly tuned as a result of encapsulation 128. Therefore, it might be possible to obtain suitable non-linear optical properties (NLO) from host-guest complexes, ramifications of which could be gauged in various applications such as design of appropriate media in communication technology, data storage devices, advanced laser technology, etc. On the other hand, given the growing need for finding alternative energy materials, hydrogen has emerged as an environment friendly fuel resource 136-140. Nonetheless, finding a suitable hydrogen storage medium at 5 ACS Paragon Plus Environment


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ambient conditions remains a challenge to a large extent. The crucial point herein is whether a potential host can store hydrogen in a reversible manner or not so that adsorption and desorption can take place in a facile manner

140.

Organic host molecules

constitute a suitable candidate for adsorbing hydrogen to this end. Similarly, sequestration of pollutants is crucial for the preservation of our environment. Our group has utilized various organic cavitands such as ExBox+4, CB[6-7], octa acid cavitand as well as clathrate hydrates in order to assess their gas storage potential. Detailed results and discussion will be presented in the following sections. Methods Understanding the reactivity of confined atoms and molecules by employing Hartree-Fock-Slater and QFDFT formalisms Hartree-Fock as well as Kohn-Sham DFT approaches were adopted by various research groups

11-17, 141-143

in order to understand the impact of confinement on the physical

properties of atoms. To this end, Dirichlet type of boundary condition was imposed on the wave function of the system under consideration. Chattaraj and co-workers

11-13

studied the variation of chemical reactivity for several atoms with confinement within a spherical box. Effect of ionization therein was also considered. It is worthwhile to outline the CDFT based reactivity descriptors which have been utilized in order to understand the change in reactivity. For an N-electron system with energy E, electronegativity (χ) and hardness (η) could be expressed as follows 63: ∂𝐸

(1)

𝜒 = ―𝜇 = ― (∂𝑁)𝑣(𝑟) 1

∂2𝐸

𝜂 = 𝑆 = (∂𝑁2)

𝑣(𝑟)

∂𝜇

(2)

= (∂𝑁)𝑣(𝑟)

Herein, v(r) and µ are external and chemical potentials respectively. Electronegativity was introduced by Pauling as the ‘power of an atom in a molecule to attract electrons to itself’ 144. On the other hand, hardness was defined by Pearson 74, 75 through his hard–soft acid–base and maximum hardness (MHP) principles. Within the premise of DFT, hardness can also be expressed as follows 80: 1

(3)

𝜂 = 𝑁∬𝜂(𝑟,𝑟′)𝑓(𝑟′)𝜌(𝑟)𝑑𝑟𝑑𝑟′


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Here, 𝜂(𝑟,𝑟′)is the hardness kernel and 𝑓(𝑟)is the Fukui function

83.

One can utilize the

following expressions in order to represent the hardness kernel and the Fukui function: 𝛿2𝐹[𝜌]

(4)

𝜂(𝑟,𝑟′) = 𝛿𝜌(𝑟)𝛿𝜌(𝑟′) and 𝑓(𝑟) = (

∂𝜌(𝑟) ∂𝑁 )𝑣(𝑟)

∂𝜇

(5)

= (∂𝑣(𝑟))𝑁

The Hohenberg-Kohn universal functional 63 is being represented by𝐹[𝜌(𝑟)] as: 𝐹[𝜌] = 𝐶𝐾∫𝜌

1

53

23

3

where 𝐶𝐾 = 10(3𝜋2)

𝑟.∇𝜌

4 𝑑𝑟 ― 𝐶𝑋∫𝜌 3𝑑𝑟 𝑟2 1 𝜌(𝑟)𝜌(𝑟′) + 2∬ |𝑟 ― 𝑟′| 𝑑𝑟𝑑𝑟′

𝑑𝑟 ― 40∫

―∫

𝜌 9.81 + 21.437𝜌

𝑑𝑟

―1 3

(6)

3 3 13

and 𝐶𝑋 = 4(𝜋)

We can define the energy functional in the following manner: (7)

𝐸[𝜌(𝑟)] = 𝐹[𝜌(𝑟)] + ∫𝜌(𝑟)𝑣(𝑟)𝑑𝑟

It is to be noted that one may completely characterize a many-electron system by fixing the N and v(r). Therefore, electronegativity (χ) and hardness (η) provide a measure of the response of the system when N changes at fixed v(r). The static electric dipole polarizability (α) represents the linear response of the electron cloud of a system when a weak external electric field is applied. Hardness and polarizability are inversely related and therefore a minimum polarizability principle (MPP) has also been postulated

30, 90.

The electrophilicity index (𝜔) measures the propensity to receive electrons and it can be defined as below 78: 𝜇2

𝜒2

(8)

𝜔 = 2𝜂 = 2𝜂 Electronegativity (𝜒) may be expressed as 84 𝑍

𝜌(𝑟)

(9)

𝜒 = ―𝜇 = 𝑟𝐶 ―∫|𝑟 ― 𝑟𝐶|𝑑𝑟 where 𝑟𝐶defines a point (a measure 84 of the covalent radius of an atom). A finite difference approximation

63

to eqs (1) and (2) provides the following

expressions: 𝜒 = ―𝜇 =

𝐼+𝐴 2

(10)

and (11)

𝜂=𝐼―𝐴

where I and A are the ionization potential and the electron affinity respectively. 7 ACS Paragon Plus Environment


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Hartree-Fock-Slater equation for atoms and ions was solved in order to obtain selfconsistent field (SCF) electronic wave function. Dirichlet boundary conditions were imposed on the wave function in order to impose the effect of confinement. The reactivity parameters were calculated from this SCF wave function. The reactivity descriptors for different confined atoms and ions (He, Li, Be, B, C, N, O, F, Ne, C+, C+2, C+3, C+4) were computed at some selected values of the cut-off radii (𝑟𝐶) and we have presented the variation of global softness

11

for a representative case in Figure 1. It

becomes clear that the systems become harder as we impose the effect of confinement through variation of the 𝑟𝐶. The systems also become harder with the degree of ionization. The variation in polarizability as a function of the cut-off radii was also analyzed. As the confinement radius is reduced, the polarizability decreases monotonically. We can also observe that for very small values of the cut-off radii, polarizability values approach almost zero. Upon ionization, a system becomes more difficult to polarize. The variation of electronegativity

11

as a function of confinement

radii has been presented in figure 2. Electronegativity is not very sensitive to the effect of confinement except for a very small value of the cut-off radius where the value of electronegativity increases quite sharply. Similar behavior is noted in the case of variation of 𝜔. So, it becomes clear that as we keep increasing the effect of confinement by decreasing the size of the spherical box, systems become harder and less polarizable as well as more difficult to excite. The analysis of the dynamic evolution of various reactivity parameters during time dependent processes such as atom-field interactions and ion-atom collisions within a cylindrical box, was carried out within the premise of QFDFT by Sarkar et al

14.

