molecules

Article Quantum Chemical Calculations on CHOP Derivatives—Spanning the Chemical Space of Phosphinidenes, Phosphaketenes, Oxaphosphirenes, and COP− Isomers

Alicia Rey 1, Arturo Espinosa Ferao 1,* and Rainer Streubel 2,* 1 Department of Organic Chemistry, Faculty of Chemistry, University of Murcia, Campus de Espinardo, 30100 Murcia, Spain; [email protected] 2 Institut of Inorganic Chemistry, Rheinischen Friedrich-Wilhelms-Universiy of Bonn, Gerhard-Domagk-Str. 1, 53121 Bonn, Germany * Correspondence: [email protected] (A.E.F.); [email protected] (R.S.); Tel.: +34-868-887489 (A.E.F.); +49-228-73-5345 (R.S.) Academic Editor: J. Derek Woollins



 Received: 16 November 2018; Accepted: 16 December 2018; Published: 17 December 2018

Abstract: After many decades of intense research in low-coordinate phosphorus chemistry, the advent of Na[OCP] brought new stimuli to the field of CHOP isomers and derivatives thereof. The present theoretical study at the CCSD(T)/def2-TZVPP level describes the chemical space of CHOP isomers in terms of structures and potential energy surfaces, using oxaphosphirene as the starting point, but also covering substituted derivatives and COP− isomers. Bonding properties of the P–C, P–O, and C–O bonds in all neutral and anionic isomeric species are discussed on the basis of theoretical calculations using various bond strengths descriptors such as WBI and MBO, but also the Lagrangian kinetic energy density per electron as well as relaxed force constants. Ring strain energies of the superstrained 1H-oxaphosphirene and its barely strained oxaphosphirane-3-ylidene isomer were comparatively evaluated with homodesmotic and hyperhomodesmotic reactions. Furthermore, first time calculation of the ring strain energy of an anionic ring is described for the case of oxaphosphirenide.

Keywords: main group elements; phosphinidene; phosphaketene; oxaphosphirene; phosphacyanic acid; phosphafulminic acid; oxaphosphirenide; phosphaethynolate

1. Introduction The chemistry of low-coordinate phosphorus compounds such as phosphinidenes (I), phosphaalkenes (II), and phosphaketenes (III) (Scheme1) have received attention from experimentalists and theoreticians over many decades due to their particular bonding situation and reactivity [1–4]. Somewhat similar is the situation for strained ring systems containing phosphorus for which phosphiranes (IV) and 1H-phosphirenes (V)[5] may serve as good cases in point. An existing synthetic challenge is represented by oxaphosphiranes (VI)[6,7], only experimentally described as a ligand in transition metal complexes, being valuable due to a high potential in polymer chemistry, and oxaphosphirenes (VII)[8,9] (a 3-phosphinyl-1H-oxaphosphirene was computed as one of the possible CHOP isomers [10]) for which not even a (failed) attempt exists in the literature; the latter may stem from a (discouraging) degree of antiaromaticity [11]. The first stable derivative of a phosphaketene, possessing the general formula RP=C=O, was reported by Appel (R = Mes* = 2,4,6-tri-tert-butylphenyl) [12,13], and which remained the only derivative for a long time. It was Grützmacher who then described a novel approach to III using sodium phosphaethynolate Na[OCP] [14]. This new salt, bearing the OCP− (phosphaethynolate) anion [15,16], enabled a

Molecules 2018, 23, 3341; doi:10.3390/molecules23123341 www.mdpi.com/journal/molecules Molecules 2018, 23, x 2 of 16 Molecules 2018, 23, x 2 of 16 longMolecules time.2018 , It23 , 3341was Grützmacher who then described a novel approach to III using sodium2 of 16 long time. It was Grützmacher who then described a novel approach to III using sodium phosphaethynolate Na[OCP] [14]. This new salt, bearing the OCP− (phosphaethynolate) anion phosphaethynolate Na[OCP] [14]. This new salt, bearing the OCP− (phosphaethynolate) anion [15,16], enabled a systematic exploration of its use in the field of P-heterocyclic chemistry [17]. systematic[15,16], enabled exploration a systematic of its use exploration in the field of of its P-heterocyclic use in the field chemistry of P-heterocyclic [17]. Interestingly, chemistry the anion [17]. Interestingly, the anion reacts as an ambident nucleophile, i.e., it could be used to form transient reactsInterestingly, as an ambidentthe anion nucleophile,reacts as an i.e.,ambident it could nucl beeophile, used to i.e., form it could transient be used phosphaalkynes to form transient that phosphaalkynes that underwent cyclotrimerization to yield 1,3,5-triphosphinines [18,19] or to obtain underwentphosphaalkynes cyclotrimerization that underwent to cyclotrimerization yield 1,3,5-triphosphinines to yield 1,3,5-triphosphinines [18,19] or to obtain new [18,19] phosphaketene or to obtain new phosphaketene derivatives [20]. The parent phosphaketene (phosphaisocyanic acid) H–P=C=O derivativesnew phosphaketene [20]. The derivatives parent phosphaketene [20]. The parent (phosphaisocyanic phosphaketene (phosphaisocyanic acid) H–P=C=O has acid) been H–P=C=O recently has been recently isolated and spectroscopically characterized [21]. Both H–P=C=O and the PCO isolatedhas been and recently spectroscopically isolated and characterized spectroscopically [21]. Both characterized H–P=C=O [21]. and theBoth PCO H–P=C=O radical wereand preparedthe PCO radical were prepared by reaction of CO with P atoms or PH radicals, which in turn were produced byradical reaction were ofprepared CO with by P reaction atoms orof PHCO with radicals, P atoms which or inPH turn radicals, were which produced in turn from were P4 producedand PH3 from P4 and PH3 discharge or photolysis.[22] Preliminary calculations on the geometry and relative dischargefrom P4 and or PH photolysis3 discharge [22 or]. photolysis.[22] Preliminary calculations Preliminary on calculations the geometry on the and geometry relative and energies relative of energies of H–P=C=O [23,24] and its phosphacyanic acid (H–O–C≡P) isomer [25,26] have been H–P=C=Oenergies of [23H–P=C=O,24] and [23,24] its phosphacyanic and its phosphacyanic acid (H–O–C acid≡P) (H–O–C isomer≡P) [25 isomer,26] have [25,26] been have reported, been reported, including their interconversion [27,28] and the less stable phosphafulminic acid (H–CPO) includingreported, including their interconversion their interconversion [27,28] and [27,28] the lessand stablethe less phosphafulminic stable phosphafulminic acid (H–CPO) acid (H–CPO) (at the (at the MP2/DZ+P//HF/3-21G* level [28,29]). Worth mentioning is also a more recent study on MP2/DZ+P//HF/3-21G*(at the MP2/DZ+P//HF/3-21G* level [level28,29 ]).[28,29]). Worth mentioningWorth mentioning is also a moreis also recent a more study recent on compliance study on compliance constants (reciprocals of the bond relaxed force constants) for the parent phosphaketene constantscompliance (reciprocals constants (reciprocals of the bond of relaxed the bond force rela constants)xed force forconstants) the parent for phosphaketenethe parent phosphaketeneIII and its III and its “cyclic isomer H–P(μ-CO)” (1H-oxaphosphirene) VII [30]. “cyclicIII andisomer its “cyclic H–P( isomerµ-CO)” H–P( (1Hμ-oxaphosphirene)-CO)” (1H-oxaphosphirene)VII [30]. VII [30].

