Unusual Complexes of P (CH) 3 with FH, Clh, And

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UnusualArticle Complexes of P(CH)3 with FH, ClH, and ClF 3 JanetUnusual E. Del Bene Complexes1,* , Ibon Alkorta 2,of* andP(CH) José Elguero with2 FH, ClH, and ClF Janet1 Department E. Del Bene of Chemistry,1,*, Ibon Alkorta Youngstown 2,* and State José University, ElgueroYoungstown, 2 OH 44555, USA 2 Instituto de Química Médica (IQM-CSIC), Juan de la Cierva, 3, E-28006 Madrid, Spain; [email protected] 1 Department of Chemistry, Youngstown State University, Youngstown, OH 44555, USA * Correspondence: [email protected] (J.E.D.B.); [email protected] (I.A.); Tel.: +330-609-5593 (J.E.D.B.); 2 Instituto de Química Médica (IQM-CSIC), Juan de la Cierva, 3, E-28006 Madrid, Spain; [email protected] +34-91562-2900 (I.A.) * Correspondence: [email protected] (J.E.D.B.); [email protected] (I.A.); Tel.: +330-609-5593 (J.E.D.B.); +34-91562-2900 (I.A.) Received: 27 May 2020; Accepted: 16 June 2020; Published: 19 June 2020 Received: 27 May 2020; Accepted: 16 June 2020; Published: 19 June 2020 Abstract: Ab initio MP2/aug’-cc-pVTZ calculations have been performed to determine the structures andAbstract: binding Ab energiesinitio MP2/aug’-cc-pVTZ of complexes formed calculations by phosphatetrahedrane, have been performed P(CH)to determine3, and HF,the HCl,structures and ClF.and Fourbinding types energies of complexes of complexes exist onformed the potential by phosphatetrahedrane, energy surfaces. P(CH) Isomers3, andA form HF, HCl, at the and P atom ClF. nearFour thetypes end of complexes of a P-C bond, exist onB atthe a potential C-C bond, energyC at surfaces. the centroid Isomers of theA form C-C-C at the ring P atom along near the the C3 symmetryend of a P-C axis, bond, and B Dat ata C-C the Pbond, atom Calong at the thecentroid C3 symmetry of the C-C-C axis. ring Complexes along theA C3and symmetryB are stabilized axis, and byD at hydrogen the P atom bonds along when the C FH3 symmetry and ClH areaxis. the Complexes acids, and A byand halogen B are stabilized bonds when by hydrogen ClF is the bonds acid. Inwhen isomers FH andC, theClH dipole are the moments acids, and of theby twohalogen monomers bonds when are favorably ClF is the aligned acid. In but isomers in D the C, alignmentthe dipole ismoments unfavorable. of the two For monomers each of the are monomers, favorably aligned the binding but in energies D the alignment of the complexes is unfavorable. decrease For each in the of orderthe monomers,A > B > C the> Dbinding. The most energies stabilizing of the Symmetrycomplexes Adapteddecrease in Perturbation the order A Theory > B > C (SAPT) > D. The binding most energystabilizing component Symmetry for Adapted the A Perturbationand B isomers Theory is the (SAPT) electrostatic binding interaction,energy component while thefor the dispersion A and B interactionisomers is the is theelectrostatic most stabilizing interaction, term while for C theand dispersionD. The barriers interaction to converting is the most one stabilizing isomer toterm another for C areand signiﬁcantly D. The barriers higher to forconverting the A isomers one isomer compared to another to B. Equation are significantly of motion higher coupled for clusterthe A isomers singles andcompared doubles to B (EOM-CCSD). Equation of motion intermolecular coupled couplingcluster singles constants and doubles J(X-C) (EOM-CCSD) are small for bothintermolecularB and C isomers.coupling J(X-P)constants values J(X-C) are are larger small and for positive both B inand the C Aisomers.isomers, J(X-P) negative values in are the largerB isomers, and positive and have in theirthe A largest isomers, positive negative values in the inthe B isomers,D isomers. and Intramolecular have their largest coupling positive constants values1 J(P-C)in the experienceD isomers. 1 littleIntramolecular change upon coupling complex constants formation, J(P-C) except experience in the halogen-bondedlittle change upon complex complex FCl:P(CH formation,3) Aexcept. in the halogen-bonded complex FCl:P(CH3) A. Keywords: hydrogen bonds; halogen bonds; dipole interactions; coupling constants Keywords: hydrogen bonds; halogen bonds; dipole interactions; coupling constants

1.1. Introduction SymmetrySymmetry in Chemistry is is one one of of the the cornerstones cornerstones of of chemistry, chemistry, both both in in terms terms of of the the beauty beauty it itbestows bestows on on molecules, molecules, and and its its importance importance for for life. life. There There is is no no question that highlyhighly symmetricalsymmetrical moleculesmolecules are intrinsicallyintrinsically beautiful and fascinating.fascinating. Moreover, symmetry in chemistry, particularlyparticularly chirality,chirality, isis importantimportant forfor lifelife itself,itself, asas ﬁrstfirst demonstrateddemonstrated byby PasteurPasteur [[1–4].1–4]. In additionaddition to thethe highlyhighly symmetricalsymmetrical ArchimedeanArchimedeanstructures structures mainly mainly known known thanks thanks to the to fullerenes, the fullerenes, the ﬁve Platonicthe fivestructures Platonic whichstructures do notwhich have do atoms not have in the atoms center, in the but center, only on but the only periphery, on the periphery, are also intrinsically are also intrinsically beautiful. Thebeautiful. Platonic The structures Platonic arestructures illustrated are illustrated in Figure1. in Figure 1.

Figure 1. Five Platonic structures: tetrahedron, octahedron, hexahedron (cube), dodecahedron, andFigure icosahedron. 1. Five Platonic structures: tetrahedron, octahedron, hexahedron (cube), dodecahedron, and icosahedron.

Octahedron-type molecules are unknown, [1] but icosahedron geometries are found in boron Moleculesderivatives2020 , 25such, 2846; as doi: the10.3390 dodecaborate/molecules25122846 dianion [2] and the closo-carboraneswww.mdpi.com [3]. The/journal three/molecules other

Molecules 2020, 25, 2846; doi:10.3390/molecules25122846 www.mdpi.com/journal/molecules Molecules 2020, 25, 2846 2 of 14

