Attochemistry of Ionized Halogen, Chalcogen, Pnicogen, and Tetrel

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Feature Article

Attochemistry of Ionized Halogen, Chalcogen, Pnicogen and Tetrel Non-Covalent Bonded Clusters Sankhabrata Chandra, and Atanu Bhattacharya J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b09813 • Publication Date (Web): 09 Nov 2016 Downloaded from http://pubs.acs.org on November 26, 2016

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The Journal of Physical Chemistry

Attochemistry of Ionized Halogen, Chalcogen, Pnicogen and Tetrel Non-Covalent Bonded Clusters SANKHABRATA CHANDRA AND ATANU BHATTACHARYA* Department of Inorganic and Physical Chemistry, Indian Institute of Science Bangalore, Karnataka, India 560012, *[email protected], Ph: 91-8022933349

Abstract: In general, charge migration can occur via pure electron-electron correlation and relaxation or via coupling with nuclear motion. We must understand both aspects of charge migration through the non-hydrogen noncovalent bonds to harness full potential of the halogen-, chalcogen-, pnicogen- and tetrel-bonded photosensitive functional materials. This feature article, however, is focused on the pure relaxation- and correlation-driven charge migration, subsequent charge localization and finally on charge directed reactivity in the nonhydrogen noncovalent bonded clusters. Pure relaxation- and correlation-driven charge migration can occur in several hundred attosecond time scale and this is why chemical dynamics associated with this pure electronic charge migration can be named as “Attochemistry”. One of the efficient ways to elucidate the Attochemistry is via the vertical ionization by monitoring a non-stationary electronic charge density which evolves in time while the nuclear configuration remains unchanged. So far, Attochemistry of several halogen, chalcogen, pnicogen, and tetrel bonded clusters has been studied theoretically by our group. All the interesting predictions have been summarized in this feature article. The timescales of relaxation- and correlation-driven charge migration through the halogen, chalcogen, pnicogen, and tetrel noncovalent bonds are found to be quite similar (approximately in the range of 300-600 attosecond) in different (1:1) AX:NH3 and AX:OH2 complexes (where A represents different substituents, such as NH2, CN, etc.). Basis sets do not exhibit any effect on the predicted charge migration time scale. Charge migration is ceased at very long intermolecular distance, for which (physically) no intermolecular noncovalent bonding interaction is present. Strength of the electron-electron correlation interaction influences the charge migration through these non-covalent bonds, making charge migration faster with higher correlation interaction. Initial nuclear configuration affects the charge migration through the non-hydrogen non-covalent bonds. For large clusters, in which both hydrogen and non-hydrogen noncovalent bonds are formed, non-hydrogen noncovalent bonds are found to facilitate the charge migration preferentially over the hydrogen bonds. As a result of nuclear wavepacket delocalization, the attosecond charge oscillation in non-covalent bonded clusters decoheres. This renders charge localization. Subsequent charge-directed reactivity is discussed. This article is the first review on the Attochemistry of non-hydrogen noncovalent bonded clusters.

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I. Introduction: Often, intermolecular noncovalent bonds are described using a general notation AX.....B, in which the X atom of the electron acceptor molecule, AX, acts as a bridge to the atom B of the electron donor molecule. The nature of the X atom defines the name of the respective X.....B noncovalent bond. If X represents a hydrogen atom, X.....B is called the hydrogen bond. Similarly, X.....B is called the halogen, chalcogen, pnicogen and the tetrel noncovalent bonds when X belongs to the halogen (e.g., Cl), chalcogen (e.g., S), pnicogen (e.g., P) and the tetrel (e.g., Si) family of elements, respectively. Many physical and chemical aspects of non-hydrogen noncovalent bonds have attracted immense attention, recently. One of them includes charge migration through these bonds. For a long time, charge migration (see Supporting Information S1) through hydrogen bonds has been investigated rigorously because it plays an important role in biological electron transport1 and molecular conductance.2 However, recently, researchers are finding importance of charge migration through other non-hydrogen noncovalent bonds, such as halogen, chalcogen, pnicogen and tetrel bonds.3-9 For example, bromoaromatic aldehydebased organic crystals exhibit bright green phosphorescence via electronic coupling and charge migration through halogen bond between adjacent monomeric units.3 It is believed that halogen bonding contact promotes the charge migration through this noncovalent bond. This charge migration ultimately hinders nonradiative decay path, facilitating singlet-triplet intersystem crossing. Halopentrafluorobenzene-based liquid crystal, which is an important material for the construction of optically nonlinear system,5 is formed via only halogen bonding contacts. Charge migration through their halogen bonds may also play an important role. Strength of the chalcogen bonding interaction6 is considered to be a direct consequence of the charge migration through this noncovalent bond. Similarly, dominant contribution of the pnicogen noncovalent bonding energy is predicted to come from the energy associated with the charge (electron) migration process.7 Furthermore, charge redistribution induced by tetrel (or carbon) noncovalent bond formation is proposed to be an initial step in organic SN2 reaction.8,9 These interesting recent examples show that charge migration through the nonhydrogen noncovalent bonds is ubiquitous in modern crystal engineering, supramolecular chemistry and novel molecular electronics. Therefore, we must understand all aspects of charge migration through the non-hydrogen noncovalent bonds. Charge migration is a complex process. In general, two conceptually different mechanisms are found: (1) pure electronic mechanism which is driven only by electronelectron correlation and relaxation, and (2) coupled electron-nuclear mechanism which involves nuclear motion along with the charge migration. Recent theoretical works10-13 show that the vertical ionization allows one to investigate the first mechanism. This mechanism involves no nuclear rearrangement and is driven purely by electron-electron relaxation- and correlation. This is why the first mechanism features pure electronic aspect of the charge migration phenomenon. For harnessing full potential of the non-hydrogen noncovalent bonded functional photosensitive supramolecular materials, in which charge migration through these noncovalent bonds is ubiquitous, we must understand pure electronic aspects of the charge migration through these noncovalent bonds. Pure electronic aspects of charge migration (driven purely by electron-electron relaxation and correlation) are collectively named as the “Attochemistry” (see Supporting Information S2) in the present feature article because such pure electronic charge migration can occur in several hundred attosecond or a few femtosecond time scale.13,14 Here, we, first, give a short introduction to the molecular Attochemistry and then discuss the Attochemistry of the halogen, chalcogen, pnicogen, and tetrel bonded clusters.