Scheme 1. Low-coordinate (I–III) and strained (IV–VII) phosphorus compounds. Scheme 1. Low-coordinate ( I–III) and strained (IV–VII) phosphorus compounds.

Herein, the the potential potential energy energy surface surface (PES) (PES) for for the the parent parent 1H-oxaphosphirene 1H-oxaphosphirene (1a; (hereafter,1a; hereafter, just Herein, the potential energy surface (PES) for the parent 1H-oxaphosphirene (1a; hereafter, just oxaphosphirene)just oxaphosphirene) and four and other four substituted other substituted derivatives derivatives (1b–e) (Figure (1b– e1)) were (Figure explored,1) were constituting explored, oxaphosphirene) and four other substituted derivatives (1b–e) (Figure 1) were explored, constituting aconstituting representative a representative set that covers set electron-donating that covers electron-donating and -withdrawing and -withdrawing groups. The groups. PES for The anionic PES a representative set that covers electron-donating and -withdrawing groups. The PES for anionic derivativesfor anionic derivativesof the formula of the COP formula−, conjugated COP−, conjugatedbase of 1a and base its of isomers,1a and its is isomers, also presented. is also presented. The ring derivatives of the formula COP−, conjugated base of 1a and its isomers, is also presented. The ring strainThe ring energy strain for energy parent for cyclic parent isomers cyclic is isomers also estimated. is also estimated. strain energy for parent cyclic isomers is also estimated.

Figure 1. 1H-Oxaphosphirene-Oxaphosphirene deri derivativesvatives studied. Figure 1. 1H-Oxaphosphirene derivatives studied. 2. Results and Discussion 2. Results and Discussion 2. Results and Discussion 2.1. PES of the Parent Oxaphosphirene (1a) 2.1. PES of the Parent Oxaphosphirene (1a) 2.1. PES of the Parent Oxaphosphirene (1a) The small ring size and the presence of a double bond in the oxaphosphirene ring in 1 is expected The small ring size and the presence of a double bond in the oxaphosphirene ring in 1 is to entailThe high small strain. ring Additionally,size and the the presence availability of a of double an electron bond pair in atthe O togetheroxaphosphirene with the electronring in pair1 is expected to entail high strain. Additionally, the availability of an electron pair at O together with the ofexpected the double to entail bond high could strain. constitute Additionally, an antiaromatic the availability 4π electron of an arrangement electron pair that at mightO together be minimized with the electron pair of the double bond could constitute an antiaromatic 4π electron arrangement that byelectron a geometric pair of distortion. the double This bond energetically could constitute disfavourable an antiaromatic combination 4π should electron facilitate arrangement the existence that might be minimized by a geometric distortion. This energetically disfavourable combination should ofmight other be (more) minimized stable by isomers, a geometric most of distortion. them being This acyclic energetically in nature. disfavourable With this aim, thecombination PES of the should parent facilitate the existence of other (more) stable isomers, most of them being acyclic in nature. With this oxaphosphirenefacilitate the existence ring system of other1a (more)was thoroughly stable isomer exploreds, most and of allowedthem being the acyclic location in of nature. ten closed-shell With this aim, the PES of the parent oxaphosphirene ring system 1a was thoroughly explored and allowed the molecularaim, the PES CHOP of the species,parent oxaphosphirene together with aring fragmentation system 1a was pathway thoroughly (Scheme explored2). Only and allowed significant the location of ten closed-shell molecular CHOP species, together with a fragmentation pathway differenceslocation of withten closed-shell a previous reportmolecular computed CHOP at species, the rather together similar with (see thea fragmentation Computational pathway Details) (Scheme 2). Only significant differences with a previous report computed at the rather similar (see QCISD(T)/6-311++G(3df,2p)//MP2/6-311++G(d,p)(Scheme 2). Only significant differences with a previous level report [9] deserve computed comments. at the rather Another similar previous (see the Computational Details) QCISD(T)/6-311++G(3df,2p)//MP2/6-311++G(d,p) level [9] deserve reportthe Computational described the geometryDetails) QCISD(T)/6-311++G(3d and relative energies off,2p)//MP2/6-311++G(d,p) five of the closed-shell minimalevel [9] at thedeserve more comments. Another previous report described the geometry and relative energies of five of the modestcomments. B3LYP/6-311G** Another previous level [report8]. described the geometry and relative energies of five of the closed-shell minima at the more modest B3LYP/6-311G** level [8]. closed-shellFirst of minima all, in that at the report, more themodest parent B3LY structureP/6-311G**1a was level described [8]. as an acyclic isomer having First of all, in that report, the parent structure 1a was described as an acyclic isomer having the the connectivityFirst of all, in ofthat a report, formyl-phosphinidene the parent structure (HC(O)–P) 1a was described but featuring as an acyclic double isomer C=P andhaving single the connectivity of a formyl-phosphinidene (HC(O)–P) but featuring double C=P and single C–O bonds, C–Oconnectivity bonds, of as a deduced formyl-phosphinidene exclusively from (HC(O)–P) their bond but featuring distances double (1.645 C=P and and 1.326 single Å, respectively). C–O bonds, as deduced exclusively from their bond distances (1.645 and 1.326 Å, respectively). Such a Suchas deduced a formyl-phosphinidene exclusively from wastheir claimedbond distances as minimum (1.645 at and the HF/6-31G**1.326 Å, respectively). level (P–C 1.801Such Å;a