As

before, the impact of confinement was incorporated through the imposition of a Dirichlet type of boundary condition on the systems confined in a cylindrical box. The solution of the generalized non-linear Schrödinger equation (GNLSE) 27 provides the time dependent r r  ( r , t) j ( r , t) from which various reactivity descriptors are density and current density calculated. The GNLSE has the following form: r  r ,t r r  1 2     v r , t  r , t  i ; i  1 eff  2  t

   

 


(12)

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r 1 2 ( r , t ) exp(i ) and    where, r j r , t   reim  im re   

 

(13) The effective potential is given by the following expression: r r r  TNW  Exc  (r , t ) r veff r , t     r r d r   vext (r , t )   r  r

 

(14) Here TNW and EXC are the non-Weizsäcker part of the kinetic energy functional and exchange-correlation functional respectively. TNW could be expressed in the following manner: 5 r TNW  Ck  3 dr  a  N   



4

3

r r dr 1 r 3 1 0.043

(15)

3   30    

1

3

a  N   a0  a1 N

1

,

3

 a2 N

2

3

a0  0.1279 a1  0.1811 a2  0.0819 , , ,

Herein, N is the total number of electrons. The EXC could be expressed as a combination of a modified Dirac exchange functional (EX) 73 and a Wigner type correlation functional (EC) 63 in the following fashion:

  4  3  43 r r Ex     C x   dr   dr  2 2 3 1  r / 0.0244     





(16) Ec      

 9.81  21.437 

1

r dr 3

(17) Dynamic polarizability is evaluated as follows:

 t  

z Dind t 

Fz  t 

(18) 9 ACS Paragon Plus Environment


where

z Dind t 

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is the electronic part of the induced dipole moment which can be expressed

as: r r z Dind  t   z   r , t  dr

and

Fz  t 

(19)

is the z-component of the external field.

Effect of confinement and excitation was imposed simultaneously on the system under consideration by Sarkar et al while solving the GNLSE 14. If the degree of confinement is increased, then hardness increases both in the ground and the excited states. Upon the simultaneous effect of excitation and increase in the degree of confinement, the ground state hardness trend could be retrieved. The time evolution of chemical potential is presented in Figure 3. An in-phase oscillation with the applied perturbation is observed in the time evolution of chemical potential for the case of He atom ground state. Upon increasing the frequency of the external field, an increase in oscillation of chemical potential is observed. It is quite apparent that the chemical potential (which is negative of electronegativity) decreases upon increasing the degree of confinement. This implies that the system gets more stabilized upon increasing the degree of confinement. Upon introducing the confinement, polarizability decreases as compared to the free atom. The excited state polarizability is higher as compared to that in the ground state in both confined as well as unconfined states, as expected from minimum polarizability principle (MPP). The collision process between a proton and a helium atom in its ground state (1S) and excited state (1P) within a confined environment has been considered and the time evolution of hardness and polarizability associated with it is presented in Figures 4 and 5 respectively. In the encounter region, hardness attains a maximum value and polarizability attains a minimum value. With an increase in the extent of confinement, the maximum value of hardness increases and minimum value of polarizability decreases. Therefore, from MHP and MPP, it can be inferred that the system tends to get stabilized as the extent of confinement increases. Proton is a hard acid according to hard-soft-acidbase (HSAB) principle. Therefore it prefers to bind with the most confined helium atom in ground and excited states with the most favorable interaction with the ground state where the system is the hardest. Herein, The HSAB principle is validated in a dynamical context. The general trends noted herein were further validated by Khatua et al while 10 ACS Paragon Plus Environment

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analyzing the reactivity patterns of atoms (hydrogen and helium) and hydrogen molecule subjected to an external magnetic field in a confined environment

16, 17.

In case of

hydrogen atom, the hardness increases with the increase in the strength of the applied magnetic field. Therefore, the system gets more stabilized in higher intensity magnetic fields as formation of new types of magnetic bonds becomes possible. Upon imposition of the confinement effect, ground state hardness decreases with an increase in the degree of confinement, when the field amplitude is small. However, upon increasing the degree of confinement further, hardness increases. Unlike the ground state, in the case of the excited state, hardness increases with a gradual increase in the degree of confinement. The MHP is aptly demonstrated herein as the ground state is more stable than the excited state. It is to be noted that the hardness of the excited state changes quiet sharply due to slight change in the field amplitude at both confined and unconfined states unlike in the ground state. He atom also shows extra stability

145-147

like H atom in high intensity

magnetic field at the confined state in the excited state. Similar conclusions were arrived at by Khatua et al while analyzing the reactivity of confined hydrogen molecule in presence of external magnetic field

17.

The electron density and Laplacian of electron

density of the confined hydrogen molecule at the two dimensional molecular plane were analyzed therein. It was inferred that with an increase in the degree of confinement the concentration of the electron density between the H atoms increases thereby indicating the enhanced stability 148 of the system with increment in the degree of confinement. Results and Discussion Confinement induced catalysis of some chemical reactions Reaction cavities are considered to play an important role as far as accelerating the rate of enzyme catalyzed reactions are considered. Enzyme catalyzed reactions are also highly regioselective in nature. Nevertheless, the detailed mechanistic insights of enzyme catalyzed reactions are not very well understood. It is widely believed that suitable binding of the substrates inside the cavities leading to favorable conformation between the reacting moieties plays a crucial role in the afore-mentioned class of reactions

149.