Octahedron-type molecules are unknown, [1] but icosahedron geometries are found in boron derivatives such as the dodecaborate dianion [2] and the closo-carboranes [3]. The three other structures could exist as pure carbon derivatives, although in some cases, with external substituents needed for stabilization. These include tetrahedrane (CH)4,[4,5] cubane (CH)8,[6–8] and dodecahedrane (CH)20 [9–11]. Chemists have searched the Periodic Table for structures which could be obtained by replacing C or CR by X or XR. Theoretical studies of tetrahedrane molecules in which C is replaced by elements from Si to Pb and from B to Tl, [12,13] CR is replaced by SiR or GeR, [9] or CH is replaced by N, have demonstrated that these are stable systems [14–16]. An early study of replacing CR by P was carried out on phosphacubanes by Reitz et al. [17]. Di-tert-butyldiphosphatetrahedrane has been recently synthesized and characterized by Wolf et al. [18]. White phosphorus, P4, which has a tetrahedral structure, has been the subject of many theoretical studies [19–22]. As is the case for C4, all tetrahedral (CR)4 molecules lack a dipole moment. This usually leads to weaker noncovalent interactions, even in cases in which the interacting molecule may have a large positive σ-hole. Yáñez demonstrated that phosphatetrahedrane and diphosphatetrahedrane behave as carbon bases in the gas phase [23]. Boldyrev et al. studied the molecules CnHnP4–n (n = 0–4) and their transformation into planar structures [24]. We have investigated the P4 molecule in complexes stabilized by hydrogen, halogen, and pnicogen bonds [25]. The “elusive phosphatetrahedrane” was ﬁnally isolated by Cummins et al. [26] in the form of the tris-tert-butyl derivative. In the present study, we have searched the potential energy surfaces of phosphatetrahedrane, P(CH)3 interacting with FH, ClH, and ClF. The structures and binding energies of the isomers that exist on these surfaces have been determined, as well as the transition structures that convert one equilibrium isomer to another. To gain further insight into the binding energies of these complexes, SAPT analyses have been carried out. Finally, EOM-CCSD spin–spin coupling constants across intermolecular bonds have been computed for all complexes. It is the purpose of this paper to present the results of this study.

2. Results and Discussion

2.1. Parent Molecule P(CH)3 and Its Molecular Electrostatic Potential (MEP)

The parent molecule P(CH)3 is pyramidal with C3v symmetry. Although the experimental structure of this molecule is not known, a derivative P(C-t-butyl)3 has been synthesized. An X-ray diﬀraction study of this molecule reported P-C distances of 1.837 to 1.860 Å, and C-C bond distances of 1.467 to 1.481 Å. The computed P-C distances of P(CH)3 are 1.857 Å and the C-C distances are 1.465 Å. In addition, the one-bond coupling constant 1J(P-C) has been measured experimentally and 1 found to have an unsigned value of 37.9 Hz. The computed EOM-CCSD value of J(P-C) for P(CH)3 is –40.3 Hz. Thus, the computed structure and P-C coupling constant for P(CH)3 are consistent with the experimental values for the t-butyl derivative. The MEP of the P(CH)3 molecule is illustrated in Figure2. A triply degenerate MEP minimum with a value of 0.018 au is located at the P atom almost perpendicular to the C symmetry axis. − 3 Three additional triply degenerate minima with values of 0.006 au are associated with the midpoint − of each C-C bond in the ring. There is also a minimum of 0.005 au located on the C axis at the P − 3 atom. At these minima, P(CH)3 should act as an electron donor. There are also two unique maxima on this surface. One is a three-fold degenerate MEP maximum associated with the three C-H bonds. The second maximum has a value of 0.005 au, and is found below the centroid of the C-C-C ring on the C3 symmetry axis. Bond formation in this region should have P(CH)3 acting as the acid, that is, as an electron acceptor. The Electron Localization Function (ELF) analysis indicates that the deepest MEP minima on the 0.001 au electron density isosurface of 0.018 au arises from simultaneous contributions − from the P-C bond basins and the P lone pair, as illustrated in Figure3. Molecules 2020, 25, 2846 3 of 14 Molecules 2020, 25, 2846 3 of 14 Molecules 2020, 25, 2846 3 of 14

Figure 2. Molecular Electrostatic Potential (MEP) of P(CH)3 on the 0.001 au electron density isosurface. The color coding ranges from red < −0.01 au to blue > +0.04 au. The locations and values of Figure 2.2.Molecular Molecular Electrostatic Electrostatic Potential Potential (MEP) (MEP) of P(CH) of P(CH)3 on the3 on 0.001 the au 0.001 electron au densityelectron isosurface. density Theisosurface.local color minima coding The and color ranges maxima coding from ofranges redinterest< from0.01 on red this au < − to 0.01surface blue au> toare + blue0.04 indicated > au. +0.04 The au.by locations Theblack locations and and light values and blue values of dots, local of − minimalocalrespectively. minima and maxima and maxima of interest of interest on this surfaceon this are surface indicated are byindicated black and by lightblack blue and dots, light respectively. blue dots, respectively.

Figure 3. ELFELF 0.8 0.8 isosurface. isosurface. Yellow, Yellow, red red and and green green indicate indicate the thehydrogenoid, hydrogenoid, monosynaptic, monosynaptic, and and disynaptic basins, respectively. Figuredisynaptic 3. ELF basins, 0.8 respectively.isosurface. Yellow, red and green indicate the hydrogenoid, monosynaptic, and 2.2. Overviewdisynaptic of basins, the Equilibrium respectively. Binary Complexes 2.2. Overview of the Equilibrium Binary Complexes On the XY:P(CH)3 surfaces with each of the acids, four unique equilibrium complexes have 2.2. OverviewOn the XY:P(CH)of the Equilibrium3 surfaces Binary with Complexes each of the acids, four unique equilibrium complexes have been found. XY stands for FH, ClH, and FCl in these complexes. Diﬀerent starting structures been Onfound. the XYXY:P(CH) stands3 forsurfaces FH, ClH, with and each FCl of in the thes acids,e complexes. four unique Different equilibrium starting structurescomplexes based have based on the electrostatic potential of the phosphatetrahedrane and its symmetry have been used beenon the found. electrostatic XY stands potential for FH, of ClH, the phosphatetraand FCl in theshedranee complexes. and its Different symmetry starting have beenstructures used inbased the in the search for equilibrium structures. The structures, total energies, and molecular graphs of the onsearch the electrostaticfor equilibrium potential structures. of the phosphatetraThe structureshedrane, total andenergies, its symmetry and molecular have been graphs used ofin the equilibrium complexes are reported in Tables S1–S4 of the Supplementary Materials, and the structures searchequilibrium for equilibrium complexes structures.are reported The in structuresTables S1–S4, total of energies,the Supplementary and molecular Materials, graphs and of the of equilibrium complexes A, B, C, and D are illustrated for FH:P(CH)3 in Figure4. In what follows, equilibriumstructures of complexesequilibrium are complexes reported A , inB , CTables, and DS1–S4 are illustrated of the Su forpplementary FH:P(CH)3 inMaterials, Figure 4. andIn what the these structures will be discussed in the order A, B, C, D. In addition, two other structures A-tr and structuresfollows, these of equilibrium structures willcomplexes be discussed A, B, C in, and the Dorder are illustratedA, B, C, D for. In FH:P(CH)addition, 3two in Figure other structures4. In what B-tr are stationary points on the potential surfaces, and will also be discussed. We were not able to ﬁnd follows,A-tr and theseB-tr are structures stationary will points be discussed on the potential in the order surfac Aes,, B ,and C, D will. In also addition, be discussed. two other We structures were not any complexes on the potential energy surfaces in which P(CH)3 formed C-H—X hydrogen bonds Aable-tr andto find B-tr areany stationary complexes points on the on thepotential potential energy surfac surfaceses, and willin which also be P(CH) discussed.3 formed We wereC-H—X not even when the starting geometries included the hydrogen-bonding interaction. ablehydrogen to find bonds any even complexes when the on starting the potential geometri energyes included surfaces the inhydrogen-bonding which P(CH)3 formed interaction. C-H—X 2.3.hydrogen Binary bonds Complexes even A when the starting geometries included the hydrogen-bonding interaction.