Molecules 2018,, 23,, 3341x 33 of of 16 formyl-phosphinidene was claimed as minimum at the HF/6-31G** level (P–C 1.801 Å; C=O 1.193 Å; ◦ C=OP–C–O 1.193 angle Å; 126.3°) P–C–O [26], angle but 126.3 never)[ found26], but at neverthe working found atlevel the of working theory level(see the of theoryComputational (see the ◦ ◦ ◦ ComputationalDetails): the relatively Details): small the P–C–O relatively bond small angle P–C–O of 86.5° bond found angle in of1a 86.5 (83.9°–88.7°found infor1a the(83.9 full–88.7 set of ◦ forcompounds the full set 1, except of compounds 1b featuring1, except an angle1b featuring of 99.4°), an far angle below of the 99.4 typical), far value below for the an typical open-chain value 2 ◦ forC-sp an2-centered open-chain bond C-sp angle-centered (ca. 120°), bond strongly angle ( ca.suggests120 ), the strongly cyclic suggests nature of the 1a cyclic, although nature with of 1a a, althoughcertainly elongated with a certainly endocyclic elongated P–O bond endocyclic (Table P–O1) for bond which (Table no bond1) for critical which point no bond (BCP) critical was found. point (BCP)Moreover, was the found. “acyclic” Moreover, structure the “ “acyclic”3” reported structure by Fu and “3” coworkers reported by [9] Fu turns and out coworkers to be erroneously [9] turns ◦ outdrawn to bebecause, erroneously according drawn to their because, data, accordingthe P–C–O to angle their (84.35°) data, the is P–C–Oeven more angle acute (84.35 than) the is even one morereported acute herein than for the 1a one and, reported therefore, herein unambiguously for 1a and, therefore, corresponds unambiguously to an oxaphosphirene corresponds species. to an oxaphosphireneThe P–O bond in species. 1a is by Thefar the P–O weakest bond in (most1a is flexible) by far the bond weakest according (most to flexible) its lowest bond relaxed according force 0 toconstant its lowest (k0 = relaxed 0.869 mdyn/Å), force constant compared (k = to 0.869 the mdyn/Å),P–C (4.527 comparedmdyn/Å) and to the C–O P–C (5.510 (4.527 mdyn/Å) mdyn/Å) bonds, and C–Oin agreement (5.510 mdyn/Å) with the bonds, reported in agreement compliance with cons thetants reported computed compliance at the CCS constantsD(T)(fc)/cc-pVTZ computed atlevel the 0 CCSD(T)(fc)/cc-pVTZ[22]. The relaxed force level constants [22]. The k0, relaxedobtained force from constants the compliancek , obtained matrix from method the compliance [31–33], matrix have methodreceived [31much–33], attention have received in recent much years attention as a me inasure recent of years bond as strength a measure in ofa variety bond strength of bonding in a varietysituations of bondingincluding situations organophosphorus including organophosphorusderivatives [30,34]. derivatives [30,34].

H C P O P 5a P P H H O O O 12at H 3aap P 3asp P O O H H 1a 4a H H H P C O P C O COP 7a 6a H 8a P O 2a H H-P +CO P O 10a 9a 11 Scheme 2.2. IsomersIsomers derived from parentparent oxaphosphireneoxaphosphirene 1a1a.. Singlet Singlet (closed-shell) structuresstructures represented in black, black, triplet triplet ones ones in in red, red, and and those those that that were were found found in inboth both electronic electronic states states are are in inblue. blue.

Lewis structural formulae for all closed-shell molecular isomers CHPO found 1a–9a (Scheme1) Lewis structural formulae for all closed-shell molecular isomers CHPO found 1a–9a (Scheme 1) were drawn according to the best electronic description, as deduced from standard bond-strength were drawn according to the best electronic description, as deduced from standard bond-strength descriptors, natural charges (Table1), and NBO (natural bond orbital) analysis [ 35,36]. With this aim, descriptors, natural charges (Table 1), and NBO (natural bond orbital) analysis [35,36]. With this aim, widespread used bond orders quantities, such as the Wiberg bond index (WBI) [37] and the Mayer widespread used bond orders quantities, such as the Wiberg bond index (WBI) [37] and the Mayer bond order (MBO) [38–42], were computed. They provide values approaching 1 for single bonds, 2 for bond order (MBO) [38–42], were computed. They provide values approaching 1 for single bonds, 2 double bonds, and so forth. Also, properties derived from the topological analysis of the electron for double bonds, and so forth. Also, properties derived from the topological analysis of the electron density, in line with Bader’s AIM (atoms-in-molecules) theory [43–45], in particular the electron density, in line with Bader’s AIM (atoms-in-molecules) theory [43–45], in particular the electron density itself (ρ) and the Lagrangian kinetic energy (G) computed at the bond critical point (BCP), were density itself (ρ) and the Lagrangian kinetic energy (G) computed at the bond critical point (BCP), calculated. The latter was only recently used in characterizing bond strength in phosphorus-containing were calculated. The latter was only recently used in characterizing bond strength in three-membered heterocycles [46] and, soon afterwards, the Lagrangian kinetic energy density per phosphorus-containing three-membered heterocycles [46] and, soon afterwards, the Lagrangian electron (G/ρ) was reported as a remarkable bond-strength property [47] which correlates with ring kinetic energy density per electron (G/ρ) was reported as a remarkable bond-strength property [47] strainwhich energiescorrelates (within with ring a series) strain when energies computed (within at a the series) ring when critical computed points [48 at]. the ring critical points [48].