Stabilization of the transition state also plays an important role in accelerating enzymecatalyzed reactions. Mock and co-workers were able to demonstrate that by introducing 11 ACS Paragon Plus Environment


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CB[6] into the reaction medium, the 1, 3 dipolar cycloaddition reaction between alkyne (substrate1) and alkyl azide (substrate2) could be accelerated

98, 99.

The product, 1, 4

disubstituted triazole, was formed in a regioselective manner. Mock’s experiment constitutes an example of artificial enzyme-mimetic reaction. Mock postulated that CB[6] at

first

randomly

binds

both

substrates

to

yield

1:1

complex

substrate1/substrate2@CB[6]. Both of these 1:1 complexes can bind a second substrate yielding a ternary complex. The ternary complex can subsequently produce the product triazole. The rate limiting step was postulated by Mock to be the release of the product from the host. The reaction mechanism becomes complicated by the substrate inhibition of the host. Herein, the 1:1 complex such as substrate1@CB[6] can bind another substrate1 thereby leading to formation of a homoternary complex instead of a heteroternary complex. Therefore, the possibility of the intended cycloaddition reaction gets hindered. Mock’s group subsequently analyzed the kinetic outcome of similar reactions in presence of bulkier substituent groups within the substrates. In order to provide rationale behind the observed features, Mock compared the binding strengths of the binary with that of the ternary complexes. It was believed that CB[6] helps in increasing the local concentration of the reactants. The cavity of CB[6] can also facilitate the formation of the ternary complex in an optimum manner thereby accelerating the rate of the reaction as compared to the free state reaction. Stoddart’s group

104

demonstrated

that Mock’s rationale behind the catalytic role of CB[6] was correct. They undertook experiments where the same substrates utilized by Mock were employed in the presence of larger homologues of CB family namely CB[7] and CB[8]. Even though CB[7]/CB[8] can form ternary complexes with the reactants, no triazole formation was noted. Therefore, the crucial role of the confining effect of CB[6] cavity was exemplified. Despite the limitations of this route in terms of diminished catalytic turnover vis-à-vis product inhibition, these developments paved the way for further exploration of this route for catalyzing chemical reactions. We point out a few examples in this regard. Sanders et al. made use of a porphyrin trimer in order to catalyze a Diels–Alder reaction oxidation of a benzyl alcohol was catalyzed by Bols et al. cyclodextrin. Rebek’s group

152-154

151

150.

The

by employing a bridged

developed and employed several molecular cages

which can catalyze reactions. Raymond and co-workers demonstrated the ability of a 12 ACS Paragon Plus Environment

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Ga4L612– self-assembled nanocage to catalyze a Nazarov cyclization reaction

155-156-.

Raymond’s group also addressed the catalytic turnover issue by proposing new reaction schemes. Photochemical reactions were shown to get accelerated by employing several hosts, details of which could be found in reference 105. In this domain, computational chemistry can provide additional insights in determining the quantitative rationale behind the observed experimental features 106-114. In most of the afore-mentioned cases, the host and the guests interact in a non-covalent fashion. Therefore, one could employ dispersion corrected DFT in order to model processes mimicking confinement induced reactions since the large system size prohibits utilization of more accurate ab-initio wave function based methodologies. The host-guest complexes can adopt numerous conformations. However, given the large size of the systems under consideration, a comprehensive exploration of the concerned potential energy surfaces (PES) is computationally demanding. It is to be noted, nonetheless that, the relative orientation of the reactants inside the cavitands plays an important role in determining the kinetic outcome of the reaction under consideration. Therefore, it is prudent to explore the PES of the host-guest complexes in detail. Maseras and co-workers employed DFT to computationally reproduce the results obtained by Mock’s experiments.

106, 108

Their

calculations revealed important insights into the 1, 3 dipolar cycloaddition reaction happening inside CB[6]. They showed that the release of the product from the host is the rate limiting step in the catalytic cycle. They had also accounted for the observed regioselectivity in the concerned reaction. Li and co-workers

107

employed Monte Carlo

simulations and DFT computations in order to elucidate the reaction mechanism of the reaction between p-quinone and cyclohexadiene inside a self-assembled capsule. They demonstrated that the encapsulation of the reactants into the capsule is driven by noncovalent interaction between the host and the guests. They were able to show that the relative position and conformation of the reactants inside the host leads to various reactivity due to the variation in host-guest interaction. Crucial point that emerged from this study is the ability of the host in bringing down the energy barrier associated with the cycloaddition reaction. Calvaresi and co-workers

113

employed a QM/MM investigation

in order to understand the kinetics of the bromination reaction of N-phenylacetamide inside carbon nanotube (CNT). They have shown that confining effect of the CNT 13 ACS Paragon Plus Environment


Page 14 of 52

enables an almost regioselective yield of the para substituted product in addition to the acceleration in the rate of the reaction. Our group has tried to understand how different confining regimes affect the thermodynamic and kinetic outcome of some model DielsAlder reactions

109.

To this end, a classic [4+2] cycloaddition reaction between 1, 3-

butadiene and ethylene to yield cyclohexene was studied inside two organic hosts, ExBox+4 and CB[7] (in the gas phase) (Figures 6, 7). In the free gaseous state, the cycloaddition reaction between 1, 3-butadiene and ethylene takes place slowly at ambient temperature and pressure conditions. Upon encapsulation of the reactants inside ExBox+4, the reaction becomes slower and thermodynamically less favorable as compared to the unconfined reaction (Table 1). The reason behind this outcome could be attributed to the increase in the entropic cost associated the afore-mentioned reaction inside ExBox+4 moiety. The guests are forced to interact with the pyridinium rings of the host in a parallel displaced fashion. Therefore, the host prohibits the reactants to attain the favorable conformation so that the reaction gets facilitated. The reactants therefore need to reorganize themselves inside the host so as to take part in the cycloaddition reaction. CB[7] host, on the other hand, helps the reactants to attain a suitable conformation. As a result of which the entropic cost associated with the pre-organization of the reactants inside CB[7] gets reduced as compared to the free state reaction. Therefore, the concerned reaction becomes thermodynamically and kinetically more favorable inside CB[7]. However, purely geometrical consideration is probably not the only reason for the afore-mentioned computational observation. Due to the effect of confinement, the orbital interaction between the HOMO of the diene and LUMO of the dienophile becomes more feasible as compared to that in the free state. More importantly, confinement imposed by CB[7] stabilizes the transition state involved in the cycloaddition reaction. This factor should play an important role in dictating the thermodynamic and kinetic outcome. To this end, topological descriptors within the purview of Atoms-in-Molecules (AIM)

