Kinetic and potential energy contributions to a chemical bond from the

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Kinetic and Potential Energy Contributions to a Chemical Bond From the Charge and Energy Decomposition Scheme ETS-NOCV Filip Sagan, and Mariusz P. Mitoraj J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b01420 • Publication Date (Web): 06 May 2019 Downloaded from http://pubs.acs.org on May 6, 2019

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The Journal of Physical Chemistry

Kinetic and potential energy contributions to a chemical bond from the charge and energy decomposition scheme ETS-NOCV Filip Sagan, Mariusz P. Mitoraj* Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, R. Gronostajowa 2, 30-387 Krakow, Poland AUTHOR INFORMATION Corresponding Author Mariusz Paweł Mitoraj, Jagiellonian University, Faculty of Chemistry, Department of Theoretical Chemistry, Gronostajowa 2, 30-387 Kraków, Poland, tel./fax +48 12 686 2379, email: [email protected]. ABSTRACT This work provides novel physical insight into the nature of a chemical bond by exploring qualitative and quantitative relation between the Natural Orbitals for Chemical Valence (NOCV) based deformation density bonding channels Δρi (i= σ, π, δ, etc.) and the corresponding kinetic ΔTi and potential energy ΔVi contributions within the charge and energy decomposition scheme ETS-NOCV implemented in the Kohn-Sham based Amsterdam Density Functional (ADF) package. It is determined, that inter–fragment dative and covalent-type electron charge reorganizations upon formation of a series of strong and weak bonds employing main-group elements are due to lowering of the negative kinetic energy contributions, as opposed to the intra–fragment polarizations (e.g. hyperconjugations in ethane) which are, in contrary, driven by the potential energy (electrostatic) component. Complementary, formation of -contributions in N2 is accompanied by lowering of both kinetic and potential energy constituents. Remarkably,

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well-known globally stabilizing back-donation (M  ligand, where M is a transition metal) and donation (ligand M) processes, ubiquitous in organometallic species, have been discovered for the first time to be driven by the opposite ΔTi/ΔVi mechanisms – namely, the former contribution is associated with the negative kinetic term (which outweigh the positive potential energy), whereas the latter charge delocalization into electrophilic transition metals leads to an attractive electrostatic stabilization (and positive kinetic energy). TOC GRAPHICS

KEYWORDS Charge and energy decomposition ETS-NOCV, Bonding Analysis, Kinetic and potential energies.


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Introduction In depth understanding of factors determining the nature of a chemical bond is of paramount importance for physical chemistry.1 To this end, nowadays a number of methods and quantities suitable for in depth bonding analyses are available on the market which are defined in either function or real space resolution.1 As examples of the former group one can list for example the valence bond (VB) type approaches2 well known and recognized Natural Bond Orbitals (NBO)3, Domain Averaged Fermi Holes (DAFH)4, Localized-orbital Locator profiles (LOL)5 as well as a variety of widely applied energy and charge decomposition schemes [e.g. symmetry adapted perturbation theory (SAPT)6 by Jeziorski, Moszyński and Szalewicz, Morokuma type EDA7, Head-Gordon's EDA based on Absolutely Localized Molecular Orbitals (ALMO)8, populational space approach to EDA by Korchowiec9, Local Energy Decomposition based on CCSD(T) by Neese and coworkers10 and other1.Within the second group one can distinguish for example the QTAIM theory11, Electron Localization Function (ELF)12, reduced density gradient (NCI)13, Interacting Quantum Atoms (IQA) energy decomposition scheme14 or Density Overlap Regions Indicator (DORI).15 The existence of so many bonding models and descriptors is desirable since it allows to capture various peculiarities of chemical bonding.1 On the other hand, one can notice, that each method possesses its own quantities, names and parameters leading to a sort of nomenclature dichotomy, what in turn can cause significant difficulties in terms of getting a unified and clear interpretation of the nature of chemical bonding.16 From this respect coming to the roots based on the kinetic (T) and potential (V) energies as the fundamental constituents of Hamiltonian seems very promising direction for further development of bond theories. It is crucial to emphasize, that the importance of lowering in kinetic energy due to formation of simple covalent bonds has been recently emphasized by Ruedenberg and coworkers17-20; such interpretation is in line with the conclusions by Hellmann21 and others22-27. Unfortunately, T/V parameters in most of recently popular chemical bonding descriptors/methods are explicitly not available and thus, they are not analyzed and discussed quantitatively. From this respect, in this work we provide unprecedented qualitative and quantitative relation between formation of various types of deformation density bonding channels i (i= , , , etc.) and the corresponding kinetic Ti and potential energy Vi contributions within our