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Background of Molecular Attochemistry: Electrons hold matter together and that is why they determine many properties of matter, including the structure and reactivity (dynamics). Traditionally, however, chemical structures and reactivities are often described neglecting direct role of the electrons based on two simplified description of the interaction between electrons and nuclei (two constituents of matter).15,16 One of them includes the adiabatic Born-Oppenheimer approximation.15 The nucleus has much larger mass than the electron and that is why electronic configuration is assumed to adapt instantaneously to the nuclear motion which occurs on a femtosecond time scale: the H-H bond vibration (4400 cm-1), for example, exhibits a period of 7.5 femtosecond. Pure electronic motion, on the other hand, occurs on attosecond time scale: a frequently used classical but intuitive picture of pure electronic motion is that an electron in its ground state orbiting a hydrogen nucleus exhibits a period of ~150 attosecond. Therefore, as long as chemistry is driven under the Born-Oppenheimer approximation, electrons may not play a direct role in chemical reactions and attosecond time scale may not be important in chemical dynamics. Is it important for non Born-Oppenheimer chemical dynamics? The adiabatic Born-Oppenheimer approximation breaks down when the energy gap between the adiabatic electronic states becomes comparable to the energy contained in the nuclear degrees of freedom, rendering a situation when electronic motion starts playing important role in overall reactivity of the chemical system. Extensive research on photochemistry evidences that the electronic motion cannot be neglected in photochemistry of polyatomic molecules, particularly when photochemistry occurs through the conical intersections17,18 (these are regions in the multidimensional potential energy landscape where two electronic adiabatic states become degenerate and where the Born-Oppenheimer approximation completely breaks down). However, conical intersections are the regions where the electron dynamics slows down from its natural time scale (attosecond) to the time scale of nuclear motion (femtosecond).19 Therefore, electronic motion can be important in non Born-Oppenheimer chemical dynamics but attosecond time scale may not be important. Is pure electronic (attosecond) time scale, then, at all important in chemistry?13 We attempt to answer this question below. Another approximation, frequently used to describe structure and reactivity in chemistry, is the one-electron approximation.16 Under this approximation, electrons are considered to be individual particles moving under the influence of an average field generated by all other electrons. Well-known Hartree-Fock theory, which gives us the concept of molecular orbital (the eigen function of one electron Fock operator), was developed under this approximation.16 An attractive feature of the Hartree–Fock theory is realized based on the interpretation given by Koopmans:20 in closed-shell Hartree-Fock theory, the first ionization energy of a molecular system is equal to the negative of the orbital energy of the highest occupied molecule orbital (HOMO). Koopmans theorem is valid only if orbitals of the cation are identical to those of the neutral molecule (called frozen orbital approximation). This theorem becomes invalid under two circumstances: (1) orbital relaxation: following vertical ionization, if there is a change in the Hartree-Fock orbitals due to change of mean field; and (2) electron correlation: following ionization if Hartree-Fock wave function (single Slater determinant wave function) fails to represent the entire manybody wave function (in that case, multiconfiguration wave function is necessary to represent post-ionization event). Recent literature shows that several important and perhaps hithertounknown pure electronic processes can occur, which can serve as a prelude to the subsequent chemical dynamics of ionized molecules and clusters, when Koopmans theorem breaks down.10-13 The positive charge created after the ionization can migrate throughout the system on a time-scale of several hundred attosecond or a few femtosecond: this ultrafast redistribution of the electronic cloud can influence subsequent nuclear dynamics which will 3 ACS Paragon Plus Environment


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show up at later time. As a consequence, this brings about the idea of “charge directed reactivity” following ionization.21-25 Therefore, attosecond time scale becomes important in chemistry when an ionization process is involved and when Koopmans theorem breaks down. Attochemistry of Non-covalent Bonded Clusters: Ionization is a process by which an atom or a molecule acquires a positive or a negative charge by losing or gaining electron (or electrons).26 Ionization can occur by various means, such as via the loss of an electron after collisions with subatomic particles, by collisions with other atoms, molecules and ions, or simply through the interaction with light. Recent literature demonstrates that the vertical ionization is one of the efficient ways to initiate pure correlation- and relaxation-driven charge migration in molecules.10-13 Cederbaum and co-workers27-30 and Levine and coworkers31,32 performed extensive theoretical calculations that model charge migration processes in various isolated polyatomic molecules following this vertical ionization scheme. However, a very few study has been undertaken, so far, to explore the electron-electron relaxation- and correlation-driven charge migration dynamics (Attochemistry) in noncovalent bonded molecular clusters. Remacle and Levine33,34 studied the vertical ionization-induced charge migration in hydrogen-bonded dimers to explore the differences in initial hole localization and redistribution using the symmetry argument. They considered the asymmetric water-water and methanol-water dimmers for their studies. In the water-water dimer, they predicted that the HOMO of the neutral dimer was a superposition of two cationic molecular orbitals (the HOMO and the lowest unoccupied molecular orbital (LUMO) of the cation) and was localized on one of the water molecules. Furthermore, a hole created on one water molecule migrates to the other molecule with periodicity of 4.13 femtoseconds. Recently, for the first time, we have explored the Attochemistry (pure relaxation- and correlation-driven charge migration dynamics) of the non-hydrogen non-covalent bonded clusters (such as, halogen, chalcogen, pnicogen, and tetrel bonded clusters), adopting the vertical ionization scheme.35-37 In this feature article, we have summarized, compared and contrasted different aspects of the Attochemistry of non-hydrogen noncovalent bonded clusters, including the influence of substituents, strength of correlation interaction, directionality, initial nuclear configurations, non-covalent bond length, basis-set, cluster formation, and the effect of pre-ionization nuclear wavepacket width. Subsequent hole directed reactivity of the radical cations is also presented.