148

theory were employed in order to decipher the nature of bonding at the transition states. Results showed that the developing C-C bond at the transition state involved in the reaction inside CB[7] acquire more covalent character as compared to other two cases under consideration. Furthermore, energy decomposition analysis (EDA) showed that CB[7] host can interact with the guests, during the course of the reaction, more favorably 14 ACS Paragon Plus Environment

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as compared to ExBox+4. In order to verify whether CB[7] can promote other Diels-Alder reactions or not, DFT based computation was carried out

111.

To this end, dienes, viz. ,

furan, thiophene, cyclopentadiene, benzene and a classic dienophile, ethylene were employed (Figures 8, 9). Results indicated that all the afore-mentioned Diels-Alder reactions become thermodynamically and kinetically more favorable inside CB[7] as compared to the corresponding free state reactions, at ambient temperature and pressure conditions (Table 2). The main reason for these observation could be rationalized based on the formation of suitable encounter complex of the reactants inside CB[7] thereby reducing the entropic cost in bringing the reactants together as well as the stabilization of the transition states involved in the reaction due to the effect of confinement. A similar rationale was provided by Himo and co-workers

110

in their recent computational study

while explaining the experimentally observed rate acceleration and selectivity of 1, 3 Huisgen cycloaddition reaction observed inside Rebek's synthesized cavitand. It is to be noted, however, that straightforward extrapolation of computationally obtained Gibbs free energy changes associated with chemical reaction to experimentally observed kinetics data is difficult to obtain. Maseras and co-workers 108, 114 employed microkinetic modelling methodology in order to correlate computationally obtained data with that of experiments. The concentrations of all species involved in a given reaction over time can be obtained by assigning a reaction rate to each one of them and providing initial concentrations. The kinetic model can provide insights into the variation of concentration of different moieties over time and therefore provide an account of the chemical kinetics. Maseras’s group developed a kinetic model that can take into account the different behavior of the host-guest complexes in solution. Their developed model can follow the reaction mechanism from start to end thereby providing a comprehensive account of the process. Based on the afore-mentioned developments, it can be stated that confinement induced facilitation of chemical reactions deserve further attention from both experimental and computational view points. Particular emphasis is to be placed on developing ways in limiting product inhibition, artificially limiting non-productive alignment of the reactants inside the hosts, etc. It needs to be examined whether one could utilize any external perturbation to modulate the arrangement of the reactants in a desired way. 15 ACS Paragon Plus Environment


Page 16 of 52

Confinement induced changes in chemical bonding in rare gas atoms Due to the effect of confinement, interesting changes in chemical bonding could be observed. Detailed discussion on this topic could be found in the existing literature 4. We would like to focus on the impact of confinement on the nature of bonding in the cases of rare gas (Rg) atoms. Stimulated by the successful experimental incorporation of He inside various cage moieties, Frenking and co-workers

123

undertook computational

investigation to understand the nature of bonding between pair of rare gas atoms encapsulated inside C60. Based on electron density analysis within the premises of AIM theory, Frenking et al claimed that a genuine Xe-Xe covalent bond exists at the encapsulated state. Cerpa et al 124 analyzed the nature of interaction between He atoms in the case of the He2@C20H20 system. Despite the short internuclear distance of two He atoms in the case of He2@C20H20 system compared to unconfined He-He distance in He2, they showed that genuine chemical bond does not exist. Nevertheless, confined environment can unravel interesting features as far as the reactivity and bonding scenario of rare gas atoms are concerned. Khatua et al carried out a DFT based computational

125

investigation to understand the reactivity of rare gases encapsulated inside B12N12 and B16N16 cages. They found that the internuclear distance between He atoms encapsulated inside these cages are smaller as compared to the unconfined He2 system. In the cases of He2@B12N12 and He2@B16N16, the He-He distances were computed to be 1.306 Å and 1.456 Å, respectively. Similar situation was observed in the case of Ne2@B12N12, where the computed Ne-Ne distance (1.608 Å) was found to be shorter than that in the free Ne2 moiety. An atom-centered density matrix propagation (ADMP) simulation carried out at finite temperature revealed that Ne2@B12N12 system is neither kinetically nor thermodynamically stable. He2@B12N12 and He2@B16N16 were found to be kinetically stable. Based on AIM method based electron density analysis, it was concluded that there exists some degree of covalent character in the He-He bond in the case of He2@B12N12. In the case of the He2@B16N16 system, the He-He bond is devoid of any covalent character. However, the mode of interaction between He atoms is far stronger as compared to the corresponding case at the free state. It was also shown that in cases such as Ar/Kr/Xe@B12N12/B16N16, there exists some degree of covalent character in the mode 16 ACS Paragon Plus Environment

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of interaction between the host and guests. Confinement induced binding for rare gas atoms inside pristine and -BN doped (3, 3) single walled carbon nanotube (SWCNT) was studied by our group through DFT calculations

126.