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charge and energy decomposition scheme ETS-NOCV28 for the entire spectrum of chemical bonds starting from sizeable donor-acceptor ones (involving both main and transition metals), going through typical covalent connections to end up with several types of non-covalent interactions. Methodology Kinetic T and potential V energy resolution of the ETS-NOCV method The Natural Orbitals for Chemical Valence (NOCVs) are eigenvectors i which constitute an unitary U matrix obtained from a simple diagonalization the deformation density matrix Porb expressed in the basis of orthogonalized fragment orbitals k :

𝑀

𝑜𝑟𝑏 UT𝑃 U=v , i =∑𝑘 = 1𝑈𝑖𝑘𝑘

[1]

where v is a resulting diagonal matrix collecting NOCV’s eigenvalues and M stands for a number of fragment-orbitals. Porb (expressed in Löwdin representation) is calculated as a difference between a density matrix of a molecule and those obtained for molecular fragments. It has been shown, that NOCV’s allow for unprecedented decomposition of molecular deformation density orb into chemically meaningful bonding contributions orb(i) with different symmetries (e.g. , , , etc.) even for molecules with no symmetry:

M/2

M/2

orb =∑i = 1vk( ― 2―k + 2k) = ∑i = 1orb (i)

[2]

It is crucial, that only a few contributions orb(i) constitute the main shape of overall orb.28-38 Our aim in this work is to provide a bridge between orb(i) and the corresponding changes in the kinetic Torb(i) and potential Vorb(i) energy contributions for a range of chemical


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bonds starting from typical donor-acceptor (involving main and transition metals), going through covalent types to end up with weak non-covalent interactions. In order to achieve this goal we have used our NOCV’s combined with the energy decomposition scheme (ETS) developed by Ziegler and Rauk39,40 In the latter scheme total interaction energy ΔEtotal between two fragments is divided into the following components ΔEtotal = ΔEdist + ΔEelstat + ΔEPauli + ΔEorb. ΔEdist is called distortion term and it corresponds to the energy needed for geometry change from the fragment’s optimal geometry to the one in the molecule. Next term (ΔEelstat) is the electrostatic interactions between fragments in their position within the molecule. The third term separates Pauli repulsion (ΔEPauli) between occupied orbitals of fragments. Finally, ΔEorb term which corresponds to Δρorb (see Eq. 2) accounts for an energy change upon charge delocalization due to formation of a chemical bond.39,40 It is crucial to point out that, ΔTorb and ΔVorb sum up to ΔEorb, and they do not obey the virial theorem (since ΔEorb constitutes only a part of ΔEtotal ). In this work we propose to derive a simple relation between orb(i) and Torb(i) / Vorb(i) due to the following formula of calculation ΔEorb:

M/2

M/2

TS TS TS TS ΔEorb = Tr(PorbFTS)=Tr(UTPorbUUTFTSU)=Tr(Porb NOCVFNOCV)=∑i = 1viFii = ∑i = 1vi(Tii + Vii )=

∑M/2 [Torb(i) + Vorb(i)]=∑M/2 Eorb(i) i=1

i=1

[3]

where FTS is a Kohn-Sham Fock matrix defined for the potential in a midpoint between the sum of fragment potentials and the potential of the final molecule, as formulated by ETS39,40 and UUT TS is a unity matrix. Finally, Porb NOCV and FNOCV are the corresponding matrices unitary transformed

to NOCV representation (by U/UT ). Finally, taking advantage by the fact, that NOCV’s appear in pairs28,36-38 (-k, k) corresponding to the same absolute NOCV’s eigenvalues |vk|, one can define an outflow 𝑜𝑢𝑡𝑓𝑙𝑜𝑤

𝑜𝑟𝑏

(i) and inflow 𝑖𝑛𝑓𝑙𝑜𝑤 𝑜𝑟𝑏 (i) of electron density within each orb(i):


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M/2

M/2

M/2

2 2 𝑜𝑢𝑡𝑓𝑙𝑜𝑤 (i) + 𝑖𝑛𝑓𝑙𝑜𝑤 orb =∑i = 1vk( ―  ―k + k) = ∑i = 1orb (i) = ∑i = 1[𝑜𝑟𝑏 𝑜𝑟𝑏 (i)]