The binary complexes A form at the local minimum identiﬁed in the MEP with a value of 0.018 au. − The acid lies in the plane deﬁned by the adjacent P-C and C-H bonds, so there are three such equilibrium structures on the potential energy surface. The structures, total energies, and molecular graphs of these complexes are reported in Table S1. The binary complexes of P(CH)3 with FH and ClH are stabilized by F-H P and Cl-H P hydrogen bonds, while the complex with ClF is stabilized by a ··· ··· P Cl halogen bond. ···

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A B

C D

FigureFigure 4. The 4. The equilibrium equilibrium isomers isomers A, B (A, C–D and) of D FH:P(CH) of FH:P(CH)3. 3.

2.3. BinaryTable1 Complexes presents theA binding energies, intermolecular distances, selected angles, charge-transfer energies, and coupling constants across intermolecular bonds for these complexes. The most stable The binary complexes A form at the local minimum identified in the MEP with a value1 of −0.018 complex is the halogen-bonded complex FCl:P(CH)3 with a binding energy of 32 kJ mol− , followed by au. The acid lies in the plane defined by the adjacent P-C and C-H bonds, so there are three such the hydrogen-bonded complexes FH:P(CH)3 and ClH:P(CH)3 with binding energies of 20 and 17 kJ equilibrium1 structures on the potential energy surface. The structures, total energies, and molecular mol− , respectively. The corresponding intermolecular F-P and Cl-P distances are 3.41 and 3.87 Å in thegraphs hydrogen-bonded of these complexes complexes, are reported respectively, in Table and S1. 2.55 The Å inbinary the halogen-bonded complexes of P(CH) complex.3 with The FH C-P-X and ClH are stabilized by F-H⋯P and Cl-H⋯P hydrogen bonds, while the complex with ClF is stabilized angles vary between 65 and 77◦, consistent with the observation made from the MEP that complex by a P⋯Cl halogen bond. formation should occur at P in a direction almost perpendicular to the local C3 axis. The H-X-P angles Table 1 presents the binding energies, intermolecular distances, selected angles, charge-transfer of 5◦ indicate that the hydrogen bonds deviate only slightly from linearity, while the P-Cl-F angle energies, and coupling constants across intermolecular bonds for these complexes. The most stable of 169◦ aligns the Cl-F molecule to accept a pair of electrons from P through the σ-hole on Cl for the –1 formationcomplex is of the the halogen-bonded halogen bond. In complex the halogen-bonded FCl:P(CH)3 with complex, a binding there isenergy a signiﬁcant of 32 kJ·mol elongation, followed of the P-Cby the bond hydrogen-bonded that interacts with complexes Cl, as evident FH:P(CH) from3 Table and 1ClH:P(CH). While this3 bondwith binding length is energies 1.881 and of 1.875 20 and Å in17 –1 thekJ·mol complexes, respectively. with FH The and corresponding ClH, respectively, intermolecular it increases dramaticallyF-P and Cl-P to distances 1.946 Å inare the 3.41 complex and 3.87 with Å FCl.in the Further hydrogen-bonded discussion of complexes, bond length respectively, changes and and1J(P-C) 2.55 Å coupling in the halogen-bonded constants for isomers complex.A, B The, C, andC-P-XD willangles be givenvary between below. 65 and 77°, consistent with the observation made from the MEP that complex formation should occur at P in a direction almost perpendicular to the local C3 axis. The 1 o H-X-PTable angles 1. Binding of 5° indicate energies that ( ∆ E,the kJ hydrogen mol− ), distances bonds (R,deviate Å), selected only slightly angles (from<, ), linearity, charge-transfer while the 1 − P-Cl-Fenergies angle (CT,of 169° kJ mol aligns− ), and the spin–spin Cl-F molecule coupling to constants accept a acrosspair of intermolecular electrons from bonds P through [J(X-P), Hz] the for σ-hole on Clcomplexes for the formation XY:P(CH)3 ofisomers the halogenA. bond. In the halogen-bonded complex, there is a significant elongation of the P-C bond that interacts with Cl, as evident from Table 1. While this bond length is Acid ∆E R(X-P) a R(P-C) b < 1 < 2 P σ*X-Y J(X-P) c 1.881 and 1.875− Å in the complexes with FH and ClH, respectively, it increaseslp→ dramatically to 1.946 Å in FHthe complex 20.0 with 3.412 FCl. Further 1.881 discussion C-P-F of= bond65 length H-F-P changes= 5 and 1J(P-C) 17.6 coupling constants 28.0 for isomersClH A 16.5, B, C, and 3.870 D will be 1.875 given below. C-P-Cl = 68 H-Cl-P = 5 16.4 3.3 ClF 31.6 2.552 1.946 C-P-Cl = 77 P-Cl-F = 169 83.1 d, 36.5, 17.0 e 232.0 a R is F-P for the complex with FH and Cl-P for complexes with ClH and ClF. b The P-C bond that interacts with FH, c 2h 1p ClH, and FCl. The P-C bond distance in P(CH)3 is 1.857 Å. J(X-P) for hydrogen-bonded complexes and J(Cl-P) for FCl:P(CH) . d σ(P-C) σ*Cl-F. e Cl σ*P-C. 3 → lp→

Molecules 2020, 25, 2846 5 of 14

1 Charge-transfer energies Plp—σ*X-H of 17.6 and 16.4 kJ mol− are found for the hydrogen-bonded complexes. This energy changes dramatically in the halogen-bonded FCl:P(CH)3 complex. The largest charge-transfer energy arises from electron donation by a σ(P-C) bonding orbital to an antibonding 1 Cl-F orbital, with an energy of 83 kJ mol− . There is a second Plp—σ*Cl-F charge-transfer with an 1 1 energy of 36.5 kJ mol− . The smallest charge-transfer energy of 17 kJ mol− is a reverse charge-transfer, from the chlorine lone pair to an antibonding P-C orbital. Spin–spin coupling constants 2hJ(X-P) are also reported in Table1, and have values of 28 and 3 Hz for the hydrogen-bonded complexes with FH and ClH, respectively. 1x(Cl-P) is 232 Hz for the halogen-bonded FCl:P(CH)3 complex. The components of these coupling constants are reported in Table S5 and indicate that although these coupling constants are dominated by the Fermi contact (FC) term, the paramagnetic spin orbit (PSO) and spin dipole (SD) terms make non-negligible contributions. Figure S1 of the Supplementary Materials provides a plot of 2hJ(F-P) versus the F-P distance along the intrinsic reaction path connecting F and P. 2hJ(F-P) varies from 9 Hz at an F-P distance of 3.71 Å to 64 Hz at a distance of 3.21 Å. The second-order trendline in Figure S1 has a correlation coefficient of 0.998, and suggests that the F-H ... P hydrogen bond is a traditional hydrogen bond. Figure S2 is a plot along the intrinsic Cl-P reaction path for FCl:P(CH)3. The third-order trendline has a correlation coefficient of 0.999. The curvature of this trendline at short distances suggests that complexes with these distances would have chlorine-shared halogen bonds [27,28]. Thus, the Cl ... P halogen bond in FCl:P(CH)3 isomer A would appear to have increased chlorine-shared character. The properties of the complexes with P(CH)3 may be compared to the properties of the same acids with PH3. The X-P distances in the complexes XY:P(CH)3 are longer than the corresponding distances in the XY:PH3 complexes, which are 3.270, 3.800, and 2.183 Å for the complexes with FH, ClH, and ClF, respectively. The binding energies of the complexes FH:PH3 and ClH:PH3 are 21.4 and 1 14.9 kJ mol− , respectively, which are similar to those for the corresponding complexes with P(CH)3. 1 However, the FCl:P(CH)3 binding energy of 31.6 kJ mol− is significantly less than that of FCl:PH3 1 which is 51.2 kJ mol− . This large difference may be attributed primarily to the weakening of the interacting P-C bond of P(CH)3, as indicated by the significant lengthening of this bond.