In the case of pristine SWCNT, the

observed He–He distance inside the host was found to be 2.596˚A. In the case of BNdoped SWCNT, He-He distance was computed to be 1.824˚A. The computed Ar–Ar and Kr–Kr distances were found to be 2.781 and 2.756˚A respectively inside BN-doped SWCNT. AIM analysis revealed that there exist some degree of covalent character in the Kr-Kr bond in the case of Kr2@BN-doped SWCNT whereas He-He and Ar-Ar bonds could be classified as closed-shell type in the corresponding cases. Both Ar and Kr atoms interact with the host in partly covalent fashion. Pan et al examined

127

the rare gas

encapsulation processes inside B40 borospherene cage. They found that although the encapsulated rare gases interact among themselves in a non-covalent way in the cases of He2/Ne2@B40, some degree of covalent character exists in the corresponding cases in Ar2/Kr2@B40. As a result of these observation, one can state that an appropriate confinement helps rare gas atoms to exhibit far greater reactivity as compared to their corresponding free state counterparts. Recently, a thermodynamically stable compound of helium and sodium, Na2He, has been synthesized and computationally characterized at high pressure conditions

157

by Dong et al. They have demonstrated that in presence of

He atoms, strong electron localization takes place within the material. They have shown that the synthesized material acts as an electride and He forms eight-center two-electron bonds within empty Na8 cubes. The plausible existence of Na2HeO at pressures above 15 GPa was also predicted computationally therein. High-pressure experiment carried out on solid XeF2 revealed that XeF2 can undergo several phase transitions if the pressure is increased up to 100 GPa

158.

Results indicated that the concerned compound becomes

metallic above 70 GPa. The coordination number of Xe was shown to increase upon application of pressure. Kurzydzowski et al. through their computational analyses argued that

the

I4/mmm

structure

observed

at

ambient-pressure

thermodynamically most stable phase of XeF2 up to 105 GPa

159.

prevails

as

the

The I4/mmm structure

transforms to a Pnma structure above 105 GPa. Above 105 GPa, bent F−Xe−F molecules were observed in the performed calculations. Peng et al. performed an extensive structure search aided by DFT calculations on this system

160.

They considered xenon−fluorine



Page 18 of 52

compounds with various stoichiometries. They argued that application of pressure stabilizes xenon−fluorine compounds such as XeF4, XeF6, Xe2F, Xe3F2, XeF. Above 81 GPa, XeF2 becomes unstable yielding metallic products. They showed that these compounds contain Xe-Xe covalent bonds. Confinement induced changes in response properties The geometrical constraints imposed by some host molecules can enable a guest to exhibit interesting changes in response properties. The linear as well as non-linear optical (NLO) response properties of several systems and the impact of confinement therein have been extensively studied 162-176. Theoretical studies revealed that both static and dynamic polarizabilities of atoms decrease upon increasing the confinement

161-164.

An opposite

trend has been found in theoretical studies pertaining to hyperpolarizabilities of atoms under the effect of confinement

168.

Theoretical computations on a series of crystalline

systems reveal that the polarizability of an anion within a crystal could be substantially smaller as compared to the unconfined counterpart

172-174.

Combination of model

potentials and high-level quantum chemical methods were employed to understand the changes in electric response of molecules, by several groups 175, 176. It was shown that the first and second hyperpolarizabilities diminish upon increasing the confinement. Skwara et al showed that apart from the geometric effects, other factors such as host to guest charge transfer, covalent interaction, etc. can influence the response properties of a given host-guest complex 133. Bartkowiak et al analyzed the electric response of cyanoacetylene molecule confined by repulsive potentials of cylindrical symmetry

128.

The chosen

potential was considered to mimic the topology of a carbon nanotube. The impact of the external potential on vibrational contributions to electric-dipole properties was also considered therein. Dipole moment, polarizability and second hyperpolarizability of the guest were shown to get diminished upon exposure to the confinement effects whereas the vector component of the electronic first hyperpolarizability increased substantially. It becomes apparent that more studies are required in this direction so that general conclusions could be drawn. Experimentally, Yu et al analyzed the NLO response properties of some chromophore species confined in the pores of anionic metal–organic systems 177. Several dye molecules encapsulated in the interlayer spaces of clay materials 18 ACS Paragon Plus Environment

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exhibit increment in the NLO response properties 178, 179. Host–guest systems such as dye materials confined into the 1D nanochannels of aluminophosphate can exhibit interesting 180.

second-order NLO properties

Sulfonates moieties intercalated into the layers of

metal–organic frameworks can exhibit NLO properties

181.

Dye molecules confined

within the pores of zeolites demonstrate significant NLO response

182.

It is apparent that

the geometric arrangement of the concerned host–guest moiety plays an important role in determining the optical response properties

183.

An ideal geometry to observe significant

NLO properties should be a non-centrosymmetric arrangement of the host–guest system. This alignment can prevent destructive interference between second-harmonic generated photons. It is worth noting at this point that confinement can restrict the intramolecular vibrations of a guest inside a host-guest complex, ramifications of which could be gauged in various spectroscopic signatures. Boudjema et al demonstrated

184

that the vibronic

components in the high energy part of the S0 -> S1 absorption band of anthracene molecule get totally diminished upon confinement inside the ZIF-8 metal organic framework. Recently synthesized ExBox+4 can form stable host-guest complexes with variety of aromatic guests

185.

We have tried to understand how the optical response

properties of ExBox+4 change upon encapsulation of some organic guests such as coronene (Cor), B-doped coronene (BCor), tetrathiafulvalene (TTF), N-doped coronene (NCor), tetracyanoethylene (TCNE), biphenyl (BiPh) and tetracyanoquinodimethane (TCNQ)

186.

Since introduction of some electron donor and acceptor functional groups

into organic molecules might enhance its NLO response, we have considered three (in silico) functionalized variants of ExBox+4 as well and considered the afore-mentioned guest encapsulation therein (Figure 10). Upon encapsulation of guest molecules, the electronic properties of ExBox+4 undergo a noteworthy change. In all the cases of guest@ExBox+4, the mean polarizability (𝛼)values increase whereas the HOMO-LUMO gaps decrease as compared to the corresponding values of the pristine host. However, first hyperpolarizability (𝛽) values exhibit a notable extent of fluctuation. BCor/NCor/TCNE/TCNQ molecules increase the 𝛽 of the host whereas Cor/BiPh/TTF molecules lower the 𝛽value of the host. BCor/NCor/TCNQ/TCNE molecules upon getting encapsulated inside the host facilitates the extent of polarization principally along the x and z directions which is evident by analyzing the components of the 19 ACS Paragon Plus Environment


hyperpolarizability tensor along the x and z directions. BiPh/Cor/TTF molecules, however, disrupts the degree of polarization of the host-guest complex. In order to rationalize the afore-mentioned optical response properties of the guest@ExBox+4 complexes, we have carried out TDDFT calculations. According to the qualitative twostate model, 𝛽is proportional to the oscillator strength (f) associated with a given electronic transition and inversely proportional to the cube of the electronic transition energy (𝛥𝐸)

187, 188.