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[4]

The corresponding T/V energy terms can be extracted from Eorb(i) = Torb(i) + Vorb(i): M/2

M/2

outflow inflow outflow inflow Eorb = ∑i = 1(Torb(i) + Vorb(i)) = ∑i = 1(Torb (i) + Torb (i) + Vorb (i) + Vorb (i)) [5]

Equations 3–5 have been implemented in the developer version of the ADF program.41,42 We have applied in ETS-NOCV analyses the ADF/BP-D3/DZP with the exceptions for Ni and Cr complexes, where TZP has been used and benzene dimer together with M|CO adducts where BPD3/TZ2P have been utilized. All computational details are summarized in Table S1 in the ESI. It is notable, that BP and BP-D3 have been proven to provide reliable results for transition metal systems as well as for non-covalent interactions.43,44 It must be emphasized, that very elegant reviews on applicability of ETS and ETS-NOCV schemes are available in Ref. [40] and Ref. [33], respectively.


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Results and Discussion At first stage, let us consider a simple model system of hydrogen cation and carbon monoxide [H]+–CO. The overall bonding is determined here mostly by the orbital interaction term (Eorb = –0.2593 a.u.), Table S2. It shall be referenced, that the overall interaction energy ΔEint = –0.2368 a.u. (from BP-D3/DZP) compares well with the previously reported by Lupinetti et al. (ΔEint = –0.2378 a.u.) due to correlated MP2 and CCSD(T) calculations. 45 The majority of Eorb corresponding to ΔΕorb(1)= –0.2209 a.u. stems from the donation from the lone electron pair of carbon (Lp) into the empty 1s(H+) orbital, as can be deduced from the most important NOCV-based deformation density channel 1 (Equation 2), Figure 1.


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Figure 1: Balance of the kinetic and potential energies for the most crucial NOCV based deformation density contributions (1, 2, rest) for H+|CO system. Energies are in Hartree. According to Eq. 5 it can be further decomposed into kinetic and potential energy terms – it is found, that the negative kinetic term ΔTorb(1)= –0.400134 a.u. outweighs the potential one which is positive ΔVorb(1)= +0.18045 a.u., Figure 1. The former can be interpreted as the ‘release’ of the kinetic ‘pressure’, built when the orthogonalized fragments were brought to their equilibrium positions in the final configuration of [H+]–CO, upon a bond formation. According to Eq. 4 each of these terms can be analyzed in terms of separated processes of electron density outflow and inflow from a given fragment. The negative ΔTorb(1) originates solely from the kinetic energy lowering due to the -electron depletion from CO moiety (ΔTorb(1-outflow) = – 1.2789 a.u.) which is only partially countered by an increase in the kinetic contribution (ΔTorb(1inflow) = +0.8775 a.u.) upon electron density accumulation in the vicinity of [H+], Figure S1. Similarly, the gain of potential energy contribution (ΔVorb(1-inflow) = –1.3636 a.u.) due to the latter process is unable to compensate for the potential energy loss (ΔVorb(1-outflow) = +1.5441 a.u.) caused by depopulation of lone pair of CO, what gives rise to the overall positive ΔVorb(1)= +0.1805 a.u. Charge depletion from CO leads to overall destabilizing component ΔEorb(1outflow)=+0.2652 a.u. [due to positive ΔVorb(1-outflow)], whereas the charge buildup in the vicinity of [H+] is clearly favorable ΔEorb(1-inflow)= –0.4861 a.u. as a result of the ΔVorb(1inflow)= –1.3636a.u. (caused by the appearance of electrons-nuclei stabilization). We have additionally analyzed such charge transfer components (OC)M+ (ΔΕorb(1), 1) for the derivatives containing the main group cations as electron acceptors, Table 1. We have consistently determined, that the stabilization within ΔΕorb(1) which exhibits the donation (OC)Lpns (M+ for n=2–4, n–principal quantum number), is due to negative ΔTorb(1) values, Table 1. Although our data are based on decomposition of solely orbital interaction term, these results clearly highlight the importance kinetic energy also for dative bonding.17-27,47-48 The second strongest [though far weaker than ΔΕorb(1)] are the two degenerated (orthogonal) deformation density components 2,3 corresponding to ΔΕorb(2,3) = –0.0129 a.u., which also contribute to CO[H+] bonding and they describe the polarization of CO fragment within its π orbitals, Figure 1, in the middle. Accumulation of electron density within a wide area of carbon atom at the expense of the oxygen leads to enhancement of CO covalency, what in turn explains