II. Attochemistry Clusters:

of

Non-hydrogen

Non-covalent

Bonded

The time-dependent quantum chemistry teaches us that solution (using variable separation method) of the time dependent Schrodinger equation for a pure state (also called stationary state, characterized by its own characteristic time-dependent phase factor) depends on time: ψ ( x, t ) = ψ ( x ) e −iEt h . However, the probability density of this pure state is independent of time:

ψ ( x, t ) = ψ ( x ) e−iEt h ψ * ( x ) eiEt h = ψ ( x ) ψ * ( x ) = ψ ( x ) ..........(1) 2

2

We obtain time-dependence in the probability density only when a state (more specifically a non-stationary state) is prepared via linear combination (coherent superposition) of stationary (pure) states, each with its own characteristic time-dependent phase factor. Considering linear combination of two pure states, for example, the probability density of the non-stationary state is given by,


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ψ ( x, t ) = a1ψ 1 ( x ) e −iE t h + a2ψ 2 ( x ) e −iE t h 2

1

2

2

2 2 = a1 ψ 1 ( x ) + a2 ψ 2 ( x ) + 2 Re  a1* ψ 1* ( x ) a2 ψ 2 ( x ) e −i( E2 − E1 )t h  ..........(2) 2

2

Equation (2) has three terms: first and second ones come from pure ψ 1 ( x ) and ψ 2 ( x ) , and third one comes from an (oscillatory) interference term. This interference term is a result of having a superposition of eigenstates with different energies – called a wavepacket. All the time-evolving features of the non-stationary state ψ ( x, t ) are buried inside this interference term. For an example, time dependence of the probability density of this non-stationary state can be simply expressed by its characteristic oscillation period, τ = h ; where, oscillation ∆E ω 1 ( E2 − E1 ) ∆E = ⋅ = . frequency is given by υ = h 2π 2π h

With the basic idea presented above, we now ask what happens when one removes an electron from a particular molecular orbital (following vertical ionization)? Under one electron approximation, a localized hole is created at the HOMO, if the electron is removed from the HOMO. The HOMO of the neutral molecule or cluster may not be a stationary orbital of the cation. It can happen that neutral HOMO is a linear combination of several cationic states. In that case, vertical ionization (which is simply manifested by removal of an electron from the HOMO) coherently populates more than one cationic eigen states. This creates an electronic wavepacket which evolves in time (according to the law of superposition). The reason of wavepacket generation via the vertical ionization is the electron-electron relaxation and correlation. Without electron-electron relaxation and correlation, vertical ionization prepares only a pure cationic state and as a result, hole density of a pure state does not evolve in time. About a decade ago, Levine and Remacle proposed a simple procedure to investigate the time evolution of a non-stationary electronic state prepared via the vertical ionization.13 After removal of an electron from the HOMO of neutral (featuring the vertical ionization) a localized hole is created in the neutral HOMO. Under the unrestricted self-consistent field (SCF) scheme, the neutral HOMO can be expressed as a linear combination of all cationic orbitals and projections (determined by overlap integrals) of the neutral HOMO onto both the α- and the β-cationic orbitals can be taken as expansion coefficients. Finally, the time evolution of the hole orbital associated with two spins can be represented by introducing the time dependent phase factor (see Supporting Information S3 for more details):33

Ψα (t )

=

N

∑

α

Φαλ ΨHOMO

Φαλ e( −iEλ t / ћ ) ..........(3)

Φβλ ΨHOMO

Φβλ e ( − iEλ t / ћ ) ..........(4)

λ=1

Ψβ(t )

=

N

∑

β

λ=1

Here, ΨHOMO is the HOMO of the neutral cluster, Φ λ is the λth cationic MO of the cluster, Ψα (0) and Ψβ(0) are the hole orbitals with spin labels α and β, respectively. Ultrafast charge migration dynamics in ionized halogen, chalcogen, pnicogen, and tetrel bonded clusters was studied using equations (3) and (4). Figure 1 (and Supporting Information S4) shows the hole migration dynamics through the Cl…..N halogen, S…..N 5 ACS Paragon Plus Environment


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chalcogen, P.....N pnicogen, and Si.....N tetrel noncovalent bonds for selected (1:1) complexes (H2NCl:NH3, H2NSH:NH3, H2NPH2:NH3, and H2NSiH3:NH3, respectively), computed at the DFT level of theory (with wB97XD functional and 6-31+G(d,p) basis set). Comparison of different levels of theory (DFT vs CASSCF) was made earlier.35-37 Figure 1 shows that at the moment of ionization, the hole density is purely localized on the H2NX-end; however, this hole density rapidly gets delocalized over the respective noncovalent bond in approximately 400-500 attosecond. Similar time scale is also predicted for many other halogen, chalcogen, pnicogen, and tetrel bonded clusters.35-37 Quite interestingly, the initial hole density (created by vertical ionization) is found to evolve in time for some non-hydrogen noncovalent bonded complexes and others do not show any temporal evolution of the hole density. This can be easily understood by analysing the projection weights (represented by

Φβλ ΨHOMO

2

Φαλ ΨHOMO

2

for α-cationic orbitals and by

for β-cationic orbitals) of the neutral HOMO onto all stationary cationic MOs.

To illustrate this point we take examples of NCCl:NH3 and HOCl:NH3 complexes, as shown in Figure 2. It is evident in this figure that the initial hole density (or in other words, the neutral HOMO density) is mostly a linear combination of two stationary cationic MOs, namely cationic LUMO-β and cationic HOMO-β for NCCl:NH3 complex. Therefore, the period (τ ) of the hole migration is nothing but an oscillation of the charge density, as

( 2)

discussed earlier, mostly between these two stationary cationic orbitals. The time scale τ

of the charge migration is then calculated from the energy difference ( ∆E ) between these

(

two stationary cationic orbitals where, τ = h

)

. The ∆E is calculated to be 3.69 eV for ∆E NCCl:NH3 and therefore, charge migration timescale is predicted to be 550 attosecond for this complex. This prediction is clearly evident in the dynamics simulation presented in Figure 2. On the other hand, the neutral HOMO density for HOCl:NH3 complex is mostly represented by only one stationary MO (namely LUMO-β) of the respective cation (see Figure 2). Therefore, the hole, which is created initially at the neutral HOMO of HOCl:NH3 complex, stays localized on the same site and as a result, hole density does not evolve in time. Having understood the driving force behind the Attochemistry following the vertical ionization of halogen, chalcogen, pnicogen and tetrel bonded clusters, several interesting aspects of their Attochemistry were revealed. They are discussed below.