Molecules such as NCor/BCor reduce the vertical excitation energy

associated with the crucial electronic transitions of the host substantially Therefore, the host-guest complexes can exhibit fairly high NLO activity. On the other hand, molecules such as Cor increases the vertical excitation energy associated with the crucial electronic transitions of the host. Therefore, Cor@ExBox+4 exhibits negligible hyperpolarizability. It becomes evident that as a result of encapsulation inside the host, guest molecules can tune the electronic properties of the host to a significant extent. This could be gauged in the cases of the functionalized ExBox+4 moieties as well. As a result of guest encapsulation, the light absorption capability of ExBox+4 gets modified significantly. Encapsulation of molecules such as BCor/NCor/TCNQ enables the host to absorb light encompassing the UV-VIS as well as the infrared (IR) domains. Given the fact that harnessing the IR part of the solar radiation by molecules and materials is of paramount importance, encapsulation of suitable guests inside potential candidate materials and molecules could be thought off to be an attractive choice for practical applications. Encapsulation of a guest inside a host can affect the intra-molecular charge-transfer processes. Thereby, the electronic properties of the host can be affected significantly. We have shown that due to the encapsulation of Be+2, Mg+2, Na3O+ and K3O+ moieties inside the basket shaped octa acid 180 cavitand (OA), the HOMO-LUMO gap as well as the light absorption property of the host could be tuned substantially 190. Therefore, OA can absorb light over a wide range of frequencies as a result of encapsulation of the afore-mentioned guests. Confinement can have profound impact on the magnetic properties of a system. Singh et al 191 reported that a very high ferromagnetic exchange of the order of 200 cm-1 could be achieved in endohedral complex Gd2@C79N. They further showed that very strong Dy–radical exchange quenches the quantum tunneling of magnetization effects in Dy2@C79N molecule. They also demonstrated that the barrier height for magnetization 20 ACS Paragon Plus Environment

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reversal in Dy2@C79N molecule gets reduced due to the strong host-guest exchange interaction. They have also shown

192

that in complexes such as (DyOSc)2@C82, very

high barrier heights (of the order of 1400 cm-1) could be achieved for magnetization reversal. Therefore, they postulated that endohedral metallo-fullerenes could be very useful in designing efficient single molecular magnets. Endohedral gas adsorption Selective adsorption and storage of environmentally important gas molecules could be achieved through utilization of various supramolecular hosts. Ideally, the interaction energy between the adsorbate and the adsorbent should lie in between that of physisorption and chemisorption so that desorption can take place smoothly at ambient conditions

140.

It is postulated that molecules with high available surface area as well as

large free pore volume with low molecular weight can be thought off to be good candidates for gas adsorption

193, 194.

Zuttel et al. demonstrated the reversible hydrogen

adsorption on single wall carbon nanotubes

195.

Yang et al. showed that a hybrid

composite of acid-treated multiwalled carbon nanotubes and MOF-5 can act as a good candidate for hydrogen adsorption

196.

Wang et al. demonstrated the effect of

functionalization on the hydrogen adsorption capacity of the microporous metal–organic framework

197.

They concluded that at low pressure conditions, the gas adsorption

properties are affected by adsorbate–adsorbent interaction while at high pressure the surface areas and pore volumes play the decisive role. Metal organic frameworks (MOF) as well as covalent organic frameworks (COF) were utilized by various groups to analyze their hydrogen storage capacity

198-201.

Das et al undertook a DFT based investigation to

access the gas storage potential 202 of ExBox+4. The presence of high charge and aromatic rings makes this host a potential candidate for various gas sequestration processes. The hydrogen storage capacity was found to be ~ 4.3 wt% and this value compares reasonably well with that of other candidate materials. Upon introduction of Li dopants, the hydrogen storage capacity was shown to improve (6.23 wt%). Adsorption of up to 16 CO molecules was shown to be thermodynamically feasible inside this host. Stoddart et al demonstrated that ExBox+4 moiety exhibits propensity to scavenge aromatic guests

203.

The nature of interaction between aromatic guests and ExBox+4 were analyzed by 21 ACS Paragon Plus Environment


Bachrach et al and Das et al

204, 205.

Page 22 of 52

At high pressure (∼200 MPa) and low temperature

(~250 K) conditions, clathrate hydrates have been synthesized with hydrogen molecules as guests 206. Clathrate hydrates are inclusion compounds. They encapsulate various guest molecules inside the polyhedral cavities 206.

hydrogen bonded water molecules

207, 208.

Clathrate hydrates are composed of

But for the encapsulation of various guests inside

clathrate hydrates, the structure of clathrate hydrates would collapse into that of liquid water. Chattaraj et al demonstrated

139

that 512 and 51262 clathrate hydrates can

accommodate up to two hydrogen molecules whereas 51268 can encapsulate up to six hydrogen molecules. Adsorption and desorption rates were found to be suitable for hydrogen storage at ambient conditions. It was also shown that the endohedral mode of adsorption should be the energetically favorable path for hydrogen adsorption. It was found that due to the encapsulation of hydrogen, hardness values increase with concomitant decrease in electrophilicity thereby reaffirming the fact that guest encapsulation enhances the stability of these systems. Further, encapsulation of rare gases inside clathrate hydrates could dictate the structural arrangement and stability of the host. Londono et al. showed that in the case of He–clathrate hydrates, He encapsulation stabilizes the ice II structure. He encapsulation, however, destabilizes the formation of ice III, V and IX structures 209. Belosludov et al. demonstrated 210 that the He hydrate prefers to form Ic ice structure. The stability of the Ic structure increases significantly when the cavity is completely filled with He. Mondal et al. showed

211

through DFT computation,

that 512, 51268 and their HF doped clathrate hydrate analogues can encapsulate He, Ne and Ar gases in a thermodynamically favorable manner. Research is also going on in order to find suitable molecules/materials which can selectively adsorb greenhouse gases. Lee et al. have demonstrated

212

the ability of porous zirconium-organic material in selectively

binding CO2. Schröder et al. demonstrated the CO2 adsorption capacity of a binary supramolecular organic framework selectively over CH4 and CO

214.