2.4. Binary Complexes B

The B isomers of the binary complexes XY:P(CH)3 arise as a carbon-carbon bond of P(CH)3 donates a pair of electrons to XY through its σ-hole. There are three such equilibrium complexes on the XY:P(CH)3 surface, one at each C-C bond. Table S2 of the Supplementary Materials provides the structures, total energies, and molecular graphs of these equilibrium complexes. Table2 reports their binding energies, the X-C distances, and the distances from X to the midpoint of the C-C bond (γ), the P-γ-X angles, charge-transfer energies, and coupling constants across the intermolecular bonds. Figure5 illustrates the structures of the B isomers.

1 a a o Table 2. Binding energies ( ∆E, kJ mol− ), distances (R(X-γ) and R(X-C), Å)), angles P-γ-X (<, ), − 1 charge-transfer energies (CT, kJ mol− ), and spin–spin coupling constants across intermolecular bonds (J(X-C), Hz) for complexes XY:P(CH)3 isomers B.

Acid ∆E R(X C)/R(X γ) a

and Table 2. The distances from X to one of the two C atoms range from 2.92 Å in the complex with ClF to 3.54 Å in the complex with ClH. The charge-transfer energies of these complexes are approximately 2 kJ·mol–1, and are, therefore, much less than the charge-transfer energies of the A isomers. They arise from electron donation by the C-C bond to a σ antibonding X-Y orbital. The order of decreasing charge-transfer energies is the same as the order of decreasing binding energies.

Table 2. Binding energies (–ΔE, kJ·mol–1), distances (R(X-γ)a and R(X-C), Å)), angles P-γ-Xa (<, o), charge-transfer energies (CT, kJ·mol–1), and spin–spin coupling constants across intermolecular bonds (J(X-C), Hz)c for complexes XY:P(CH)3 isomers B.

Acid −ΔE R(X−C) / R(X−γ)a

(a) (b)

(c)

FigureFigure 5.5. StructuresStructures ofof ((aa)) FH:P(CH)FH:P(CH)33,(, (bb)) ClH:P(CH)ClH:P(CH)33,, andand ((c) FCl:P(CH)FCl:P(CH)33 isomers B.

TheThe bindingDFT-SAPT energies data for of thetheB Aisomers and B complexes are less than in thoseTable of 3 theallowA isomers,for further and insight extend into over the a 1 smallerbinding range, energies from of 14.1 these kJ mol isomers.− at a distanceThere is of only 2.19 Åone from destabilizing Cl to the midpoint interaction, of the and C-C bondthat is when the 1 ClHfirst-order is the acid,exchange to 17.3 energy kJ mol which− at avaries distance from of 27 2.83 kJ.mol Å from−1 for theClH:P(CH) midpoint3 isomer of the B C-C to 270 bond kJ. tomol the–1 for Cl atomFCl:P(CH) when3 ClFisomer is the A. acid.The remaining The angles SAPT defined terms byP, are the stabilizing midpoint and of the are C-C sufficient bond, and to overcome X are similar the whenexchange FH andterm, FCl leading are the to acids, SAPT but binding smaller energies when ClH [−Δ isE(SAPT)] the acid, which as evident range from from Figure 10 kJ5. moland–1 Table for the2. TheB isomers distances of fromClH:P(CH) X to one3 and of the FCl:P(CH) two C atoms3 to 35 range kJ.mol from–1 for 2.92 the Å inA the isomer complex of FCl:P(CH) with ClF to3. 3.54The Åelectrostatic in the complex interaction with ClH. term The is the charge-transfer most stabilizing energies term offor these all of complexes these isomers are approximatelyexcept ClH:P(CH) 2 kJ3 1 molisomer− , andB, in are, which therefore, case the much dispersion less than term the is charge-transferthe leading stabilizing energies term. of the ForA FCl:P(CH)isomers. They3 isomer arise B, fromthe dispersion electron donationterm is about by the 1 kJ C-C.mol bond–1 less to stabilizing a σ antibonding than the X-Y electrostatic orbital. Theterm. order The SAPT of decreasing binding charge-transferenergies are less energies than the is MP2 the same binding as the energies order of except decreasing for FCl:P(CH) binding3 energies. isomer A which has a SAPT bindingThe energy DFT-SAPT that is data 3 kJ for.mol the–1 greaterA and thanB complexes the MP2 energy. in Table 3 allow for further insight into the binding energies of these isomers. There is only one destabilizing interaction, and that is the first-order 1 1 exchange energyTable 3. which SAPT variesenergies from (kJ.mol 27 kJ–1) mol for −equilibriumfor ClH:P(CH) XY:P(CH)3 isomer3 complexesB to 270 isomers kJ mol A− andfor B FCl:P(CH). 3 isomer A. The remaining SAPT(1) terms are stabilizing(1) and(2) are sufficient(2) to overcome the exchange term,a XY:P(CH)3 A XY = Eel Eex Eind Edisp δHF −ΔE(SAPT) 1 leadingHF to SAPT binding –26.1 energies [ ∆E(SAPT)] 34.9 which –9.3 range from –12.2 10 kJ mol− –6.2for the B isomers 18.8 of − 1 ClH:P(CH)HCl3 and FCl:P(CH) −20.93 to 35 kJ mol 34.5− for the A isomer –5.3 of FCl:P(CH) –15.0 3. The electrostatic –7.8 interaction 14.5 FCl −134.2 270.1 –56.3 –50.1 –63.9 34.5 term is the most stabilizing term for all of these isomers except ClH:P(CH)3 isomer B, in which case the XY:P(CH)3 B XY = dispersionHF term is the leading –17.8 stabilizing 30.3 term. For FCl:P(CH) –8.4 3 isomer –11.9 B, the dispersion –4.5 term is 12.4 about HCl1 –11.9 27.4 –4.6 –16.3 –4.2 9.6 1 kJ mol− less stabilizing than the electrostatic term. The SAPT binding energies are less than the MP2 ClF –22.8 48.4 –3.9 –21.4 –9.9 9.5 1 binding energies except for FCl:P(CH)3 isomer A which has a SAPT binding energy that is 3 kJ mol− a −ΔE(SAPT) is the DFT-SAPT interaction energy equal to the negative of the sum of the component energies. greater than the MP2 energy.