Table 1. Endocyclic bond strength parameters and natural charges.

Molecules 2018, 23, 3341 4 of 16

Table 1. Endocyclic bond strength parameters and natural charges.

Bond d (Å) WBI MBO ρ (au) G (au) G/ρ (au) Atom qnat (e) P–C 1.671 1.571 1.694 0.183 0.234 1.279 P 0.469 1a P–O 2.046 0.779 0.785 1 1 1 C −0.137 C–O 1.288 1.338 1.339 0.353 0.463 1.311 O −0.525 P–C 1.956 0.997 0.991 0.116 0.044 0.376 P 0.359 2a P–O 1.870 0.626 0.735 0.101 0.105 1.041 C 0.236 C–O 1.229 1.582 1.555 0.393 0.700 1.780 O −0.537 P 0.736 P–C 1.677 2.107 1.984 0.202 0.254 1.253 3asp C −0.318 P–O 1.649 0.818 1.036 0.162 0.246 1.521 O −0.909 P 0.726 P–C 1.664 2.238 2.101 0.204 0.251 1.235 3aap C −0.311 P–O 1.644 0.819 1.030 0.165 0.251 1.523 O −0.912 P–C 1.672 2.005 1.917 0.198 0.251 1.265 P 0.589 4a P–O 1.773 0.642 0.794 0.126 0.164 1.306 C −0.302 C–O 1.873 0.520 0.472 1 1 1 O −0.775 P 1.540 P–C 1.562 2.421 2.341 0.206 0.322 1.561 5a C −0.867 P–O 1.475 1.401 1.903 0.233 0.518 2.225 O −0.917 P 0.049 P–C 1.683 1.674 1.719 0.163 0.248 1.522 6a C 0.346 C–O 1.152 2.022 2.212 0.477 1.014 2.128 O −0.424 P 0.327 P–C 1.547 2.696 2.833 0.202 0.380 1.878 7a C −0.184 C–O 1.299 1.115 1.184 0.333 0.450 1.350 O −0.641 P 0.421 P–O 1.591 0.928 1.197 0.152 0.323 2.125 8a C 0.084 C–O 1.249 1.309 1.359 0.328 0.737 2.249 O −0.639 P 0.081 P–O 1.919 0.410 0.550 0.074 0.077 1.039 9a C 0.538 C–O 1.145 1.908 2.079 0.463 1.059 2.289 O −0.558 P 0.298 P–C 1.941 0.851 0.965 0.130 0.043 0.332 syn-6at C 0.223 C–O 1.169 1.978 2.202 1.113 0.506 0.454 O −0.454 P 0.297 P–C 1.963 0.815 0.950 0.125 0.038 0.308 6at C 0.225 C–O 1.167 1.991 2.199 0.458 0.952 2.077 O −0.460 P 0.339 P–C 1.846 1.016 1.142 0.161 0.103 0.640 12at C 0.014 C–O 1.212 1.821 1.994 0.418 0.736 1.759 O −0.473 P–C 1.820 1.471 1.572 0.146 0.086 0.589 P −0.249 14 P–O 1.967 0.728 0.735 1 1 1 C −0.123 C–O 1.278 1.370 1.270 0.351 0.537 1.530 O −0.628 P −0.436 P–C 1.618 2.241 2.581 0.178 0.307 1.718 15 C 0.088 C–O 1.199 1.638 1.876 0.426 0.768 1.802 O −0.652 P 1.146 P–C 1.597 2.847 2.727 0.185 0.261 1.414 16 C −1.078 P–O 1.519 1.156 1.571 0.211 0.430 2.036 O −1.068 P −0.528 P–O 1.756 0.647 0.782 0.100 0.168 1.685 17 C 0.110 C–O 1.179 1.662 1.784 0.408 0.955 2.338 O −0.583 P −0.350 P–C 1.792 1.377 1.544 0.152 0.142 0.933 15t C −0.037 C–O 1.216 1.639 1.859 0.405 0.735 1.815 O −0.613 1 No BCP found. MoleculesMolecules 2018 2018, 23, 23, x, x 5 5of of 16 16

P P −0.350−0.350 P–CP–C 1.7921.792 1.3771.377 1.5441.544 0.1520.152 0.1420.142 0.9330.933 1515t t CC −0.037−0.037 C–OC–O 1.2161.216 1.6391.639 1.8591.859 0.4050.405 0.7350.735 1.8151.815 Molecules 2018, 23, 3341 OO −0.613−0.6135 of 16 1 No1 No BCP BCP found. found.