213.

Kim et al. demonstrated that CB[6] adsorbs CO2

Lim et al analyzed the C2H2 adsorption properties of

CB[6] 215. Nau et al showed the strong binding of hydrocarbons to Cucurbituril 216. Pan et al analyzed 217 the gas adsorption capacity of CB[6] through gas-phase DFT calculations and concluded that the different gas molecules exhibit the following order of preference to bind with the host: Cl2> C2H2 > C2H6 > Br2 > CS2 > H2O > HCl > CO2 > C2H4 >HBr > 22 ACS Paragon Plus Environment

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CH4 > H2S > F2 > CO > HF > NO2 > N2 > NO > H2. They postulated that upon functionalization, the gas uptake capacity of CB[6] could be improved. Pan et al analyzed 218

the gas (C2H2, C2H4, C2H6, CH4, F2, Cl2, NO2, NO, CO2, CO, SO2, H2S, N2, and H2)

adsorption capacity of CB[7] through gas-phase DFT calculations and concluded that CB[7] exhibits an affinity for binding SO2 as compared to other considered gases. According to gas phase DFT calculations

219,

octa acid cavitand prefers to encapsulate

polar and π electron cloud containing guest molecules as compared to non-polar guests at ambient conditions. Experimental studies

220-221

indicate that OA exhibits propensity to

selectively bind various biologically important molecules. Conclusions The current state of understanding the behavior of confined systems highlights that confinement can bring about diverse changes in chemical reactivity. Confined environments could be utilized in order to unravel fascinating changes in bonding, optical as well as magnetic properties. Confinement could also be utilized to design efficient reaction vessels. Confined environments could be utilized to store environmentally as well as biologically important molecules. Computational chemistry can assist in providing suitable design principles for experimental realization of interesting new chemistry at the confined state. Even though gas-phase DFT calculations can provide qualitatively correct trends in many situations, utilization of multi-scale modelling techniques might be required in order to address complex scenarios present in real life experiments. Associated computational and methodological developments can help to shed light on hitherto unforeseen chemistry occurring at the confined space. Acknowledgements P. K. C. thanks Professors George C. Schatz and Anne B. McCoy for kindly inviting him to contribute a Feature article in The Journal of Physical Chemistry. He would also like to thank DST, New Delhi for the J. C. Bose National Fellowship. D. C. thanks the CTS Visitors’ programme of IIT Kharagpur for the financial assistance. We would like to thank Drs. Utpal Sarkar, Munmun Khatua, Sukanta Mondal, Sudip Pan and Ranjita Das for their help in preparing this manuscript. 23 ACS Paragon Plus Environment


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Figures

6

0.29 Softness of N Softness of N

+

0.28

Softness (s)

Softness (s)

5

4

3

+

Softness of N

0.27

0.26

0.25

2

0.24

1 1

2

3

4

5

6

7

8

9

1

10

2

3

4

5

RC

RC

6

7

8

9

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A-1(Boeyens method) A-2(Boeyens method with ΔSCF)

6

0.29

Softness of N

5

Softness of N

Softness of N

0.28

+

4

Softness (s)

Softness (s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3

2

+

0.27

0.26

0.25

1 1

2

3

4

5

RC

6

7

8

9

10

0.24

B-1(Dirichlet method)

1

2

3

4

5

RC

6

7

8

B-2 (Dirichlet method with ΔSCF)

Figure 1: Plots of softness (S, a.u.) vs cut- off radius (rC, a.u.) for N (red ––––) and N+ (violet ––––) confined in a spherical box. Herein A-1, A-2, B-1, B-2 techniques refers to the following: a) A-1: Boeyens cut- off function method 117. Reactivity parameters are calculated using eqs. (3) and (9); b) A-2: Boeyens cut- off function method. Reactivity parameters are calculated using eqs. (11) and (12) augmented by a standard ΔSCF 41 ACS Paragon Plus Environment

9

10


procedure; c) B-1: Dirichlet boundary condition method. Reactivity parameters are calculated using eqs. (3) and (9); d) B-2: Dirichlet boundary condition method. Reactivity parameters are calculated using eqs. (11) and (12) augmented by a standard ΔSCF procedure. Herein, Boeyens method implies multiplication of the SCF wave function by a   r        exp   RC   R step function of the form . Here C is the cut- off radius of the spherical box on whose surface the wavefunction vanishes142 and  is a parameter whose value is taken to be 20 as suggested by Boeyens. (reprinted with permission from ref 11; Copyright 2009 American Chemical Society).

10

3.180

3.178

Electronegativity of N Electronegativity of N

6

Electronegativity ()


8

+

4

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+

3.174

3.172

3.170

3.168

3.166

0 1

2

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9

1

10

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6



8


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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+

Electronegativity of N 4

2

3.176

3.174


+

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3.166 0 1

2

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4

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1

2

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5

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B-2 (Dirichlet method with ΔSCF)

9

10

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Figure 2: Plots of electronegativity (  , a.u.) vs cut- off radius (rC, a.u.) for N (blue –––) and N+ (red –––) confined in a spherical box. See Figure caption 1 for details. (reprinted with permission from ref 11; Copyright 2009 American Chemical Society).

Figure 3: Time evolution of chemical potential (µ, in a.u.) when helium atom in ground state is placed in intense laser field. (Amplitude = 10-6, 0.01 and 100 a.u.). Black line (Length of the cylinder = 6 a.u.) represents unconfined system, red line (Length of the cylinder = 4.8 a.u.) and blue line (Length of the cylinder = 4.2 a.u.) represent confined systems. (Radius of the cylinder=4.2025 a.u.).ω0=π. (reprinted with permission from ref 14; Copyright 2012 Royal Society of Chemistry).