Table 3. SAPT energies (kJ mol 1) for equilibrium XY:P(CH) complexes isomers A and B. − 3 XY:P(CH) A XY 3 E (1) E (1) E (2) E (2) δHF ∆E(SAPT) a = el ex ind disp − HF 26.1 34.9 9.3 12.2 6.2 18.8 − − − − HCl 20.9 34.5 5.3 15.0 7.8 14.5 − − − − FCl 134.2 270.1 56.3 50.1 63.9 34.5 − − − − XY:P(CH)3 B XY = HF 17.8 30.3 8.4 11.9 4.5 12.4 − − − − HCl 11.9 27.4 4.6 16.3 4.2 9.6 − − − − ClF 22.8 48.4 3.9 21.4 9.9 9.5 − − − − a ∆E(SAPT) is the DFT-SAPT interaction energy equal to the negative of the sum of the component energies. − Molecules 2020, 25, 2846 7 of 14

MoleculesSpin–spin 2020, 25, 2846 coupling constants across intermolecular bonds for the B isomers are also reported7 of 14 in Table2. The coupling constants are negligible at 0.1 and 0.2 Hz for the complexes with HCl and Spin–spin coupling constants across intermolecular bonds for the B isomers2h are also reported in ClF, respectively. The coupling constant with the largest absolute value is J(F-C) for FH:P(CH)3 Table 2. The coupling constants are negligible at 0.1 and 0.2 Hz for the complexes with HCl and ClF, with a value of only 1.8 Hz. It is interesting to note from Table S5 that the dominant term for respectively. The coupling− constant with the largest absolute value is 2hJ(F-C) for FH:P(CH)3 with a value 2hJ(F-Cl) is the PSO term followed by the SD term. That the FC term is negligible is quite unusual of only −1.8 Hz. It is interesting to note from Table S5 that the dominant term for 2hJ(F-Cl) is the PSO term for a hydrogen-bonded complex, but the hydrogen bonds in these B complexes are not typical followed by the SD term. That the FC term is negligible is quite unusual for a hydrogen-bonded hydrogen bonds. complex, but the hydrogen bonds in these B complexes are not typical hydrogen bonds. 2.5. Binary Complexes C and D 2.5. Binary Complexes C and D There are two additional equilibrium C and D isomers on the XY:P(CH)3 surfaces. In C the dipole There are two additional equilibrium C and D isomers on the XY:P(CH)3 surfaces. In C the moment vectors of XY and P(CH)3 are favorably aligned head-to-tail, while in D there is an unfavorable alignment,dipole moment as illustrated vectors of in XY Figure and S3P(CH) of the3 are Supplementary favorably aligned Materials. head-to-tail, One might while question in D there why is the an reverseunfavorable alignments alignment, of FH, as ClH, illustrated and ClF ininD Figurewhich S3 would of the lead Supplementary to favorable dipole Materials. alignments One aremight not thequestion equilibrium why the structures. reverse alignments This and related of FH, questionsClH, and ClF will in be D addressed which would below. lead to favorable dipole alignmentsThe structures, are not the total equilibrium energies, andstructures. molecular Thisgraphs and related of the questionsC isomers will are be reported addressed in Tablebelow. S3 of theThe Supplementary structures, total Materials, energies, and and Figure molecular6 illustrates graphs of these the C isomers. isomers Itare is reported noteworthy in Table that S3 it is of the Supplementary Materials, and Figure 6 illustrates these isomers. It is noteworthy that it is the F the F atom and not the Cl that interacts with P(CH)3 in the FCl:P(CH)3 complex. The structure in atom and not the Cl that interacts with P(CH)3 in the FCl:P(CH)3 complex. The structure in which Cl which Cl interacts with P(CH)3 is not an equilibrium structure. Table4 provides the binding energies, intermolecularinteracts with distances,P(CH)3 is andnot spin–spin an equilibrium coupling structure. constants Ta ofble the 4C providesisomers. Itthe is notbinding surprising energies, that theintermolecular binding energies distances, no longer and spin–spin follow the coupling order of bindingconstants energies of the C found isomers. for the It is hydrogen-bonded not surprising thatA andthe bindingB isomers, energies but decrease no longer instead follow in the the order order of ClH binding> ClF energies> HF. The found binding for the energies hydrogen-bonded range from A and B isomers,1 but decrease instead in1 the order ClH > ClF > HF. The binding energies range from 4.5 kJ mol− for FH:P(CH)3 to 9.2 kJ mol− for ClH:P(CH)3. The X-C and X-P distances decrease in the –1 –1 order4.5 kJ·mol ClF > ClHfor FH:P(CH)> FH. That3 to the 9.2 mostly kJ·mol weakly for ClH:P(CH) bound complex3. The X-C with and FH X-P has distances the shortest decrease X-C and inX-P the distancesorder ClF may> ClH be > attributed FH. That the at least mostly in partweakly to the bound smaller complex van der with Waals FH radiushas the of shortest F. X-C and X-P distances may be attributed at least in part to the smaller van der Waals radius of F.

(a) (b) (c)

FigureFigure 6.6. EquilibriumEquilibrium structuresstructuresC Cfor for( (aa)) FH:P(CH)FH:P(CH)33,(, (bb)) ClH:P(CH)ClH:P(CH)33,, andand ((c)) FCl:P(CH)FCl:P(CH)33. Table 4. Binding energies ( ∆E, kJ mol 1), intermolecular distances (R, Å), and spin–spin coupling −–1 Table 4. Binding energies −(–ΔE, kJ·mol ), intermoleculara distances (R, Å), and spin–spin coupling constants (J, Hz) for complexes XY:P(CH)3 isomers C . constants (J, Hz) for complexes XY:P(CH)3 isomers Ca. Acid ∆E R(X-C) R(X-P) J(X-C) J(X-P) Acid –ΔE − R(X-C) R(X-P) J(X-C) J(X-P) FH FH 4.5 4.5 3.206 3.206 4.747 4.747 3.2 3.2 12.1 –12.1 ClH 9.2 3.359 4.905 1.4 − –3.2 ClF ClH 6.9 9.2 4.645 3.359b 4.905 6.220b 1.4 0.0b 3.2 –15.8b − a b ClF There is no 6.9 charge-transfer4.645 b in the6.220 C isomers.b 0.0 X isb the F atom.15.8 b − Table 4 also reportsa Therecoupling is no charge-transfer constants J(X-C) in the C andisomers. J(X-P).b X is The the F coupling atom. constants J(X-C) are small, ranging from 0.0 Hz in the complex with ClF to 3.2 Hz in the complex with FH. Coupling with P is Tablemost4 alsointeresting, reports couplingsince the constants interaction J(X-C) is andthrough J(X-P). the The tetrahedron coupling constants of P(CH) J(X-C)3 at very are small, long rangingdistances. from J(F-P) 0.0 is Hz −15.8 in the Hz complex at a distance with ClF of to6.22 3.2 Å Hz in inthe the complex complex with with ClF FH. and Coupling –12.1 Hz with in Pthe is mostcomplex interesting, with FH. since When the the interaction acid is ClH, is J(Cl-P) through has the a tetrahedronvalue of −3.2 ofHz. P(CH) 3 at very long distances. The structures, total energies, and molecular graphs of the D isomers are reported in Table S4 of the Supplementary Materials, and these isomers are illustrated in Figure 7 which shows that the F atom of FH and ClF, and the Cl atom of ClH are adjacent to P. From Figure S3 it can be seen that