TheThe rather rather weak weak P–O P–O bond bond inin in 1a1a 1a cancan can bebe be attributedattributed attributed toto to twotwo two factors.fact factors.ors. On On one one hand, hand, the the rather rather ineffectiveineffective single single bond bond formed formed with with π -symmetryπ-symmetry between between a ap porbital orbital at at P Pand and π *(C–O),π*(C–O), as as shown shown in in thethe HOMO-1 HOMO-1 (Figure (Figure2 2a);a); 2a); thethe the NBONBO NBO analysisanalysis analysis indicatesindicate indicates thesthe the formationformation formation ofof of thethe the P–OP–O P–O singlesingle single bondbond bond betweenbetween between twotwo almostalmost almost purepure pure p p orbitals porbitals orbitals at at both at both both P (98.31%P P(98.31% (98.31% p character) p pch character)aracter) and and O and (98.15% O O (98.15% (98.15% p character). p pcharacter). character). On the On On other the the hand,other other thehand,hand, antibonding the the antibonding antibondingπ*(P–O) π and*(P–O)π*(P–O)σ*(P–O) and and characterσ *(P–O)σ*(P–O) character ofcharacter the HOMO of of the the and HOMO HOMO LUMO and (Figureand LUMO LUMO2b,c), (Figure respectively,(Figure 2b,c), 2b,c), therespectively,respectively, latter with the athe remarkablelatter latter with with a population aremarkable remarkable (0.027 population population electrons) (0.027 (0.027 according electrons) electrons) to theaccording according NBO analysis. to to the the NBO NBO analysis. analysis.

(a()a ) (b()b ) (c()c )

FigureFigure 2. 2.Computed ComputedComputed (B3LYP/def2-TZVPP) (B3LYP/def2-TZVPP) Kohn-Sham Kohn-Sham Kohn-Sham isosurfaces isosurfaces isosurfaces (0.06 (0.06 (0.06 au) au) au)for for for( a()a )HOMO-1, ( aHOMO-1,) HOMO-1, ( b()b ) (HOMO,bHOMO,) HOMO, and and and (c ()c LUMO ()c LUMO) LUMO of of 1a of 1a. 1a. .

TheThe cyclic cyclic carbene,carbene, carbene, oxaphosphirane-3-ylideneoxaphosphirane-3-ylidene oxaphosphirane-3-ylidene2a 2a ,2a, also also, also displays displays displays a a rather arather rather weak weak weak P–O P–O P–O bond bond bond (Table (Table (Table1) 0 but1)1) but withbut with with higher higher higher stiffness stiffness stiffness (k (=k (01.358k =0 =1.358 1.358 mdyn/Å) mdyn/Å) mdyn/Å) compared compared compared to to1a to 1a. In1a. In. this In this this case case case the the C–Othe C–O C–O bond bond bond also also also varies varies varies in 0 theinin the samethe same same sense sense sense (k =(k ( 7.1810k =0 =7.181 7.181 mdyn/Å), mdyn/Å), mdyn/Å), whereas whereas whereas the P–Cthe the P–Cbond P–C bond becomesbond becomes becomes comparatively comparatively comparatively weaker weaker weaker and more and and 0 elasticmoremore elastic (elastick = 1.412(k (0k =0 =1.412 mdyn/Å). 1.412 mdyn/Å). mdyn/Å). TheThe large large and and moderately moderately weak weak C–O C–O bond bond (no (no BCP BCP found) found) in in 4a 4a (Table (Table1 1),), 1), suggestssuggests suggests aa dativeadative dative 0 bondingbonding fromfrom from an an electronan electron electron pair pair pair at Oat toat O aO vacantto to a avacant orbitalvacant orbital atorbital the carbenicat at the the carbenic Ccarbenic atom (4aC C atom), atom which ( 4a(4a is′), equivalent′ ),which which is is 000 toequivalentequivalent the all-covalent to to the the all-cova bondall-cova Lewislentlent bond formulabond Lewis Lewis4a” formula orformula its resonant 4a 4a′′ ′′or or its structure its resonant resonant4a structure structure(Scheme 4a 34a′′′).′′′ (Scheme (Scheme 3). 3).

SchemeScheme 3. 3.Different Different representations representations of of isomer isomer 4a 4a.. .

The cyclic character of 4a is supported by NBO analysis that shows a formal C–O single bond TheThe cyclic cyclic character character of of 4a 4a is is supported supported by by NBO NBO analysis analysis that that shows shows a aformal formal C–O C–O single single bond bond between two almost pure p orbitals at both C and O (96.63 and 93.74 % p character, respectively), betweenbetween two two almost almost pure pure p porbitals orbitals at at both both C C and and O O (96.63 (96.63 and and 93.74 93.74 % % p pcharacter, character, respectively), respectively), the the the same holding for the single P–O bond (91.38 and 83.97% p character for P and O, respectively). samesame holding holding for for the the single single P–O P–O bond bond (91.38 (91.38 and and 83.97% 83.97%0000 p pcharacter character for for P Pand and O, O, respectively). respectively). This This This is compatible with a p-donor π-acceptor complex 4a between a hydroxide and a [C≡P]+ cation, isis compatible compatible with with a ap-donor p-donor π -acceptorπ-acceptor complex complex 4a 4a′′′′′′′′ between between a ahydroxide hydroxide and and a a[C [C≡P]≡P]+ cation,+ cation, according to the Dewar-Chatt-Duncanson model [49]. The MO drawings also support this view as accordingaccording to to the the Dewar-Chatt-Duncanson Dewar-Chatt-Duncanson model model [49] [49]. The. The MO MO drawings drawings also also support support this this view view as as far as HOMO-3 and LUMO constitute the bonding and antibonding interactions between an in-plane farfar as as HOMO-3 HOMO-3 and and LUMO LUMO constitute constitute the the bonding bonding and and antibonding antibonding interactions interactions between between an an π(C=P) orbital with a p-type atomic orbital at O, whereas HOMO and LUMO+1 are essentially the in-planein-plane π (C=P)π(C=P) orbital orbital with with a ap-type p-type atomic atomic orbital orbital at at O, O, whereas whereas HOMO HOMO and and LUMO+1 LUMO+1 are are π(C=P) and π*(C=P) combinations in the orthogonal plane (Figure3). essentiallyessentially the the π (C=P)π(C=P) and and π *(C=P)π*(C=P) combinations combinations in in the the orthogonal orthogonal plane plane (Figure (Figure 3). 3).