III. Different Aspects of Attochemistry of Non-hydrogen Noncovalent Bonded Clusters: (A) Effect of Basis Set: Under one electron approximation, all cationic MOs ( Ψ λ ) in equations (3) and (4) are expressed as a linear combination of the atomic basis orbitals (LCAO method), i.e., N

Ψλ = ∑ Ci λ Θiλ .......... (5) i =1


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Here, Θiλ is the i th atomic basis orbital of the λ th cationic MO and Ci is the respective LCAO-expansion coefficient. The Θiλ is defined via the basis set in the calculation. Therefore, it is legitimate to ask whether the computational results of the Attochemistry depend on the atomic basis orbitals. Quite interestingly, no effect of basis set on the vertical ionization-induced charge migration dynamics in halogen, chalcogen, pnicogen, and tetrel bonded clusters is found. Figure 3 compares and contrasts results obtained for H2NCl:NH3, H2NSH:NH3, H2NPH2:NH3 and H2NSiH3:NH3 complexes using three different relatively large basis sets: 6-31+G(d,p), aug-cc-pVDZ and aug-cc-pVTZ. It is clearly evident from this figure that the DFT (with wB97XD functional) results with these three basis sets predict the same time scale for the charge migration through the respective non-hydrogen noncovalent bond.

(B) Effect of Intermolecular Distance: Any physically realistic model of intermolecular charge migration must predict the fact that no charge migration should occur if molecules are separated by a long distance (say 10 Å). Physically, no intermolecular noncovalent bonding interaction should be present at this long intermolecular distance. This is, indeed, observed in different halogen, chalcogen, pnicogen, and tetrel noncovalent bonded complexes at the X…..N distance of 10 Å, as depicted in Figure 4, taking illustrative examples of NCCl:NH3, H2NSH:NH3, H2NPH2:NH3 and H2NSiH3:NH3. At this long X…..N distance, the cationic LUMO-β and the neutral HOMO remain identical. Furthermore, at this long X.....N distance, the neutral HOMO is essentially determined by the relative ionization energies (IE) of the two complex-forming moieties. The SHNH2 (IEMP2 = 9.52 eV), PH2NH2 (IEMP2 = 9.55 eV) and SiH3NH2 (IEMP2 = 9.86 eV) molecules possess vertical IEs lower than that of NH3 (IEMP2 = 10.55 eV) molecule. This is why the neutral HOMO is found to be localized on the A-Xend in H2NSH:NH3, H2NPH2:NH3, and H2NSiH3:NH3 complexes at X.....N distance 10 Å (see Figure 4). On the other hand, ClCN (IEMP2 = 12.68 eV) molecule exhibits ionization energy higher than that of NH3 molecule. This results in the neutral HOMO to be localized on the NH3-end in the NCCl:NH3 complex at the long X.....N distance. (C) Effect of Strength of Electron Correlation: It is fair to ask whether the strength of electron-electron correlation interaction influences the Attochemistry of ionized halogen, chalcogen, pnicogen, and tetrel bonded clusters. Under the Hartree-Fock (HF) approximation, each electron experiences an average field of all other electrons. This is why it is considered that HF-method does not include electron correlation. On the other hand, DFT (or MP2) captures fair amount of “correlation energy” at low computational cost. Therefore, difference between DFT- (or MP2-) binding energy and HF-binding energy can estimate a large fraction of the total correlation energy associated with the respective noncovalent bond. Figure 5 plots charge migration time scale predicted for different (1:1) complexes containing NH3 and H2O donor molecules as a function of total correlation energy computed for the respective noncovalent bond. The plots in Figure 5 clearly exhibit a trend: higher correlation energy makes the charge migration time-scale faster. Therefore, the correlation interaction must play an important role in the attosecond charge migration dynamics through the non-hydrogen noncovalent bonds. (D) Effect of Initial Nuclear Configuration: So far, only frozen neutral equilibrium geometries of the halogen, chalcogen, pnicogen and tetrel bonded clusters are considered to discuss their post-ionization Attochemistry. In this context, it is legitimate to ask to what extent the initial geometry, other than neutral equilibrium geometry, influences the hole migration triggered by the vertical ionization. To discuss this point, we have selected NCCl:OH2 complex as an illustrative example. This complex exhibits total 12 normal modes 7 ACS Paragon Plus Environment


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of vibration (see Supporting Information S5). From a simplistic point of view (and perhaps with little exaggeration), one can select classical turning point geometries obtained along each normal mode coordinate of NCCl:OH2 complex to obtain several initial geometries which are different from neutral equilibrium geometry. Using this method, new structural coordinates are presented as, qi ,new = qi ,opt ± 0.5 qij (here, i represents coordinate and j represents vibrational mode). Neutral HOMOs and cationic LUMO-βs at the vertical ion point (VI point) associated with these frozen distorted geometries are depicted in Supporting Information S5. Based on the effects of initial geometries on attosecond charge migration (see Supporting Information S6), the 12 normal modes of NCCl:OH2 can be divided into three categories, as depicted in Figure 6(a) (normal modes are shown in Figure 6(b)). It is interesting to note that the first category has almost no influence of initial geometry on the charge migration dynamics. For these initial geometries, both the time-scale and the magnitude of charge migration remain almost comparable to those observed for neutral equilibrium geometry. Initial geometries falling into the second category exhibit similar time scale to that observed for equilibrium geometry; however, magnitude of charge migration is reduced approximately to half of what predicted for equilibrium geometry. In the end, the third category features almost cessation of charge migration. Similarly, different initial geometries obtained due to rotation also influence attosecond charge migration dynamics. To illustrate this point, we address HOCl:OH2 system which does not show charge migration at its neutral equilibrium configuration: charge stays localized on the ClOH-end of the complex following vertical ionization. However, as evident in Figure 6(c), different initial geometries (for example, ‘a’ and ‘c’ configurations), which are obtained via rotation of H2O molecule with respect to the Cl…..O halogen bond, exhibit charge migration. Therefore, relative orientation of the lone pair orbital of donor H2O can influence hole migration dynamics in Cl…..O halogen bonded complex. We discuss these effects again in the General Discussion and Conclusions section.