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nicely, in line with the pioneering suggestion by Lupinetti et al. 45 , the strengthening (blue-shift) of this bond upon interaction with H+. Interestingly, as opposed to the nature of charge delocalization terms (ΔΕorb(1), 1), the -polarization stabilization is caused by the opposite mechanism, i.e. the negative potential contributions ΔVorb(2,3) = –0.0923a.u. overcompensate the rise in kinetic energies ΔTorb(2,3) = + 0.07932 a.u., Figure 1. The same trend is valid when considering other main groups systems, Table 2, Table S3. It can be classically interpreted as a relieve (drop) of electron–electron repulsion due to intra-fragment electron density reorganization. Finally, the reminder of deformation density rest with the corresponding ΔΕorb(rest) = –0.00329 a.u., Figure 1, on the right, showing a -polarization of CO, is also driven by the potential energy factor ΔVorb(rest) = –0.35735 a.u. It must be added, that intra–fragment charge delocalizations which occur herein are obtained in a single step during fragment – orbitals relaxation (bond formation) [Eq. 3], as opposed to a number of other elegant approaches8–10 where a polarization term is calculated as a separate stage of an entire energy decomposition procedure. Table 1: Balance of kinetic and potential energy terms for the donation (OC)M+ component (ΔΕorb(1), 1) in M+|CO complexes. ΔTorb(1)

ΔVorb(1)

ΔEorb(1)

[Li]+(2s) ← CO

-0.22245

0.21015

-0.01230

[Be]2+(2s) ← CO

-0.44197

0.33613

-0.10584

[Na] +(3s) ← CO

-0.15949

0.15321

-0.00628

[Mg]2+(3s) ← CO

-0.30366

0.25720

-0.04645

[K] +(4s) ← CO

-0.12015

0.11583

-0.00432

[Ca]2+(4s) ← CO

-0.18979

0.15975

-0.03004

Table 2: Balance of kinetic and potential energy terms for the -type CO polarizations (ΔΕorb(2,3), 2,3) in M+|CO complexes.

[Li]+| CO

ΔTorb(2,3)

ΔVorb(2,3)

ΔEorb(2,3)

0.01027

-0.01272

-0.00244


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[Be]2+| CO

0.02294

-0.04245

-0.01951

[Na] + | CO

0.00461

-0.00609

-0.00147

[Mg]2+| CO

0.01373

-0.02381

-0.01009

[K] +| CO

0.00060

-0.00147

-0.00088

[Ca]2+| CO

0.00796

-0.01439

-0.00643


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Figure 2. Benzene and borazine dimer (upper part) displaying polarization and charge transfer terms, respectively, together with the corresponding ΔTorb/ΔVorb. Dimers of dodecahedrane bonded through CH•••HC and BN-dodecahedrane connected through BH•••HN [where the two C-C pairs are substituted by the isoelectronic B-N units] (bottom part). In order to further study the nature of inter– and intra–fragment electron density reorganizations upon a bond formation in other systems, we have chosen a sandwich type benzene dimer (driven mostly by dispersion, Table S4), and its boron-nitrogen counterpart – borazine dimer, Figure 2A. The obtained deformation densities clearly prove, that enhanced polarity of the latter enables a transition from the typical very weak (Eorb=–0.0002a.u.) intrabenzene polarizations (caused by the Pauli repulsion within π-π clash) to formation of stronger covalent-dative charge transfer (Eorb=–0.0020a.u. ) in borazine dimer, Figure 2A. Due to more efficient interaction between monomers, the ring-ring distance in borazine dimer shortened to 3.397 Å compared to 3.551 Å in benzene dimer, which is in line with the previous reports49. In line with the previous findings (Tables 1, 2 and Figure 1), we have observed, that the latter inter– fragment charge delocalization is driven by the negative ΔTorb, whereas the benzene’s polarization is due to the dominance of stabilizing potential energy ΔVorb, Figure 2A. It is important to highlight, that the charge delocalization mechanisms (donoracceptor) based on leading stabilizing ΔTorb is also discovered in the separated hydrogen bond channels: NH•••N [orb(1), D(N-N) = 2.806 Å] and NH•••O [orb(2), D(N-O) = 2.812 Å] in adenine-thymine (A–T) base pair (Figure 3A) and other non-covalent interactions including -hole and tetrel bonding, Figure S2. Again, the intra–fragment π-polarizations [(4+5)] within A–T dimer is driven by the stabilizing potential energy ΔVorb, Figure 3. It should be noted that the bonding within A-T dimer has been deeply described by Fonseca Guerra et al.50,51 Our ETS data fits well to their findings (Table S5). We have additionally demonstrated herein, that  and π channels within A–T are determined by different ΔTorb / ΔVorb mechanisms.