MoleculesMolecules2018 2018, 23, 23, 3341, x 66 ofof 16 16

(a) (b)

(c) (d)

FigureFigure 3.3. Computed (B3LYP/def2-TZVPP) (B3LYP/def2-TZVPP) Kohn–Sham Kohn–Sham isosurfaces isosurfaces (0.06 (0.06 au) au) for for (a) (aHOMO-3,) HOMO-3, (b) (bHOMO,) HOMO, (c) ( cLUMO,) LUMO, and and (d ()d LUMO+1) LUMO+1 of of4a4a. .

ItIt is is worth worth mentioning mentioning that that isomer isomer9a 9a, resulting, resulting from from P–C P–C bond bond cleavage cleavage in in oxaphosphirene oxaphosphirene1a 1a (Scheme(Scheme2 ),2), might might be be considered considered as as a vana van der de Waalsr Waals complex complex between between carbon carbon monoxide monoxide ( 11(11)) and and singletsinglet phosphinidene phosphinidene (10a(10a)) (C (C≡≡OO→→P–H),P–H), asas deduceddeduced fromfrom thethe ratherrather elongatedelongated andand weakweak P–OP–O linkagelinkage (Table (Table1). 1). This This bond bond might migh easilyt easily cleave, cleave, although although the the corresponding corresponding TS TS could could not not be be located located atat the the working working level level of of theory theory and, and, hence, hence, more more information information is is not not available. available. AllAll closed-shell closed-shell minima minima are are the the same same as as in in Fu’s Fu’s report, report, with with the the only only exception exception of of isomer isomer3a 3aapap thatthat waswas described described withwith aa linearlinear POCPOC moietymoiety but,but, atat thethe currentcurrent levellevel ofof theory,theory, has has a a zig-zag zig-zag geometry.geometry. Indeed,Indeed, wewe have have confirmed confirmed the the linear linear arrangement arrangement upon upon geometry geometry optimization optimization at at the the SCS-MP2/def2-TZVPSCS-MP2/def2-TZVP level.level. Species 3a3aapap can onlyonly bebe formedformed fromfrom itsitsmost most stable stable conformer conformer3a 3aspsp throughthrough the the cyclic cyclic isomer isomer4a 4a.. The The TS TS (transition (transition state) state) for for converting converting3a 3aspspinto into4a 4ais is the the only only one one not not reportedreported in in Fu’s Fu’s work. work. All All ground ground states states and and TSs TSs have have similar similar energies energies at at both both computational computational levels levels (rmsd(rmsd = = 1.77 1.77 kcal/mol). kcal/mol). AA fullfull energyenergy diagramdiagram withwith allall CHPO CHPO isomers isomers and and the the interconversion interconversion paths paths isis collected collected in in Figure Figure4. 4. The The TS TS for for the the dissociation dissociation of of9a 9ainto into singlet singlet phosphinidene phosphinidene ( 10a(10a)) and and CO CO ( 11(11)) couldcould not not be be located. located.

Molecules 2018, 23, 3341 7 of 16 Molecules 2018, 23, x 7 of 16

FigureFigure 4. Computed4. Computed (CCSD(T)/def2-TZVPP//B3LYP-D3/def2-TZVP) (CCSD(T)/def2-TZVPP//B3LYP-D3/def2-TZVP) zero-point zero-point corrected corrected energy energy profileprofile for for the the interconversion interconversion of of CHOP CHOP isomers. isomers.

TheThe overall overall PES PES points points to cyclic to cyclic systems systems1a and 1a2a andas thermodynamically 2a as thermodynamically disfavoured disfavoured compared to thecompared most stable to the acyclic most stable phosphaketene acyclic phosphaketene6a (and phosphacyanic 6a (and phosphacyanic acid 7a) and acid displaying 7a) and displaying little kinetic stability,little kinetic as deduced stability, by as the deduced little barriers by the little for their barriers conversion for their intoconversion6a. The into other 6a. cyclicThe other isomer cyclic4a is ratherisomer unstable 4a is rather both unstable thermodynamically both thermodynamically and kinetically. and kinetically. AlthoughAlthough a a formyl-phosphinidene formyl-phosphinidene was was no nott located located at the at theclosed-shell closed-shell PES of PES 1a, excitation of 1a, excitation of 1a of to1a itsto itsfirst first triplet triplet state state is isaccomplished accomplished with with structural structural reorganization reorganization leading leading to tothe the triplet triplet t formyl-phosphinideneformyl-phosphinidene12a 12at (Scheme (Scheme 22,, FigureFigure 44),), as previously re recognizedcognized [8]. [ The8]. The same same excitation excitation in oxaphosphirane-3-ylidene 2a leads to syn-6at that isomerizes to the anti conformer 6at. The latter in oxaphosphirane-3-ylidene 2a leads to syn-6at that isomerizes to the anti conformer 6at. The latter species can isomerize to the aforementioned species 12at or split into the “stable” species triplet species can isomerize to the aforementioned species 12at or split into the “stable” species triplet phosphinidene (10at) and carbon monoxide (11). phosphinidene (10at) and carbon monoxide (11). 2.2. Isomers of Substituted Oxaphosphirenes 2.2. Isomers of Substituted Oxaphosphirenes In case of the other differently substituted oxaphosphirenes 1a–e, the energies of the same set of In case of the other differently substituted oxaphosphirenes 1a–e, the energies of the same set isomers was computed. In almost all cases the most stable closed-shell species follow the same order of isomers was computed. In almost all cases the most stable closed-shell species follow the same as for the parent compounds, starting by the most stable phosphaketene (phosphaisocyanate) orderR–P=C=O: as for the6 > parent7 > 1 > 5 compounds, ≥ 2 > 9 (Figure starting 5). On the by thecontrary, most in stable case phosphaketeneof the fluoro-substituted (phosphaisocyanate) species, 7b R–P=C=O:is strongly6 destabilized> 7 > 1 > 5(also≥ 2 both> 9 conformers(Figure5). 3b On as thewell contrary, as 5b to a inlesser case extent), of the whereas fluoro-substituted 2b and 9b species,(also 10b7b )is are strongly comparatively destabilized stabilized. (also This both results conformers in a different3b as well order as of5b stabilityto a lesser 6b > extent), 2b > 9b whereas> 1b > 2b5band > 7b9b (Figure(also 10b4). Triplet) are comparativelyelectronic states stabilized.display similar This stability results than in a(singlet) different oxaphosphirenes order of stability 1, 6bwith> 2b two> 9b general> 1b > exceptions:5b > 7b (Figure 1) splitting4). Triplet into electronictriplet phosphinidene states display (10 similart) and carbon stability monoxide than (singlet) (11) oxaphosphirenesare usually favored1, with and two2) the general fluorinated exceptions: substitu 1)ent splitting comparatively into triplet favors phosphinidene all triplet state species (10t) and carbon(syn-6b monoxidet, 6bt and ( 1112b) aret), especially usually favored the pair and10bt 2) + the11 (obtained fluorinated after substituent dissociation). comparatively Compound favorssyn-6et all tripletis not state stable species and spontaneously (syn-6bt, 6bt andsplits12b intot), 10e especiallyt + 11. the pair 10bt + 11 (obtained after dissociation). Compound syn-6et is not stable and spontaneously splits into 10et + 11.