(E) Effect of Donors: Electron donors (e.g., H2O and NH3) are often found to control strength and nature of noncovalent bonds (see Supporting Information S7).2-5 Therefore, it is interesting to investigate how different donors may also affect Attochemistry of halogen, chalcogen, pnicogen and tetrel bonded clusters. The direction of charge migration may change with the change of donor molecule. We illustrate this point by taking example of halogen bonded NCCl:NH3 and NCCl:OH2 complexes (see Figure 7). For the complex containing H2O donor, charge migrates from the AX-end to the H2O-end. On the other hand, charge migrates in opposite direction (i.e., from the NH3-end to the AX-end) in the complex containing NH3 donor. In general, ionization energies of two molecules constituting intermolecular noncovalent bonds determine the initial hole localization following vertical ionization. Experimental first ionization energies of NH3, ClCN and H2O are 10.1, 12.37 and 12.65 eV, respectively (see Supporting Information S8). Therefore, it is speculative that in NCCl:NH3 and NCCl:OH2 complexes the initial hole will be localized only on the NH3-end and ClCN-end, respectively. In addition to ionization energy, strength of noncovalent bonding interaction can also play an important role in determining initial localization of the hole.22 (F) Directionality in Large Cluster: A close inspection of the structures of different isolated large (A-X)m:(NH3)n and (A-X)m:(OH2)n clusters (m and n >1), where A represents F, Cl, CN, and NH2 substituents, and X features Cl, SH, PH2, and SiH3, reveals that these clusters may feature both hydrogen and non-hydrogen non-covalent bonding interactions. As an illustrative example, we can inspect (NCCl)m:(NH3)n neutral clusters, depicted in Figure 8(a). 8 ACS Paragon Plus Environment

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Neutral HOMO and cationic LUMO-β plots, shown in this figure for respective cluster, predict that the hole, which is initially localized on the NH3-end of the cluster, migrates partially only through the Cl…..N halogen bonding contact. Respective time scale of the charge migration as a function of cluster size is given in Figure 8(b). Similar charge migration is not observed through the N…..H hydrogen bonding contact in the same cluster. Theoretical prediction of this preferential attosecond charge migration through non-hydrogen noncovalent bonds over hydrogen bonds is quite intriguing. Indeed, these trends can provide insight into structure-function relations in the relevant non-hydrogen non-covalent bonded molecular crystals, in which charge migration through these noncovalent bonds becomes ubiquitous. Definitely further systematic study is necessary to carefully extract such useful information as a function of cluster size.

(G) Single Electron vs Multi-electron Scheme: True stationary hole density following the vertical ionization of a molecule or a molecular cluster, ρ h ( r ) , is defined as the difference between the stationary electron density of the neutral, ρ n ( r ) , and the stationary electron density of the initially created cation, ρ c ( r ) : ρ h ( r ) = ρ n ( r ) − ρ c ( r ) ………. (6) This is multi-electron perspective of the hole density. The same argument is also true when the time-dependent hole density, ρ h ( r , t ) , is expressed under multi-electron picture. However, so far, we have expressed the hole density using single electron scheme. Under the single electron scheme, the hole density is represented in terms of molecular orbital (more specifically lowest unoccupied-β Kohn-Sham orbital under unrestricted DFT formalism). Therefore, it is quite instructive that we compare the cationic LUMO-β density with the hole density obtained from equation 6 to confirm that the single electron scheme does not introduce any spurious effect into the present computational results. Furthermore, in the present work, we have used the DFT to explore the hole density dynamics. The DFT, in comparison with Hartree-Fock theory, is essentially a single Slater determinant scheme. It has been argued in literature38 that single Slater determinant approach may also introduce spurious effects into computational results in determining hole density. Therefore, it is also an important task that we compare and contrast the DFT results (single Slater determinant approach) with the results obtained from multi Slater determinant approach (CASSCF). Figure 9 compares and contrasts the neutral HOMO, cationic LUMO-β and the ρ h ( r ) densities for HOCl:NH3, NCCl:NH3, and H2NCl:NH3 complexes. Quite interestingly, we note that the LUMO-β density quite resemble the ρ h ( r ) density at all levels of theory. On the other hand, both the neutral and cationic Kohn-Sham and the CASSCF molecular orbitals suggest that vertical ionization must initiate charge migration in NCCl:NH3 and H2NCl:NH3 complexes: charge migrates from the NH3-end to the ClCN-end in NCCl:NH3 and from the H2NCl-end to the NH3-end in H2NCl:NH3 complex. Therefore, the Koopmans theorem breaks down for NCCl:NH3 and H2NCl:NH3 complexes due to orbital relaxation following vertical ionization. However, the charge, created on the ClOH-end following the vertical ionization of HOCl:NH3 complex, stays localized on the ClOH-end only. Both the CASSCF theory and the DFT corroborate these conclusions. Therefore, at least qualitatively, we show that single determinant approach along with single electron scheme (orbital picture) do not spoil the computational results presented in this feature article.