Molecules 2020, 25, 2846 8 of 14

J(F-P)Molecules is 202015.8, 25 Hz, 2846 at a distance of 6.22 Å in the complex with ClF and 12.1 Hz in the complex with8 of FH. 14 − − When the acid is ClH, J(Cl-P) has a value of 3.2 Hz. these complexes have an unfavorable dipole− alignment. The binding energies of the D isomers are The structures, total energies, and molecular graphs of the D isomers are reported in Table S4 reported in Table 5, and are noticeably less than those of the C isomers. The D isomers have binding of the Supplementary Materials, and these isomers are illustrated in Figure7 which shows that the energies that range from 0.8 kJ·mol–1 for HF:P(CH)3 at a F-P distance of 3.49 Å, to 3.9 kJ·mol–1 for F atom of FH and ClF, and the Cl atom of ClH are adjacent to P. From Figure S3 it can be seen that HCl:P(CH)3 at a Cl-P distance of 3.63 Å. The binding energy of the FCl:P(CH)3 complex is slightly these complexes have an unfavorable dipole alignment. The binding energies of the D isomers are less at 3.6 kJ·mol–1, but the Cl-P distance of 3.22 Å is much shorter. reported in Table5, and are noticeably less than those of the C isomers. The D isomers have binding The D isomers have large spin–spin1 coupling constants J(X-P), and Table S5 shows that total1 J is energies that range from 0.8 kJ mol− for HF:P(CH)3 at a F-P distance of 3.49 Å, to 3.9 kJ mol− for essentially equal to the FC term. The smallest coupling constant with a value of 45 Hz is J(Cl-P) in HCl:P(CH)3 at a Cl-P distance of 3.63 Å. The binding energy of the FCl:P(CH)3 complex is slightly less HCl:P(CH)3. HF:P(CH)1 3 has a value of J(F-P) equal to 118 Hz. The largest coupling constant among at 3.6 kJ mol− , but the Cl-P distance of 3.22 Å is much shorter. the D isomers is J(F-P) for FCl:P(CH)3 with a value of 299 Hz.

(a) (b) (c)

FigureFigure 7.7. EquilibriumEquilibrium structuresstructuresD Dfor for ((aa)) FH:P(CH)FH:P(CH)33,(, (bb)) ClH:P(CH)ClH:P(CH)33, and ((c) FCl:P(CH)3..

1 Table 5. Binding energies ( ∆E, kJ mol−–1), intermolecular distances (R, Å), charge-transfer energies Table 5. Binding1 energies −(–ΔE, kJ·mol ), intermolecular distances (R, Å), charge-transfer energies (CT, kJ mol− ), and spin–spin coupling constants (J, Hz]) for complexes XY:P(CH)3 isomers D. (CT, kJ·mol–1), and spin–spin coupling constants (J, Hz]) for complexes XY:P(CH)3 isomers D.

aa a a AcidAcid –ΔE ∆E PlpP→σ*(X-Y)σ*(X-Y) R(X-P) R(X-P) J(X-P) J(X-P) lp→ FH 0.8 − 0.6 3.489 118.1 FH 0.8 0.6 3.489 118.1 ClH 3.9 2.9 3.627 44.6 ClFClH 3.6 3.9 1.6 2.9 3.627 3.219 44.6 299.3 a ClF 3.6 X is the atom 1.6 adjacent to 3.219P. 299.3 The SAPT energies for the C and Da X isomers is the atom are adjacent given to in P. Table 6. The SAPT binding energies are less than the MP2 binding energies. In fact, SAPT predicts that the HF:P(CH)3 isomer D is unbound withThe an unfavorableD isomers have electrostatic large spin–spin interaction coupling energy constants of 0.5 kJ J(X-P),.mol–1 and. As Tableusual, S5 the shows first-order that total SAPT J is essentiallyexchange term equal is to the the FCdestabilizing term. The smallestterm. Howeve couplingr, the constant electrostatic with a valueterm ofis 45not Hz the is J(Cl-P)primary in HCl:P(CH)stabilizing 3term. HF:P(CH) in these3 hasisomers a value as ofit is J(F-P) in the equal A and to 118 B isomers, Hz. The but largest rather, coupling it is the constant second-order among thedispersionD isomers term. is J(F-P)In the for FH:P(CH) FCl:P(CH)3 isomer3 with C a, value the dispersion of 299 Hz. term cancels the exchange term. In the remainingThe SAPT complexes, energies it forhas the anC absoluteand D isomers value that are is given no more in Table than6. 2 The kJ.mol SAPT–1 less binding than the energies exchange are lessterm. than All theof the MP2 other binding terms energies. are stabilizing, In fact, except SAPT predictsfor the induction that the HF:P(CH) term for the3 isomer C andD Dis isomers unbound of 1 . –1 withClF:P(CH) an unfavorable3. The sumelectrostatic of the stabilizing interaction terms energyleads to of binding 0.5 kJ mol energies− . As between usual, the 3 and ﬁrst-order 5 kJ mol SAPT for exchangethe C isomers, term isand the between destabilizing 1 and term.2 kJ.mol However,–1 for the the bound electrostatic D isomers. term is not the primary stabilizing term in these isomers as it is in the A and B isomers, but rather, it is the second-order dispersion term. In the FH:P(CH)3 isomer C, the dispersion term cancels the exchange term. In the remaining 1 complexes, it has an absolute value that is no more than 2 kJ mol− less than the exchange term. All of the other terms are stabilizing, except for the induction term for the C and D isomers of ClF:P(CH)3. 1 The sum of the stabilizing terms leads to binding energies between 3 and 5 kJ mol− for the C isomers, 1 and between 1 and 2 kJ mol− for the bound D isomers.

Molecules 2020, 25, 2846 9 of 14

1 Table 6. SAPT energies (kJ mol− ) for equilibrium XY:P(CH)3 complexes isomers C and D.

(1) (1) (2) (2) a XY:P(CH)3 C XY = E E E E δHF ∆E(SAPT) el ex ind disp − HF 2.1 5.6 0.4 5.7 0.3 3.0 − − − − HCl 5.1 13.2 0.3 12.0 1.1 5.2 − − − − FCl 3.0 9.3 0.0 8.9 0.8 3.4 − − − XY:P(CH)3 D XY = HF 0.5 3.3 0.3 2.8 0.3 0.2 b − − − − HCl 2.0 7.1 0.2 6.1 0.7 2.0 − − − − ClF 2.1 7.5 0.0 5.5 1.2 1.2 − − − a ∆E(SAPT) is the DFT-SAPT interaction energy equal to the negative of the sum of the component energies. b Based− on the SAPT analysis, this complex is not bound.