Figure 4. Time evolution of hardness (η, in a.u.) and polarizability (α, in a.u.) during a collision process between a proton and helium atom in the ground state. (reprinted with permission from ref 68; Copyright 2003 American Chemical Society).

Figure 5. Time evolution of hardness (η, in a.u.) and polarizability (α, in a.u.) during a collision process between a proton and helium atom in the excited state. (reprinted with permission from ref 68; Copyright 2003 American Chemical Society).


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Figure 6: Geometrical structures of (a) reactants, (b) TS, (c) product inside ExBox+4 respectively in the case of reaction between 1, 3 butadiene and ethylene. (reprinted with permission from ref 109; Copyright 2017 John Wiley and Sons)

Figure 7: Geometrical structures of (a) reactants, (b) TS, (c) product inside CB[7] respectively in the case of reaction between 1, 3 butadiene and ethylene. (reprinted with permission from ref 109; Copyright 2017 John Wiley and Sons)



Figure 8: Geometrical structures of (a) reactants, (b) TS, (c) product for the case of reaction in between benzene and ethylene inside CB[7] and (d) reactants, (e) TS, (f) product for the case of reaction in between cyclopentadiene and ethylene inside CB[7] respectively. (reprinted with permission from ref 111; Copyright 2017 John Wiley and Sons)


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Figure 9: Geometrical structures of (a) reactants, (b) TS, (c) product for the case of reaction in between furan and ethylene inside CB[7] and (d) reactants, (e) TS, (f) product for the case of reaction in between thiophene and ethylene inside CB[7] respectively. (reprinted with permission from ref 111; Copyright 2017 John Wiley and Sons)



Figure 10: Minimum energy structures of BCor@ExBox+4, NCor@ExBox+4, BiPh@ExBox+4, TCNQ@ExBox+4, ExBox+4, TTF@ExBox+4, Cor@ExBox+4, TCNE@ExBox+4 (in clockwise direction). (reprinted with permission from ref 186; Copyright 2017 Royal Society of Chemistry).


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Tables Table 1. Free energy change (ΔG, kcal/mol) and reaction enthalpy change ( H , kcal/mol) at 298.15 K and one atmospheric pressure for the overall reaction between 1, 3 butadiene and ethylene at the confined and unconfined states; Free energy and enthalpy ‡ ‡ of activation ( G / H , kcal/mol) at 298.15 K and one atmospheric pressure, rate constant (k, sec-1) associated with the processes. (reprinted with permission from ref 109; Copyright 2017 John Wiley and Sons)

Systems

G

ReactionFree -39.37 +4 ReactionExBox -36.51 ReactionCB[7] -40.02

H

G ‡

H ‡

k

-46.74 -41.44 -42.75

27.32 32.81 24.13

20.98 30.21 21.65

5.80*10-08 5.51*10-12 1.27*10-05

Table 2. Free energy change (ΔG, kcal/mol) and reaction enthalpy change ( H , kcal/mol) at 298.15 K and one atmospheric pressure for the overall reaction at the ‡ ‡ confined and unconfined states; Free energy and enthalpy of activation ( G / H , kcal/mol) and the rate constant (k, sec-1) associated with the processes at 298.15 K and one atmospheric pressure. Reaction between benzene, furan, cyclopentadiene and thiophene with ethylene has been represented as reaction1, reaction2, reaction3 and reaction4 respectively. (reprinted with permission from ref 111; Copyright 2017 John Wiley and Sons) Systems Reaction1Free Reaction2Free Reaction3Free Reaction4Free Reaction1CB[7] Reaction2CB[7] Reaction3CB[7] Reaction4CB[7]

G 17.95 2.54 -13.52 3.56 13.21 -5.39 -17.67 -1.90

H 3.63 -11.28 -27.70 -10.35 9.51 -9.26 -21.28 -5.07

G ‡ 49.95 37.07 32.52 45.66 43.93 30.34 25.92 39.60


H ‡ 36.93 24.19 19.46 32.71 41.15 27.70 23.03 36.69

k 1.50*10-24 4.14*10-15 9.05*10-12 2.10*10-21 3.90*10-20 3.59*10-10 6.15*10-07 5.83*10-17


Author Biography

Pratim Kumar Chattaraj

Pratim Kumar Chattaraj is an Institute Chair Professor at Indian Institute of Technology (IIT) Kharagpur. He received his PhD from IIT Bombay. He was a research associate in the University of North Carolina, Chapel Hill, USA, and FAU, Erlangen-Nürnberg, Germany. He has been actively engaged in research in the areas of density functional theory, ab-initio calculations, nonlinear dynamics, aromaticity in metal clusters, hydrogen storage, noble gas compounds, machine learning, chemical reactivity and quantum trajectories. He was honored with: University Gold and Bardhaman Sammilani medals; INSA (Young Scientist) medal; CRSI Bronze and Silver medals; IAAM medal ; Acharya P.C.Ray Medal; Associate, Indian Academy of Sciences; BM Birla Science Prize; BC Deb Memorial award. He is a Fellow of The World Academy of Sciences (TWAS), Italy, Indian Natl. Science Academy; Indian Academy of Sciences; National Academy of Sciences, India; West Bengal Academy of Science and Technology; and FWO, Belgium. He is a Sir J.C. Bose National Fellow. He is a Member of the Science Education Panel of the Indian Science Academies. He was Convener, Center for Theoretical Studies , Convener, Kharagpur Local Chapter, INSA, council member of CRSI, Dean (Faculty) and Head of the Chemistry Department of IIT Kharagpur. He is a Distinguished Visiting Professor of IIT Bombay.


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Debdutta Chakraborty Debdutta Chakraborty received his PhD from IIT Kharagpur in 2018. He worked under the supervision of Prof. P. K. Chattaraj. He received Junior and Senior research fellowships from CSIR, New Delhi, Dean of Faculty Postdoctoral fellowship from the Weizmann Institute of Science, Israel. Currently he is a research associate in the Texas Tech University, USA. His research interests are computational investigation of confined quantum systems, optoelectronic properties, analysis of reaction mechanism, quantum trajectories and chemical dynamics simulations.



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Bonding, Reactivity, and Dynamics in Confined Systems - The Journal

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