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IV. General Discussion and Conclusions: Recent literature shows that the exact nature of different A-X…..B intermolecular nonhydrogen noncovalent bonds (including halogen, chalcogen, pnicogen, and tetrel bonds) may differ from each other and the difference may come from several factors, including directionality, hydrophobicity, donor atom size, electron withdrawing ability, and etc.2-5 To the best of our knowledge, thus far, all the theoretical studies of non-hydrogen noncovalent bonds have been focused upon exploring these factors by calculating energetics, geometries and properties of the ground state wave function of the non-hydrogen noncovalent bonded clusters. In this regard, the present work features a departure, examining very fast (attosecond) charge migration through these noncovalent bonds. Furthermore, for the first time, we have attempted to review the Attochemistry of these non-hydrogen noncovalent bonded clusters based on the intrinsic characteristics of noncovalent bonding interactions, such as correlation strength, intermolecular distance, donors, initial nuclear configurations, large cluster formation, and etc. General discussion on the Attochemistry of non-hydrogen noncovalent bonded clusters must begin with a very relevant question: “how does the strength of noncovalent bonds affect predicted Attochemistry through these noncovalent bonds?” The timescales of Attochemistry of ionized halogen, chalcogen, pnicogen and tetrel bonded clusters are predicted to be quite similar (approximately in the 300-600 attosecond range). However, in general, we have observed a profound effect of nature and strength of the non-covalent bonding interactions on predicted Attochemistry. In order to address this, we shall revisit the context presented in Section II, where we have already drawn an interesting distinction between NCCl:NH3 and HOCl:NH3 halogen bonded complexes. The former complex shows charge migration while the later complex does not. In Section II, this difference was explained as due to the correlation between the neutral HOMO density and the cationic LUMO-β density of the respective complex (see Figure 2). This explanation undoubtedly does teem with the law of quantum chemical superposition (presented in equation 1 and 2); however, this do not appear to be completely tenable. What are the fundamental chemical properties of these complexes ultimately responsible for this distinction? This question is relevant because based on this understanding one may make predictions of other related nonhydrogen noncovalent bonded clusters. To address the above question, we closely examine halogen bonded NH3-based complexes with ClF, ClOH, ClCN, ClCF3 and ClCOOH molecules. Isolated NH3 molecule exhibits the lowest ionization energy as compared to the other isolated molecules, such as ClF, ClOH, ClCN, ClCF3 and ClCOOH.35 Therefore, it can be expected that FCl:NH3, HOCl:NH3, NCCl:NH3, F3CCl:NH3 and HOOCCl:NH3 complexes should feature the neutral HOMO density localized on the NH3-end of the respective complex. Indeed, the neutral HOMO densities are localized (mostly) on the NH3-end of the NCCl:NH3, F3CCl:NH3 and HOOCCl:NH3 complexes (not shown here for brevity).35 Quite counter-intuitively, however, Figure 10 depicts that the neutral HOMO density is localized on the FCl- and HOCl-ends of FCl:NH3 and HOCl:NH3 complexes, respectively. This is caused by very strong (in fact, FCl:NH3 and HOCl:NH3 complexes feature the strongest halogen bonding interaction among all complexes mentioned here: see Figure S7 in Supporting Information) halogen bonding interaction (between the lone pair electrons of NH3 and σ-hole of ClF and HOCl, respectively), due to which, lone pair orbital of NH3 molecule is extraordinarily stabilized and that is why the neutral HOMO is not localized on the NH3-end of the FCl:NH3 and HOCl:NH3 complexes anymore. 10 ACS Paragon Plus Environment

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The above argument is clearly evident in the neutral HOMO and the cationic LUMOβ density plots for FCl:NH3 and HOCl:NH3 complexes at different Cl.....N halogen bond distances, as illustrated in Figure 10. A bond critical point (performed using Atoms in Molecules theory) exists for all configurations, which are indicative of the existence of halogen bonding interaction in these complexes at the given halogen bond distance. For the halogen bond distance longer than 2.72 Å in FCl:NH3 complex (which is larger than the equilibrium distance 2.32 Å), the HOMO density exhibits the lone pair orbital of NH3 because the halogen bonding interaction energy is significantly reduced at this longer halogen bond distance. Similar trend is also found for HOCl:NH3 complex (see Figure 10). These results indicate that once the halogen bond interaction becomes weaker, the neutral HOMO is essentially determined by the relative ionization energies of the two complex-forming moieties, which may trigger charge migration following vertical ionization. In fact, when we examine other halogen bonded complexes, we find a cut-off in binding energy (here binding energy is defined as the difference between the sum of the monomer energies and complex energy), as shown in Figure 11. Complexes, showing binding energy above the cut-off energy (above the shaded area in Figure 11), exhibit no charge migration, whereas charge migration is evident in complexes featuring binding energy below the cut-off energy. The consistency of the MP2 and DFT-data sets confirms that the trend is reasonable. This trend may have a fundamental significance in understanding attosecond charge migration through nonhydrogen noncovalent bonds. Therefore, relative ionization energies of the molecules and strength of noncovalent bonding interactions must play an important role in defining the Attochemistry of nonhydrogen non-covalent bonded clusters. Undoubtedly more work is necessary to unravel all facets of the above-mentioned trend. Recently, symmetry-adapted perturbation theory (SAPT) has been proposed for intermolecular interactions.38 The SAPT renders a perturbative expression for the interaction energy. The total interaction energy can be easily calculated as the difference between the sum of the monomer energies and complex energy (as shown above). Using SAPT, one can further decompose this interaction energy into contributions from classical Coulomb interaction, exchange-repulsion, interaction of the permanent multipole moments of one monomer and the induced multipole moments of the other, dispersion interaction energy and from the Hartree-Fock (HF) correction for higher-order contributions to the total interaction energy.40 In future, it would be interesting to investigate how Attochemistry of non-hydrogen noncovalent bonded clusters are affected/influenced by these different contributions of the noncovalent bonding interactions. Furthermore, in Section III(c), we have seen that there exists a strong connection between total correlation energy and the charge migration time scale. However, exact nature of the correlation interaction contributing to the trend is not well-understood, thus far. We believe that application of SAPT would help one decipher this problem and in near future we aim at doing that. In this context, we also note that weakening the non-hydrogen non-covalent bonding interaction (which definitely would affect the correlation interaction as well) increases the charge migration time scale. Figure 12 plots the charge migration time scales for some non-hydrogen non-covalent bonded clusters as a function of the respective noncovalent bond distance. The figure clearly exhibits a trend: longer non-covalent bond yields lower cationic LUMO-β and cationic HOMO-β energy gap, which results in longer time scale of charge migration. So far, only periodic movement of the hole density at the vertical ion point of halogen, chalcogen, pnicogen, and tetrel bonded clusters has been discussed. However, at later time, this charge oscillation must stop, which may localize the charge. In the end, 11 ACS Paragon Plus Environment


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nuclear motion should start on the cationic potential energy surface and the nuclear motion on the cationic surface may well be directed by this localized charge. With regard to these points, it is quite instructive to ask two questions (very relevant to Attochemistry): (1) how does charge oscillation stop?; and (2) can site-specific localization of the positive charge in non-hydrogen noncovalent bonded clusters following vertical ionization direct the proceeding chemical reactivity? We shall end the General discussion on Attochemistry of ionized halogen, chalcogen, pnicogen and tetrel bonded clusters after addressing these two questions.