Up to this point, the discussion of coupling constants has focused on coupling across intermolecular 1 bonds. However, it is also of interest to examine how J(P-C) for P(CH)3 changes, depending on whether the P-C bond interacts or does not interact with FH, ClH, or ClF. The data required for this analysis are given in Table S6. For the B, C, and D isomers, 1J(P-C) varies by about 1 Hz relative to isolated 1 ± P(CH)3. For these, J(P-C) is essentially independent of bond formation by P(CH)3. Bond formation in these isomers occurs at relatively long distances, and does not produce a large enough change in the electron distributions of P and C to produce changes in 1J(P-C). This is also evident from the small values of the charge-transfer energies in these isomers. For the A isomers, 1J(P-C) coupling constants in complexes with FH and ClH span a slightly greater range compared to the isomers B, C, and D. However, it is the A isomer with ClF that exhibits dramatic changes. This is consistent with the stronger halogen bonding interaction between P(CH)3 and ClF which leads to a signiﬁcant lengthening of the P-C bond to 1.946 Å, and changes in the electron density of that bond. The electron density changes are evident from the charge-transfer energies, and from the coupling constant for the interacting P-C bond, which decreases in absolute value from 40 Hz in isolated P(CH) to 33 Hz in this complex. Although the noninteracting P-C bonds decrease − 3 − in length by only 0.007 Å, 1J(P-C) for these bonds increases in absolute value to 45 Hz in response to − the changes in the electron density of this isomer.

2.6. Structures A-tr and B-tr The structures, total energies, and molecular graphs of the complexes A-tr and B-tr are given in Table S7 of the Supplementary Materials, and the structures FH:P(CH)3 and FH:P(CH)3-A-tr, and ClF:P(CH)3 and ClF:P(CH)3B-tr, are illustrated in Figure8. These complexes have C 3v symmetry and are not equilibrium structures on their potential surfaces, since they have two degenerate imaginary frequencies. Rather, complexes labeled A-tr are the transition structures for converting one isomer A to another one of the A isomers, and B-tr are the transition structures for converting one isomer B to another one of the isomers B. Table7 presents the binding energies, barriers, and intermolecular distances for the transition structures XY:P(CH)3 A-tr and B-tr. The intermolecular distances in these transition structures are longer than the X-P and X-C distances in the corresponding complexes A and B, respectively. The A-tr 1 structures are bound with stabilization energies ranging from 8 kJ mol− for FH:P(CH)3 A-tr and 1 ClH:P(CH)3 A-tr to 13 kJ mol− for ClF:P(CH)3 A-tr. The B-tr isomers have binding energies that 1 1 range from 10 kJ mol− for FH:P(CH)3 B-tr to 13 kJ mol− for ClF:P(CH)3 B-tr. From these energies of corresponding equilibrium complexes and transition structures, it is possible to evaluate the barrier for converting one A or B complex to another equivalent complex. These barriers are relatively high for 1 1 the A isomers, and vary from 9 kJ mol− for ClH:P(CH)3 to 19 kJ mol− for ClF:P(CH)3. Given the structure of the B isomers, it is not surprising that the barriers to converting one isomer B to another B Molecules 2020, 25, 2846 10 of 14

1 1 are much lower. These barriers vary from 2 kJ mol− for ClH:P(CH)3 to 4 kJ mol− for FH:P(CH)3 and MoleculesFCl:P(CH) 20203., 25, 2846 10 of 14

A A-tr

B B-tr

Figure 8.8. Complexes FH:P(CH)3 (A) and ( A-tr), and ClF:P(CH) 3 ((BB)) and and ( (B-trB-tr).). 1 Table 7. Binding energies ( ∆E), barriers (∆E†, kJ mol− ), and intermolecular distances (R,Å), for the Table 7 presents the binding− energies, barriers, and intermolecular distances for the transition transition structures XY:P(CH)3 A-tr and XY:P(CH)3 B-tr. structures XY:P(CH)3 A-tr and B-tr. The intermolecular distances in these transition structures are longer than the X-P and X-C distances in theA-tr corresponding complexes B-trA and B, respectively. The A-tr

–1 3 structures are boundAcid with stabilizat∆E ion∆ Eenergies† R(X-P) ranging from∆E 8 ∆kJ·molE † R(X-C)for FH:P(CH) A-tr and –1− − ClH:P(CH)3 A-tr to 13FH kJ·mol 7.8for ClF:P(CH) 12.23 A-tr. 3.519 The B-tr 10.4 isomers 4.4have binding 3.258 energies that range from 10 kJ·mol–1 for FH:P(CH)3 B-tr to 13 kJ·mol–1 for ClF:P(CH)3 B-tr. From these energies of ClH 7.5 9.0 3.965 12.1 2.0 3.653 corresponding equilibrium complexes and transition structures, it is possible to evaluate the barrier for converting one A or BClF complex 12.9 to another 18.7 equivalent 2.985 complex. 13.0 These barriers 4.3 are 3.137 relatively high for the A isomers, and vary from 9 kJ·mol–1 for ClH:P(CH)3 to 19 kJ·mol–1 for ClF:P(CH)3. Given the structure of the3. Methods B isomers, it is not surprising that the barriers to converting one isomer B to another B are much lower. These barriers vary from 2 kJ·mol–1 for ClH:P(CH)3 to 4 kJ·mol–1 for FH:P(CH)3 and FCl:P(CH)3. The structures of the isolated phosphatetrahedrane molecule, P(CH)3, the monomers HF, HCl, and ClF, and the complexes formed by phosphatetrahedrane and the monomers were optimized at Table 7. Binding energies (–ΔE), barriers (ΔE†, kJ·mol–1), and intermolecular distances (R,Å), for the second-order Møller–Plesset perturbation theory (MP2) [29–32] with the aug’-cc-pVTZ basis set [33]. transition structures XY:P(CH)3 A-tr and XY:P(CH)3 B-tr. This basis set was derived from the Dunning aug-cc-pVTZ basis set [34,35] by removing diﬀuse functions from H atoms. Frequencies A-tr were computed to establish that the B-tr optimized structures Acid –ΔE ΔE† R(X-P) –ΔE ΔE‡ R(X-C) correspondFH to equilibrium 7.8 structures 12.2 on their 3.519 potential surfaces. 10.4 Transition 4.4 structures that 3.258 connect two equivalentClH equilibrium 7.5 structures 9.0 were also 3.965 optimized. Optimization 12.1 and 2.0 frequency 3.653 calculations ClF 12.9 18.7 2.985 13.0 4.3 3.137 were performed using the Gaussian 16 program (v 09, Carnegie Mellon University, Pittsburgh, PA, USA) [36]. Complex binding energies ( ∆E) were computed as the negative of the reaction energy for 3. Methods − the formation of the complex from phosphatetrahedrane and HF, HCl, or ClF. The electronstructures density of the propertiesisolated phosphatetrahedrane at bond critical points molecule, (BCPs) of P(CH) complexes3, the monomers have been analyzedHF, HCl, andusing ClF, the and Atoms the complexes in Molecules formed (AIM) by methodologyphosphatetrahedrane [37–40] employingand the monomers the AIMAll were [41optimized] program. at Thesecond-order topological Møller–Plesset analysis of perturbation the electron densitytheory (M producesP2) [29–32] the with molecular the aug’-cc-pVTZ graph of each basis complex. set [33]. This graphbasis set identiﬁes was derived the location from of the electron Dunning density aug- featurescc-pVTZ of basis interest, set including[34,35] by the removing electron densitydiffuse (functionsρ) maxima from associated H atoms. with Frequencies the various were nuclei, comput and saddleed to pointsestablish which that correspond the optimized to bond structures critical points.correspond The to zero equilibrium gradient line structures which connectson their apotent BCPial with surfaces. two nuclei Transition is the bond structures path. that The Naturalconnect twoBond equivalent Order (NBO) equilibrium [42] method structures has been used were to analyzealso optimized. the stabilizing Optimization charge-transfer and interactionsfrequency calculations were performed using the Gaussian 16 program (v 09, Carnegie Mellon University, Pittsburgh, PA, USA) [36]. Complex binding energies (−ΔE) were computed as the negative of the reaction energy for the formation of the complex from phosphatetrahedrane and HF, HCl, or ClF.

