Intriguing Electrostatic Potential of CO: Negative Bond-ends and Positive Bond-cylindrical-surface

The strong electronegativity of O dictates that the ground state of singlet CO has positively charged C and negatively charged O, in agreement with ab initio charge analysis, but in disagreement with the dipole direction. Though this unusual phenomenon has been fairly studied, the study of electrostatic potential (EP) for noncovalent interactions of CO is essential for better understanding. Here we illustrate that both C and O atom-ends show negative EP (where the C end gives more negative EP), favoring positively charged species, whereas the cylindrical surface of the CO bond shows positive EP, favoring negatively charged ones. This is demonstrated from the interactions of CO with Na+, Cl–, H2O, CO and benzene. It can be explained by the quadrupole driven electrostatic nature of CO (like N2) with very weak dipole moment. The EP is properly described by the tripole model taking into account the electrostatic multipole moments, which has a large negative charge at a certain distance protruded from C, a large positive charge on C, and a small negative charge on O. We also discuss the EP of the first excited triplet CO.

On the other hand, the quantum theory of atoms in molecules analysis showed that the C/O is positively/negatively charged, respectively. This is consistent with the natural bond orbital (NBO) charge of C/O which is +0.44/− 0.44 au at the level of Moller-Plesset second order perturbation (MP2) theory using the aVTZ basis set (where aVNZ denotes aug-cc-pVNZ; N = D/T/Q/5). Since CO has a small dipole moment with the negative end at the C atom, it is argued that the apparent anomaly for CO arises from the severe polarization of electron density on the C atom overriding the effect of electronegativity difference [10][11][12] . If only the dipole direction of CO is simply considered, one could erroneously expect the charge distribution of negatively/positively charged C/O.
In this regard, we investigated the anisotropic charge distribution of CO. It shows an intriguing EP map for the singlet ground state of CO (Fig. 1a). Both EPs of the C and O atom-ends along the CO bond axis (z axis) are negative, with the C atom-end being more negative. In contrast, EP of the cylindrical surface of the CO bond between C and O is positive.