Molecules 2018, 23, 3341 8 of 16

Molecules 2018, 23, x 8 of 16

FigureFigure 5. Computed 5. Computed (CCSD(T)/def2-TZVPP//B3LYP-D3/def2-TZVP) (CCSD(T)/def2-TZVPP//B3LYP-D3/def2-TZVP) zero-point zero-point corrected corrected relative relative energiesenergies for all isomersfor all isomers of oxaphosphirenes of oxaphosphirenes1a –1ae.–e Energies. Energies are are referredreferred to to the the oxaphosphirene oxaphosphirene species species (1). (1). Therefore, the overall picture for the thermodynamic instability of cyclic isomers and the Therefore, the overall picture for the thermodynamic instability of cyclic isomers and the preferencepreference for phosphaketenes for phosphaketenes does does not not change change significantlysignificantly with with the thetype type of substitution of substitution (Figure (Figure5), 5), comparedcompared to the to parentthe parent compounds compounds (Figure(Figure4 ),4), exceptexcept a a small small relative relative stabilization stabilization of the of the oxaphosphirane-3-ylideneoxaphosphirane-3-ylidene2b, and2b, and the remarkablethe remarkable destabilization destabilization ofof fluoro-phosphacyanatefluoro-phosphacyanate 7b,7b in, in case of the fluoro-substitution.case of the fluoro-substitution.

− 2.3. Anionic2.3. Anionic COP− COPIsomers Isomers Formal substitution of H in the parent compounds by a lone pair affords the set of anionic Formalspecies substitution of general offormula H in theCPO parent−, for compoundswhich only four by aclosed-shell lone pairaffords minima the were set offound: anionic the species − of generaloxaphosphirenide formula CPO 14, and for whichthe products only fourresulting closed-shell from endocyclic minima P–O were (15), found: C–O (16 the), and oxaphosphirenide P–C (17) 14 andbond the productscleavage (Scheme resulting 4). For from only endocyclic the two latter P–O ring ( 15cleavage), C–O processes, (16), and the P–C corresponding (17) bond TSs cleavage (Schemewere4). For characterized. only the twoWith latter a small ring barrier, cleavage the C–O processes, bond cleavage the correspondingof 14 affords exergonically TSs were CPO characterized.− 16, With a smallwhereas barrier, cleavage the of C–Othe P–C bond bond cleavage occurs through of 14 affordsa moderately exergonically higher barrier CPO and− giving16, whereas rise to the cleavage less stable isomer POC− 17 (Figure 6). On the contrary, cleavage of the P–O bond under the restricted of the P–C bond occurs through a moderately higher barrier and giving rise to the less stable isomer − (closed-shell) formalism leads to splitting into CO and a P- anion, but excitation of 14 to the first POC 17triplet(Figure electronic6). On state the leads contrary, to a spontaneou cleavagesly ofcleavage the P–O of the bond P–O under bond, affording the restricted the bent (closed-shell) triplet formalismspecies leads 15t towhich, splitting on falling into to CO the and electronic a P- anion, ground but (singlet) excitation state, enables of 14 to the the access first to triplet the most electronic state leadsstable to isomer, a spontaneously the linear phosphaethynolate cleavage of the anion P–O PCO bond,− 15. affording the bent triplet species 15t which, on falling to the electronic ground (singlet) state, enables the access to the most stable isomer, the linear − phosphaethynolateMolecules 2018, 23, x anion PCO 15. 9 of 16

SchemeScheme 4. Isomers 4. Isomers derived derived from from oxaphosphirenide oxaphosphirenide14 14.. SingletSinglet (closed-shell) structures structures represented represented in black andin black triplet and onestriplet in ones red. in red.

Figure 6. Computed (CCSD(T)/def2-TZVPP//B3LYP-D3/def2-TZVP) zero-point corrected energy profile for the interconversion of COP− isomers.

The oxaphosphirenide 14 can be formally considered as the direct deprotonation product from either 1a (C-deprotonation) or 2a (P-deprotonation). Although most of the negative (natural) charge can be ascribed to the O atom due to its higher electronegativity (Table 1), the largest negative variation in electric charge corresponds to the P atom (Δqnat = −0.718 or −0.608 e in 1a or 2a, respectively) and, therefore, 14 could be safely represented with a formal negative charge on phosphorus. This is also supported by the HOMO (Figure 7) being mainly located at P. The stiffness of all three bonds keep the same order found for 1a and 2a: C–O > P–C > P–O (k0 = 4.322, 1.846 and 1.099 mdyn/Å, respectively).

Figure 7. Computed (B3LYP/def2-TZVPP) Kohn-Sham isosurface (0.06 au) for the HOMO of 14.