Charge Oscillation, Localization and Charge-Directed Reactivity: So far, attosecond charge migration dynamics in ionized halogen, chalcogen, pnicogen and tetrel bonded clusters has been discussed based on a single frozen nuclear geometry (more precisely, the equilibrium geometry of the neutral). These simulations predict oscillatory motion of charge (or electron) density at a well-defined frequency. However, these simulations neglect the spatial delocalization of the nuclear wavepacket before ionization. The nuclear wavepacket width may dramatically affect the post-ionization electron dynamics, as shown recently by Robb et al.44 We have used the Wigner distribution function, which is a quantum distribution function in classical phase-space, to represent the delocalized nuclear wavepacket. This leads to a distribution of fixed nuclear geometries, which results in a distribution in initial energy gaps and therefore, results in a distribution of oscillation periods in the post-ionization charge density. Figure 13 features the oscillations of charge density observed in the case of an ensemble of fixed geometries (distributed around the neutral equilibrium geometry). For NCCl:NH3 system, 100 nuclear geometries were sampled from the Wigner distribution functions using the ab initio multiple spanning (AIMS) dynamics module implemented in Molpro 2012 package.42 Use of the Wigner distribution helps one to mimic the quantum distributions of the vibrational ground states under the harmonic oscillator approximation. For this computation, normal modes of NCCl:NH3 complex were analyzed at the MP2/631+G(d,p) level of theory. In Figure 13, we have averaged the electron dynamics for each member in the ensemble of nuclear geometries (they were simulated independently). The averaged oscillation amplitudes exhibit more than 5 oscillations, spanning over first 8 femtosecond (fs), before the coherent oscillation fully damps. Two points are very important to note here: (a) the coherent electron dynamics following ionization does not quickly (immediately after one oscillation) disappear; and (b) charge density finally gets delocalized over both the NH3and the ClCN-sides. Furthermore, it is evident that the nuclear wavepacket width of the neutral NCCl:NH3 complex leads to the damping of the coherent electron oscillations following vertical ionization. The distribution of nuclear geometry gradually ceases charge oscillation following vertical ionization of this halogen bonded species, rendering charge localization (a stationary charge density). We believe that this is a general trend not only for halogen bonded NCCl:NH3 system, but also for other non-hydrogen non-covalent bonded systems. Therefore, we have seen that as a result of the nuclear wavepacket delocalization, the charge oscillation decoheres in non-hydrogen noncovalent bonded clusters. This decoherence results in localization of the charge in the cluster. Taking an example of NCCl:NH3, we find that the partial charge is localized on both NH3- and ClCN-ends. How does this localization of charge affect subsequent chemistry? To address this question, at least qualitatively, we have explored the reaction pathways (see Figure 14 a and b) for NCCl:NH3 radical cation at 12 ACS Paragon Plus Environment

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the wB97XD/6-31+G(d,p) and CASMP2/6-31+G(d,p) levels of theory. Associated one electron stationary hole density plots obtained at different critical points on the cationic potential energy surfaces (PESs) of NCCl:NH3 complex are also given. Both the DFT and the CASMP2 levels of theory predict that the halogen bonding interaction is no longer stable on the cationic potential energy surface of NCCl:NH3. The strength of hydrogen bonding interaction dominates over that of the halogen bonding interaction. One electron stationary hole density plots of the halogen bonded and hydrogen bonded configurations of the radical cationic NCCl:NH3 complex differ significantly. One can argue that localization of positive charge on the NH3 site makes this moiety more acidic, which may in turn stabilize the hydrogen bonded configuration as compared to the halogen bonded configuration. Here we note that the in-plane orbital localized on the NH3-end is polarized to out-of-plane orbital within 500 attosecond timescale upon vertical ionization. This polarization of charge might be the driving force for conformer switching on the cationic potential energy surface (PES). Therefore, one can, at least qualitatively, contend that the reactivity of ionized NCCl:NH3 complex may be hole-directed and hole migration at the vertical ion point may have preluding effect in defining subsequent chemical reaction dynamics of NCCl….NH3 on its doublet cationic PESs. A nuclear motion coupled electron dynamics simulation43 is, however, required to obtain more details of possible charge-directed reactivity of ionized halogen bonded complex NCCl:NH3. In the end, we comment on the experimental investigation of the Attochemistry of ionized halogen, chalcogen, pnicogen and tetrel bonded clusters by means of the higher order harmonic emission (HHE) spectroscopy. The HHE occurs when an electron, which is first liberated from a molecule under an intense laser field, recombines with the parent molecular ion.44,45 The HHE reveals evolving electronic environment of the nascent radical cation by the amplitudes, phases and polarization of the emission. Recent experiments show that measurements of the phases and amplitudes of high harmonic radiation can be used to follow multi-electron dynamics in molecules with attosecond temporal resolution.44,45 We strongly hope that, in near future, the Attochemistry of ionized non-hydrogen noncovalent bonded clusters would be explored with the help of HHE spectroscopy. Currently we are setting up HHE-based experiments in our laboratory to explore the Attochemistry of the halogen, chalcogen, pnicogen and tetrel bonded ionized clusters.