Results
Simple molecular orbital (MO) picture based on atomic orbital overlaps have difficulties in providing a proper explanation for the EP of CO. The two π bonding MOs and one σ bonding MO in CO form a Figure 1. EP maps, electronic properties and frontier MOs of the ground state CO (X 1 Σ + ) and the first excited triplet state CO t (a 3 Π). EP maps for the ground (a) and first excited ((b) top and (c) front views) states of CO at the MP2/aVTZ level (density isovalue: 0.001 au). Bond-length (d in pm), dipole moment (μ z in D), and quadrupole moment (Q zz in D + Å) are given at the CCSD(T)/aV5Z level. For the singlet CO, both C and O atom-ends show negative EP, whereas the cylindrical surface of the CO bond, positive EP. For CO t , the C atom-end gives positive EP, whereas the O atom-end, negative EP. MO energies and orbital shapes for (d) CO and (e) CO t are given at the M06-2X/aVTZ level. triple bond (Fig. 1d). For all the bonding MOs, regardless of σ or π bonds, the electron density increases between the two atoms due to the orbital overlap, but decreases outside the two atoms. One might be tempted to think that the cylindrical surface would have negative EP, while the atom-ends would have positive EP, as opposed to the EP map in Fig. 1a.
The high electronegativity of O tends to keep significant electron population around the O atom-end. In the proximity of the C/O nuclei, the positive EP due to the C/O nuclei is not screened out by the electron density. Far from the nuclei, the positive EP due to the nuclei is over-screened, resulting in negative EP around the C and O atom-ends. Nevertheless, a large amount of electron population is between C and O because of the triple bond nature of CO. The CO triple bond length (113 pm) is very short, comparable to the N 2 triple bond length (110 pm), much shorter than the O 2 double-bond length (121 pm) 5 . Therefore, the six electrons cannot be accommodated within the short CO bond between C and O nuclei; their significant electron population is outside the C and O nuclei, resulting in negative EP in both atom-end regions and positive EP in the region between the C and O atoms. Since C has the smaller effective nuclear charge than O ((Z eff (C 2p ) = 3.14 vs. Z eff (O 2p ) = 4.45) 13 , the C atom-end has the weaker nucleus-charge screening effect. Compared with the O atom-end, the C atom-end has more diffuse electron density (as shown in 3σ HOMO, Fig. 1d), which results in negative EP at some distance away (> 200 pm) from the C atom-end. Moreover, the electron density around the C nucleus which is more dispersed than that around the O nucleus, causes the region near the C atom perpendicular to the CO axis to be the most electro-positive. It is because the negative EP due to the electron density at a distance from C is exponentially inverse-proportional to the distance, while the positive EP due to the nuclear charge of C/O is inversely proportional to the distance from C/O.
If the NBO charges of C and O were considered isotropic, it could give a very large dipole moment (μ z = ~ − 2.4 D) in the opposite direction to the experimental one (0.11 D). Owing to the highly anisotropic behavior in the C/O charge, i.e., electron transfer driven polarization effect, the dipole of CO is very small, and so its EP is strongly quadrupole driven (Q zz = − 1.85 D·Å at the coupled cluster with singles, doubles, and perturbative triples (CCSD(T))/aV5Z level; experiment: Q zz = − 1.9 ± 0.1/− 1.93 ± 0.04 D·Å) 5,14 . Hence, CO behaves electrostatically almost like N 2 15 , opposite to the σ -hole effect of halogen bonding in which the EP of the halogen atom-end is positive 16,17 . We note that the EP of CO is well described by the tripole model, as shown in Fig. 2 in which the EPs of isoelectronic molecules CO, N 2 and BF are compared. The tripole model shows the three divided regions comprised of two negative EP regions around C and O atom-ends and one positive region around the cylindrical surface of the CO bond between C and O. In other words, it can be described as either two dipoles in the opposite direction with slightly different magnitude or the split positive charge of C with a large dipole moment, which results in the dominant quadrupole effect. This tripole model can also be generalized to represent the EP maps of halide dimers showing the σ -hole effect 16,17 (Supplementary Information: Figure S1).
When CO is excited as a triplet state (CO t : subscript "t" denotes the first excited state triplet a 3 Π ), the triple bond comprised of 1π x 1π y , and 3σ bonding orbitals changes to the double bond as one electron in the 3σ bonding orbital excites to the 2π y * antibonding orbital (where the x axis is perpendicular to the plane and the y axis is on the plane) (Fig. 1e). Since CO t has now a double bond, the bond distance increases to 120.5 pm (experiment: 120.6 pm) 5 . The overcrowded electron population between the two nuclei in the ground singlet CO is significantly reduced; ergo, the electron population between two nuclei in CO t no longer spills over outside the two nuclei, as in N 2 . The large electron population between the C and O atoms in the σ MO cancels the depleted electron population of the π y * MO. The σ g bonding induces the atom-ends to be electrostatically positive along the z axis by overlap between two p z orbitals. Meanwhile, the π y * MO induces (i) negative EP due to highly increased electron density on the top and bottom of the cylindrical surface between the two nuclei ( Fig. 1b), and induces (ii) positive EP due to the depleted electron density on the front and back of the cylindrical surface (Fig. 1c). The NBO charges of C and O in CO t are + 0.83 and − 0.83 au. The dipole moment is −1.39 D (experiment: μ z = − 1.374 D) 5,18 and the quadrupole moment is Q zz = 1.41 D·Å. The vertical excitation energy is 6.49 eV (experiment 19 : 6.32 eV).
We note a significant anisotropy in hard wall radius (r w ) of C and O, specifically, a significant difference between the C/O atom-end directions (C/O-e) and C/O perpendicular directions (C/O-p) (Supplementary Information: Figure S2). At the CCSD(T) complete basis set (CBS) 20,21 limit, the r w (in pm) along the four directions of (C-e, C-p, O-p and O-e) in the singlet CO are (177, 157, 155 and 145), and those in the triplet CO t are (111, 159, 141 and 132). Further, a large difference in r w along the C-e between CO and CO t (177 pm vs. 111 pm) should be noted. The minimum r w for CO (145 pm along O-e) is much larger than that for CO t (111 pm along C-e), which could be utilized for their separation through porous materials.
To better visualize the EP map, the interactions of CO with a cation Na + and an anion Clare plotted (Fig. 3). The strongest interaction energy (E e ) for Na + appears along C-e (E e = − 39 kJ/mol), and the second strongest one appears along O-e (E e = − 26 kJ/mol) where E e is given at the CCSD(T)/CBS level. On the other hand, Clinteracts strongly with CO around the cylindrical surfaces of the bond (E e = − 15 kJ/mol). This clearly demonstrates that both the C and O atom-ends favor a cation, whereas the cylindrical surface of the CO bond favors an anion with the strongest binding site located slightly nearer to C than O (i.e., along C-p) (Supplementary Information: Figure S2).