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Figure 3. The two main deformation density channels describing NH•••N and NH•••O connections in adenine-thymine base pair together with the sum of the two most important polarization channels (A), compared to typical covalent C-C bond and hyperconjugation components in ethane molecule (B).

We have applied the same strategy of isoelectronic substitution of two carbon atoms into the corresponding boron and nitrogen within the dodecahedrane dimer in order to understand the nature of dihydrogen bonding B-H-•••+δH-N with respect to similar homopolar dihydrogen interactions C-H+•••+δH-C, Figure 2B. The latter are particularly interesting in the light of recent topical knowledge describing sterically demanding groups as a source of London dispersion stabilization which can in many cases overcompensate the Pauli repulsion and provide overall stabilization.52-57 Homopolar dihydrogen interactions C-H+•••+δH-C in dodecahedrane dimer have been also found and quantitized by Shaik et al.58 Although, there is some consensus, that inter-molecular homopolar C–H•••H–C non-covalent interactions are dispersion dominated,56,57 (Table S4) delineation of other bonding contributions including electrostatic term and particularly understanding the nature of electron density reorganization within C–H•••H–C is of


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paramount importance. The overall deformation density  (corresponding to Eorb = –0.0076 a.u.) which describes the charge delocalization due to dihydrogen bonding B-H-•••+δH-N between partially BN-substituted dodecahedrane units clearly depicts well established (BH)*(N-H) transfer, Figure 2B – it is reflected by the elongation of N–H connection by ca. 0.007 Å. Such observation is experimentally reflected in IR red shifts as indicated by a series of high quality works by Shubina and coworkers.59-62 This is expectedly due superior stabilizing Torb=–0.03201 a.u., Figure 2. Interestingly, an inspection of  corresponding to homopolar C– H•••H–C interactions between unsubstituted species reveals quite comparable pattern, namely, covalent-type outflow of electron density from (C-H) bonds is noted and the accumulation in H•••H region – this is, similarly to other charge transfer terms, driven by negative Torb=– 0.02622 a.u., Figure 2B. Exactly the same is valid in the case of formation of a typical (C-C) bond (Eorb=–0.1381 a.u.) in ethane, though, expectedly, the kinetic stabilization is now far more pronounced Torb=–0.1732 a.u., Figure 3B. Significantly weaker (Eorb=–0.004 a.u.) and degenerated -type hyper conjugation terms due to intra-methyl (C-H)*(C-H) charge delocalizations are driven by Vorb= –0.04311a.u., Figure 3B. The presence of both (C-C) and -polarization channels have been already noted in the previous works (Table S5). Consistently, the strongest lowering in kinetic energy with Torb(1)= –0.9770 a.u. (counterbalanced only partially by the positive Vorb(1)= +0.6085 a.u.) is associated with the formation of -component in covalently triple bonded N2 molecule, Figure 4. Interestingly, the two orthogonal (NN) contributions orb(2,3) are, contrary to all discussed NOCV contributions, driven by both stabilizing kinetic ΔTorb(2,3)=–0.0601a.u. and ΔVorb(2,3)=–0.037 a.u. potential energy terms giving rise to the overall stabilization Eorb (2, 3)= –0.0977 a.u. (per a single -component), Figure 4. It is necessary to reference, that the nature of chemical bonding in N2 has been already studied by other authors (Table S5) – we have added herein the new knowledge pointing out the importance of both kinetic Torb and potential Vorb contributions in the formation of (NN) and (NN) bonds.


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Figure 4. The main deformation density channels orb(1), orb(2), orb(3) and the corresponding ΔTorb/ΔVorb describing  and  contributions to N2 bonding.