Molecules 2020, 25, 2846 11 of 14 using the NBO-6 program [43]. In addition, the Electron Localization Function (ELF) [44] has been generated for P(CH)3 using the Topmod program [45] to further characterize those regions of space in which the electron density is high. Density Functional Theory–Symmetry Adapted Perturbation Theory (DFT-SAPT) has been used to investigate interaction energies. In this approach, the energies of interacting monomers are expressed in terms of orbital energies obtained from Kohn–Sham density functional theory [46,47] The SAPT [48] method allows for the decomposition of the interaction energy of a complex into diﬀerent terms related to physically well-deﬁned components, such as those arising from electrostatic, exchange, induction, and dispersion terms. The interaction energy can be expressed within the framework of the SAPT method as ∆ESAPT = Eel (1) + Eex(1) + Eind(2) + Edisp(2) (1)

(1) where Eel is the first-order electrostatic interaction energy of the monomers each with its unperturbed (1) (2) electron distribution; Eex is the first-order exchange energy term; Eind denotes the second-order induction energy arising from the interaction of permanent multipoles with induced multipole moments and charge-transfer contributions, plus the change in the repulsion energy induced by the deformation (2) of the electron clouds of the monomers; Edisp is the second-order dispersion energy, which is related to the instantaneous multipole-induced multipole moment interactions plus the second-order correction for coupling between the exchange repulsion and the dispersion interactions. In addition to the terms listed in Equation (1), a Hartree–Fock correction term δHF, which includes higher-order induction and exchange corrections, is also included [49]. The DFT-SAPT calculations have been performed with the MOLPRO program [50] at the PBE0/aug’-cc-pVTZ level of theory [51]. Equation of motion coupled cluster singles and doubles (EOM-CCSD) spin–spin coupling constants were evaluated in the CI (configuration interaction)-like approximation [52,53] with all electrons correlated. For these calculations, the Ahlrichs [54] qzp basis set was placed on 13C and 19F, and the qz2p basis on 31P, 35Cl, and the 1H atom of FH and ClH. The Dunning cc-pVDZ basis set was placed on the 1H atoms bonded to C atoms. All terms that contribute to the total coupling constant, namely, the paramagnetic spin orbit (PSO), diamagnetic spin orbit (DSO), Fermi contact (FC), and spin dipole (SD) have been evaluated. Coupling constant calculations were performed using ACES II [55] on the HPC cluster Owens at the Ohio Supercomputer Center.

4. Conclusions Ab initio MP2/aug’-cc-pVTZ calculations have been performed to determine the structures and binding energies of complexes formed by phosphatetrahedrane, P(CH)3, and the monomers HF, HCl, and ClF. The following statements are supported by the results of this study.

1. Four types of complexes, designated A, B, C, and D, have been found on the potential energy surfaces. Isomers A form at the P atom near the end of a P-C bond, B at a C-C bond, C at the centroid of the C-C-C ring along the C3 symmetry axis, and D at the P atom along the C3 symmetry axis. 2. Complexes A and B are stabilized by hydrogen bonds when FH and ClH are the acids, and by halogen bonds when ClF is the acid. In isomers C, the dipole moments of the two monomers are favorably aligned, and there exists a long-range interaction between the atom at the negative end of the dipole moment vector and the P atom. In the D isomers, the dipole moment vectors are unfavorably aligned. 3. The binding energies of the A and B isomers decrease in the order ClF > FH > ClH, while the binding energies of the C and D isomers decrease in the order ClH > ClF > HF. For ﬁxed FH, ClH, or ClF, binding energies of the isomers decrease in the order A > B > C > D. 4. Charge-transfer stabilizes isomers A, but the charge-transfer interactions are small in isomers B and D, and nonexistent in C. Molecules 2020, 25, 2846 12 of 14

5. The SAPT binding energies for the A and B isomers are smaller than the corresponding MP2 binding energies. The most stabilizing SAPT component for these isomers is the electrostatic interaction, except for ClH:P(CH)3 isomer B for which the dispersion interaction is the most stabilizing. These two terms are similar for the B isomer of FCl:P(CH)3. In contrast, the dispersion interaction is the most stabilizing term for the C and D isomers. 6. Transition structures for converting one isomer A to another A, and one isomer B to another B, have been found on the potential surfaces. The barriers for converting one isomer to another are signiﬁcantly higher for the A isomers. 7. EOM-CCSD coupling constants J(X-C) are small for both the B and C isomers. J(X-P) values are larger and positive for the A isomers, negative for the B isomers, and have their largest values for the D isomers. 1 8. Coupling constants J(P-C) in the isomers change very little from their value in isolated (PH)3, 1 except for the complex FCl:P(CH)3 isomer A. J(P-C) decreases in absolute value for the P-C bond that interacts with ClF as the P-C bond elongates signiﬁcantly. 1J(P-C) increases in absolute value for the other two P-C bonds, even though there is little change in the P-C distances relative to isolated P(CH)3.

Supplementary Materials: The following are available online, Table S1: Structures (Å), total energies (a.u.), and molecular graphs of P(CH)3 and XY:P(CH)3 complexes A; Table S2: Structures (Å), total energies (a.u.), and molecular graphs of complexes B; Table S3: Structures (Å), total energies (a.u.), and molecular graphs of complexes C. Table S4: Structures (Å), total energies (a.u.), and molecular graphs of complexes D; Table S5: PSO, DSO, FC, and SD components of total J for complexes A, B, C, and D; Figure S1: 2hJ(F-P) (Hz) versus the F-P 1x distance (Å) for FH:P(CH)3 A along the F-P intrinsic reaction path; Figure S2: J(Cl-P) (Hz) versus the Cl-P distance (Å) for FCl:P(CH)3 A along the Cl-P intrinsic reaction path; Fig: S3. Dipole alignments in the isomers C 1 and D for ClH:P(CH)3;Table S6: J(P-C) (Hz) for P-C bonds of P(CH)3 that do or do not interact with FH, ClH, and ClF in complexes A, B, C, and D; Table S7: Structures (Å), total energies (a.u.), and molecular graphs of transition structures. Author Contributions: I.A. and J.E.D.B. did the calculations. J.E.D.B., J.E. and I.A. contributed equally to the writing of this paper. All authors have read and agreed to the published version of the manuscript. Funding: This work was carried out with financial support from the Ministerio de Ciencia, Innovación y Universidades of Spain (Project No. PGC2018–094644-B-C22) and Comunidad Autónoma de Madrid (P2018/EMT–4329 AIRTEC-CM). Conﬂicts of Interest: The authors declare no conﬂicts of interest.

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