Figure 2. Tripole models (left) which reproduces the EP maps (right) of isoelectronic molecules N 2 , CO and BF at the CCSD(T)/aV5Z level along with a schematic representation (left-bottom) of the EP surface of CO (distances in pm, 2 n -pole units in e·Å n )
. N 2 has clearly three divided regions of negativepositive-negative EP in the whole space. CO having a weak dipole is practically three divided regions in the normal range of molecular interaction ranges (within 10 4 pm), while BF having moderate dipole moment has a small region (within 10 3 pm) of the negative EP around the F atom-end which is eventually surrounded by positive EP. Thus, BF behaves like a quadrupole in the near F atom-end, but like a dipole in the region far from the F atom-end as if F/B were positively/negatively charged. Here, one can note that the B in BF behaves like a singlet carbene with both positive and negative charges on B respectively along the bond-end and the radial directions of the B atom, while the C in CO partially shows such a behavior. For a comparative study, the tripole models for dihalogen atoms ( F 2 , Cl 2 and Br 2 ) are also studied (Supplementary Information: Figure S1). It should be noted that these halogen cases show the opposite EP behaviors to the N 2 , CO and BF cases which give positive EP along the bond-ends but negative EP over the bond-cylindrical surface. Now we study the interactions of CO with H 2 O, another CO, and benzene (Bz) to understand their hydrophilic/hydrophobic nature as well as their noncovalent bonding characters (Fig. 4)  perform energy decomposition with the asymptotically corrected PBE0 functional and aVTZ basis set on the MP2/aVTZ optimized geometry. We analyze the SAPT interaction energy components: electrostatic energy (E es ), effective induction energy (E ind* = E ind + E exch-ind ), effective dispersion energy (E disp* = E disp + E exch-disp ), effective exchange repulsion (E exch* = E exch -E exch-ind -E exch-disp ) 26,27 , higher order correction term (E HF ) and total SAPT interaction energy E tot (Table 1). Since the C-end has is a more negative EP than the O-end in CO, OC-HOH (E es = − 10.9 kJ/mol) shows stronger electrostatic energy than CO-HOH (E es = − 4.71 kJ/mol). On this account, the former has much larger binding energy than the latter. (C≡O)|OH 2 (E es = − 4.87 kJ/mol) also shows weak binding energy because of the positive EP on the large cylindrical surface of the CO triple bond. Meanwhile, CO t interacts more strongly with H 2 O via the OC…OH 2 electrostatic interaction because of much larger dipole moment than the singlet CO.
In the case of the (CO) 2 dimer both displaced-stacked (d) and perpendicular (p) structures show similar interaction energies (-E e = 1.6 ~ 1.5 kJ/mol), while the linear structures are hardly bound or not bound mainly due to electrostatic repulsion (CO-OC/CO-CO: E es = 0.07/0.36 kJ/mol). For most of the (CO) 2 dimer structures, |E disp* | is found to be much larger than |E es | (Table 1). However, E disp* tends to be partly cancelled by E exch* at the equilibrium structure. Thus, E tot is close to E es in most cases 28 . Though E es is small, it governs the stability of structures.
In the case of CO…Bz, the stacked conformations of CO on benzene are the most stable (S1-Bz/S2-Bz: E e = − 7.06/− 7.04 kJ/mol). They show strong electrostatic energies (E es = − 5.63/− 5.53kJ/mol), while the effective dispersion and exchange energies nearly cancel each other (E disp* + E exch* = 0.66/0.33 kJ/mol) ( Table 1). Thus, the structures are driven electrostatically. Even though the magnitude of the effective dispersion is large (E disp* = − 12.52/12.24 kJ/mol), the anisotropic charge distribution in CO governs the structures, because the high density of electron population above benzene showing negative EP is stabilized by the positive EP on the CO cylindrical surface.
The T-shaped structure of CO above benzene where the C is pointing to the benzene centroid is weakly stable (T|OC-Bz: E e = − 3.24 kJ/mol), while the opposite conformation (the O of CO is pointing to the benzene) is also weakly stable (T|CO-Bz: E e = − 2.98 kJ/mol), as expected from the similar negative EPs of the C and O atom-ends. The C/O atom-end of CO involves in weak H-bonding with the H atoms of benzene along the benzene side (PhH-CO: E e = − 2.43 kJ/mol, PhH-OC: E e = − 1.89 kJ/mol), where the C atom-end has slightly stronger binding energy than the O atom-end due to the C atom-end showing more negative EP than the O atom-end.
Once CO is excited, the highly positively charged C atom-end of CO t favors the negatively charged center of the benzene (T|OC-Bz: − 17.70 vs. T|CO-Bz: − 1.75 kJ/mol; S1-Bz/S2-Bz: − 5.56/− 16.93 kJ/mol, Supplementary Information: Figure S3). This excitation changes the conformation from the parallel structure of benzene-CO to the perpendicular structure of benzene-CO t , which could be exploited as a mechanical device of molecular rotor by alternating laser pulses corresponding to the light absorption and emission between the ground and excited states. Since benzene requires less energy from the singlet to triplet excitation than CO, benzene can be more easily excited to the triplet state than CO. In this case, the CO-Bz t conformational energetics (S2-Bz/S1-Bz: − 7.19/− 6.40 kJ/mol; (T|OC-Bz)/(T|CO-Bz): − 2.60/− 2.91 kJ/mol) are somewhat similar to those of CO…Bz (see Supplementary Information: Figures S4 and S5).