Finally, we briefly comment on the importance of Torb/Vorb in the most important DewarChatt-Duncanson (DCD) model of chemical bonding in organometallic chemistry based on (1) ethylene complex with Ni-based catalyst and (2) (CO)5Cr=CH2 complex, Figure 5. It has been demonstrated through the recent years, that ETS-NOCV is perfectly suited for qualitative and quantitative description of DCD bonding due to separation (and quantification at Eorb level) of metalligand (back-donation) and ligandmetal (donation) charge transfer processes.28-36 Namely, in both cases the -back-donation processes dxz(Cr)2p(CH2) and dxz(Ni)*(C2H4) corresponding to Eorb = –0.08064a.u. and Eorb = –0.06087a.u., respectively, are naturally (without imposing any constraints) separated from the -contributions (CH2)  dz2(Cr), (C2H4) dz2(Ni) with Eorb = –0.07858a.u. and Eorb = –0.04483a.u., respectively, Figure 5. We have further determined, that -back-donation processes are, in line with all currently discussed charge delocalization components, driven by lowering in kinetic energies, Figure 5 (left hand side). Remarkably, the -contributions are, in turn, governed by the opposite mechanism, i.g. the potential terms are now the leading stabilizing factors, Figure 5 (right hand side). Clearly, a charge transfer to quite heavy electrophilic transition metals (containing relatively compact d orbitals) enforces significant electron-nucleus stabilization leading to negative Vorb and positive Torb (an increased kinetic pressure due to receiving additional electron density), whereas alike donations to relatively diffused ns orbitals (of main group


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cations) leads to positive Vorb and negative Torb (more kinetic pressure is released). To the best of our knowledge, it is the first report which has determined, that donation and back-donation charge transfer processes in organometallic chemistry can be driven at the fundamental level by entirely different T/V mechanisms though both provides the stabilization at a global level. Richard Bader was the opponent of any energy decomposition scheme including particularly the criticism of orbital interaction term.63,64 Interestingly, have determined herein in line with his, and others, electrostatic interpretation of bonding,63-67 that potential contribution Vorb can be also crucial for a chemical bond particularly in transition metal systems.

Figure 5. The most relevant deformation densities describing ligand→metal donation [orb()] and metal→ligand back-donation [orb()] in Cr(CO)5CH2 and Ni{L}C2H4, together with the corresponding Torb/Vorb contributions.


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Conclusions To summarize, in this work we have provided the pioneering direct relation between the shapes of specific bonding channels i (e.g. , , etc.) and the fundamental constituents of hamiltonian (Ti/Vi) within our charge and energy decomposition method (ETS-NOCV)28 which has been developed due to merging of the Natural Orbitals for Chemical Valence (NOCV)36-38 and the Extended Transition State (ETS)39,40 energy decomposition scheme. It is found, that typical covalent, donor–acceptor and dative–covalent charge delocalizations in compounds containing main-group elements leads to the domination of the stabilizing kinetic energy over the repulsive potential term; the only exception is the formation of -contributions in N2 which are found to be driven by both stabilizing kinetic and potential energy terms. Electron density changes within a given fragment [intra–fragment polarizations e.g. hyperconjugations in ethane] are, in contrary, driven solely by the potential energy (electrostatic) contribution. Remarkably, it is unveiled, that donation ligandd(TM), where d(TM) is an empty transition metal-based orbital, is also driven by the electrostatic (potential) term, in contrary to the opposite d(TM)ligand charge delocalization which is determined solely by the lowering of kinetic energy, despite the fact, that both processes (donation and back-donation) lead to the overall stabilization at Eorb level. In our view, these findings open new avenues in terms of deeper physical understanding of chemical bonding in general and organometallic chemistry and thus, it facilitates better understanding of bonding–properties relationship in the spirit of the Hartwig’s book “From Bonding to Catalysis”.68 Finally, apart from the physically fundamental findings reported herein, our results not only facilitate comparison of ETS-NOCV based results with other bonding descriptors/methods, but also they contribute toward a future unification of a language used in chemical bonding discussions. Further work aiming at better understanding trends within Torb and predominantly further decomposition of Vorb (into Ven, Vee and VXC) are underway.


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ACKNOWLEDGMENT DFT calculations were partially performed using the PL-Grid Infrastructure and resources provided by the ACC Cyfronet AGH (Cracow, Poland). Mariusz Paweł Mitoraj acknowledges the financial support of the Polish National Science Center within the Sonata Bis Project 2017/26/E/ST4/00104.


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Kinetic and potential energy contributions to a chemical bond from the

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