Supporting Information: S1. Definition of “Charge Migration”; S2. Attochemistry vis-à-vis Femtochemistry: Definition of “Attochemistry”; S3. Details of Quantum Mechanical Simulation of Charge migration Dynamics; S4. Plots of Time evolution of the hole population (background subtracted and then normalized) on the NH3-end; S5: Neutral HOMOs and cationic LUMOβs for distorted geometries obtained along each normal mode co-ordinate of NCCl:OH2; S6: Snapshots of time-evolution of the hole density following removal of an electron from the HOMO obtained at the classical turning point geometries; S7. Plots of Binding energy of AX:NH3 complex as a function of X…..N non-covalent bond distance; S8. References to Ionization Energies of H2O, ClCN and NH3. This information is available free of charge via the Internet at http://pubs.acs.org

Acknowledgments: Past co-workers (Ganga Periyasamy, Bhaskar Rana and Mohammed Musthafa Iqbal) who have partly contributed to the work described in this article are gratefully acknowledged. 13 ACS Paragon Plus Environment


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The work was supported financially by the DST SERB (Grant No. SB/S1/PC-50/2013). We thank Professor E. Arunan and Professor E. D. Jemmis (IPC, IISc) for their inquisitive approaches to understand non-covalent boning interactions. The motivation for the work presented here, in part, came from many discussions held on non-covalent bonding interactions with their groups during student seminars at the IPC department. We gratefully acknowledge their silent influence on our work.

Biographies: Sankhabrata Chandra obtained his B.Sc. degree from St. Xavier’s College in 2013. Currently he is working with Dr. Atanu Bhattacharya as an integrated PhD student at Indian Institute of Science.

Atanu Bhattacharya graduated from Colorado State University in 2010 under supervision of Prof. Elliot R. Bernstein. He then spent two and half years as a postdoctoral fellow with Dr. Nicholas Camillone III at Brookhaven National Laboratory (2010−2012) and six months as a program specific researcher with Prof. Toshinori Suzuki at Kyoto University (2012−2013). He is currently working as an assistant professor at Indian Institute of Science. His primary research interests are in Attochemistry and Femtocatalysis.


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Figure 1: Snapshots of time-evolution of the hole density following removal of an electron from the HOMO of neutral H2NCl:NH3, H2NSH:NH3, H2NPH2:NH3 and H2NSiH3:NH3 complexes, computed at the wB97XD/6-31+G(d,p) level of theory. A contour value of 0.0004 is used for orbital drawing. More continuous plots of time evolution of the hole population on the NH3-end are given in Supporting Information S4.


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Figure 2: Weights of the neutral HOMO on all stationary cationic MOs for (a) NCCl:NH3 (b) HOCl:NH3 complexes, computed at the wB97XD/6-31+G(d,p) level of theory.



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Figure 3: Time scale of hole migration predicted using 6-31+G(d,p), aug-cc-pVDZ, and augcc-pVTZ basis sets for halogen bonded H2NCl:NH3, chalcogen bonded H2NSH:NH3, pnicogen bonded H2NPH2:NH3 and tetrel bonded H2NSiH3:NH3 complexes.


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Figure 4:(a) Neutral HOMOs, cationic LUMO-βs and total hole density differences for NCCl:NH3, H2NSH:NH3, H2NPH2:NH3 and H2NSiH3:NH3 complexes, computed at the wB97XD/6-31 + G(d,p) level of theory and calculated at the X…N intermolecular distance of 10 Å. (b) Bold line shows change of population as a function of time at the equilibrium geometry of the respective complex and the dotted line shows change of population as a function of time at X.....N distance of 10 Å.



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Figure 5: Charge migration time scale is plotted as a function of total correlation energy contributed to the respective noncovalent bonding interaction: (a) DFT- and (b) MP2-results.


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Figure 6: (a) Maximum change in hole population at the H2O moiety of NCCl:OH2 complex for the optimized geometry and for distorted geometries obtained along each normal mode coordinate with displacement, qi,new= qi,opt± 0.5qij, computed with the wB97XD DFT functional and the 6-31+G(d,p) basis set. Here 0th mode represents the frozen equilibrium geometry. (b) Respective modes are defined. (c) Snapshots of hole densities obtained at different geometries (a-d) obtained via rotation of H2O molecule along the Cl…..O halogen bond, computed at the wB97XD/6-31+G(d,p) level of theory.



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Figure 7: Change in direction of charge migration is observed when different donors are used.


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Figure 8: (a) Optimized structures and associated neutral HOMOs and cationic LUMO-βs are depicted for (NCCl)m:(NH3)n clusters. (b) Relative change in hole population at the ClCN molecule, which is involved in halogen bonding interaction, is depicted as a function of time.



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Figure 9: Neutral HOMO, cationic LUMO-β and ρ h ( r ) (calculated at the wB97XD/631+G(d,p) and CASSCF/6-31+G(d,p) levels of theory) for HOCl:NH3, NCCl:NH3 and H2NCl:NH3 complexes are illustrated.


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Figure 10: (a) Neutral HOMO and cationic LUMO-β density plots (wB97XD/6-31+G(d,p)) for (a) FCl:NH3 and (b) HOCl:NH3 complexes, calculated at different halogen bond distances.



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Figure 11: The Cl…..N and Br…..N halogen bonded complexes, exhibiting total interaction energy in the shaded area, show charge migration through the respective halogen bond. Charge migration dynamics has been simulated at wB97XD/6-31+G(d,p) level of theory.


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Figure 12: Charge migration time scale is plotted as a function of the respective nonhydrogen noncovalent bond distance (wB97XD/6-31+G(d,p)-results).



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Figure 13: Hole dynamics in NCCl:NH3 complex: Normalized line represents the average of the results obtained for the ensemble of nuclear geometries. The nuclear distribution (100 sampled geometries) reproduces the vibrational ground state before ionization. This nuclear distribution results in decoherence in coherent hole oscillation following vertical ionization of NCCl:NH3 complex.


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Figure 14: (a) The wB97XD/6-31+G(d,p) (b) CASMP2(8,6)/6-31+G(d,p) energy profile diagrams of NCCl:NH3 radical cation. Relative energies are presented with respect to the neutral equilibrium geometry energy (S0).



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TOC Graphics


Attochemistry of Ionized Halogen, Chalcogen, Pnicogen, and Tetrel

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