Discussion
In summary, we note that both C and O atom-ends of the CO bond show negative EP (where the C end is slightly more negative), whereas the cylindrical surface of the CO bond axis shows positive EP. This has been properly described by the tripole model which shows the three regions comprised of two negative EP regions around C and O atom-ends and one positive region around the cylindrical surface of the CO bond between C and O. Thus, both C and O atom-ends favor positively charged sites, while the cylindrical surface (in particular near the C atom) favors negatively charged sites. Such phenomena are demonstrated based on the interactions of CO with a cation/anion, H 2 O, and benzene. Clearly CO should not be considered as a molecule with a simple weak dipole moment, but needs to be interpreted as a quadrupole driven molecule (like N 2 ) with very weak dipole moment. On the other hand, the triplet CO t has a significant dipole moment; accordingly, the O-end shows negative EP, while the C-end shows positive EP. The present results could further facilitate diverse gas phase experiments involving CO-bound complexes.

Methods
EP maps and most of the MP2 calculations were carried out using the GAUSSIAN09 suite of programs 24 . Molecular orbitals were investigated at the M06-2X level of theory 29 using aug-cc-pVTZ basis set. Most of the CCSD(T) calculations were performed using the MOLPRO software 30 . SAPT calculations were carried out using SAPT2012 31 . The optimized geometry (z C = 64.57 pm and z O = 48.52 pm) and multipole moments of CO were calculated at the CCSD(T)/aug-cc-pV5Z level. Since the analytic derivatives to calculate multipole moments are not available for the CCSD(T) method, numerical differentiation using the field strength of 0.0005 au was carried out. The perturbation Hamiltonian H' of the following form is added to the one-electron Hamiltonian, and the corresponding CCSD(T) energy E(λ ) is computed.

= λ (
). H' f x; y; z Then, the corresponding moment is approximated using the four-point formula: For the calculation of physically meaningful moments, perturbation Hamiltonians are designed according to the definitions for the multipole moments given below. where ρ (r) includes both nuclear charge and electron density. With the accurate multipole moments at hand, we attempt to design a system composed of three point charges q C1 , q C2 and q O placed at z C1 , z C2 ; and z O (q: charge, z: coordinate along the CO bond axis) which reproduces the calculated moments including the monopole moment (charge balance).
The geometry and multipole moments of CO were obtained at the CCSD(T)/aug-cc-pV5Z level. The three point charges are given by (q C1 = − 0.5843 au, z 1 = − 109.48 pm), (q C2 = + 0.7917 au, z 2 = − 65.43 pm), and (q O = − 0.2074 au, z O = + 47.75 pm), while the atomic sites are located at − 64.57 pm (C) and + 48.52 pm (O), where the center of mass is at the origin. This model represents that a negative charge (− 0.5843 au) is at the distance of 44.91 pm along the C atom-end from the C atom, a large positive charge (+ 0.7917 au) is at the distance of 0.86 pm from the C atom toward the O atom, i.e. very close to the C atom, and a small negative charge (− 0.2074 au) is at the distance of 0.77 pm from the O atom site. This indicates that a large negative charge is at the distance 45 pm from the C atom-end and a small negative charge is near the O atom-end, while a positive charge is near the C atom. This electrostatic potential can be nearly exactly represented as a more simplistic tripole model in which the actual negative charges are at a certain distance from the C atom-end and at the position of the O atom, and the positive charge is at the C atom.
The simplified three site model has (q C1 = − 0.5489 au, z 1 = − 110.79 pm), (q C2 = + 0.7537 au, z 2 = − 64.57 pm, i.e. the C nucleus site), and (q O = − 0.2231 au, z O = + 48.52 pm, i.e., the O nucleus site), as shown in Fig. 2, without any significant difference in electrostatic potential from the previous model. Thus, this simplified model is finally chosen as the electrostatic potential of CO. This indicates that a large negative charge protrudes from the C nucleus (at the distance of 46.22 pm from the C nucleus), and a small negative charge is at the O nucleus site, while a large positive charge is at the C nucleus site, as schematically shown in Fig. 2. We further compared isoelectric molecules N 2 , CO and BF in Fig. 2. Finally, the N 2 , CO and BF cases are compared with the dihalogen cases of F 2 , Cl 2 and Br 2 which show positive EP along the bond-ends but negative EP over the bond-cylindrical surface (i.e., opposite EP behaviors to the N 2 , CO and BF cases; Supplementary Information: Figure S1).