MoleculesMolecules 20182018,, 2323,, xx 99 ofof 1616

Molecules 2018, 23, 3341 9 of 16 SchemeScheme 4.4. IsomersIsomers derivedderived fromfrom oxaphosphirenideoxaphosphirenide 1414.. SingletSinglet (closed-shell)(closed-shell) structuresstructures representedrepresented inin blackblack andand triplettriplet onesones inin red.red.

FigureFigureFigure 6. Computed 6.6. ComputedComputed (CCSD(T)/def2-TZVPP//B3LYP-D3/def2-TZVP) (CCSD(T)/def2-TZVPP//B3LYP-D3/(CCSD(T)/def2-TZVPP//B3LYP-D3/def2-TZVP)def2-TZVP) zero-pointzero-point zero-point correctedcorrected corrected energyenergy energy − − profileprofileprofile for the forfor interconversion thethe interconversioninterconversion of of COPof COPCOP−isomers. isomers.isomers.

The oxaphosphirenideTheThe oxaphosphirenideoxaphosphirenide14 1414can cancan be bebe formally formallyformally consideredconsideredconsidered asas as thethe the directdirect direct deprotonationdeprotonation deprotonation productproduct product fromfrom from eithereithereither1a (C-deprotonation) 1a1a (C-deprotonation)(C-deprotonation) or oror2a 2a2a(P-deprotonation). (P-deprotonation).(P-deprotonation). AlthoughAlthough mostmost most ofof of thethe the negativenegative negative (natural)(natural) (natural) chargecharge charge can be ascribed to the O atom due to its higher electronegativity (Table 1), the largest negative can becan ascribed be ascribed to the to O the atom O dueatom to due its higherto its higher electronegativity electronegativity (Table (Table1), the 1), largest the largest negative negative variation nat variation in electric charge corresponds to the P atom (Δqnat = −0.718 or −0.608 e in 1a or 2a, in electricvariation charge in electric corresponds charge to corresponds the P atom to (∆ qthenat P= atom−0.718 (Δ orq − =0.608 −0.718e in or1a −0.608or 2a ,e respectively)in 1a or 2a, and, respectively)respectively) and,and, therefore,therefore, 1414 couldcould bebe safelysafely representedrepresented withwith aa formalformal negativenegative chargecharge onon therefore, 14 could be safely represented with a formal negative charge on phosphorus. This is also phosphorus.phosphorus. ThisThis isis alsoalso supportedsupported byby thethe HOMOHOMO (Figure(Figure 7)7) beingbeing mainlymainly locatedlocated atat P.P. TheThe stiffnessstiffness supported by the HOMO (Figure7) being mainly located at P. The stiffness of all0 three bonds keep the ofof allall threethree bondsbonds keepkeep thethe samesame orderorder foundfound forfor 1a1a andand 2a2a:: C–OC–O >> P–CP–C >> P–OP–O ((kk0 == 4.322,4.322, 1.8461.846 andand 0 same1.0991.099 order mdyn/Å,mdyn/Å, found for respectively).respectively).1a and 2a : C–O > P–C > P–O (k = 4.322, 1.846 and 1.099 mdyn/Å, respectively).

Figure 7. Computed (B3LYP/def2-TZVPP) Kohn-Sham isosurface (0.06 au) for the HOMO of 14. FigureFigure 7. Computed 7. Computed (B3LYP/def2-TZVPP) (B3LYP/def2-TZVPP) Kohn-ShamKohn-Sham isosurface isosurface (0.06 (0.06 au) au) for forthe theHOMO HOMO of 14 of. 14.

2.4. Ring Strain Energy Ring strain is one of the most characteristic features in small rings, providing the driving force for their transformations into open-chain (or ring-enlarged) products [50]. The ring strain energy (RSE) for the parent saturated oxaphosphirane ring was reported to be 23.5 kcal/mol (computed at the CCSD(T)/def2-TZVPP level) [51]. As double bonds normally entail enlarged bond angles, their incorporation into small cyclic systems should be expected to result in an increase in the RSE, as occurs, for instance, in moving from cyclopropane to cyclopropene (RSE = 29.0 and 54.5 kcal/mol, respectively [52]). In the case of the parent oxaphosphirene ring system 1a, the RSE was computed by evaluating the energetics of appropriate homodesmotic reactions (Scheme5), similar to those used for other three- [46,48,51,53–57] or four-membered [47] saturated phosphorus heterocycles. In such reactions, for the cleavage of every endocyclic X–Y (or X=Y) bond, a HnX–YHm (or HnX=YHm) reagent is used, the valences of X and Y being completed with H atoms. In reactants and products, the number of every type of bonds (single/double) between X and Y, with the same hybridization states in X and Y, must be conserved, as well as the number of sp3, sp2, and sp-hybridized (and non-hybridized, in case) atoms of every element with 0, 1, 2, or 3 H atoms attached. By averaging the opposites of the zero point-corrected energies for the three homodesmotic endocyclic bond cleavage reactions of 1a, a rather high value of RSE (Table2) was obtained (see Computational Details). Molecules 2018, 23, x 10 of 16

2.4. Ring Strain Energy Ring strain is one of the most characteristic features in small rings, providing the driving force for their transformations into open-chain (or ring-enlarged) products [50]. The ring strain energy (RSE) for the parent saturated oxaphosphirane ring was reported to be 23.5 kcal/mol (computed at the CCSD(T)/def2-TZVPP level) [51]. As double bonds normally entail enlarged bond angles, their incorporation into small cyclic systems should be expected to result in an increase in the RSE, as occurs, for instance, in moving from cyclopropane to cyclopropene (RSE = 29.0 and 54.5 kcal/mol, respectively [52]). In the case of the parent oxaphosphirene ring system 1a, the RSE was computed by evaluating the energetics of appropriate homodesmotic reactions (Scheme 5), similar to those used for other three- [46,48,51,53–57] or four-membered [47] saturated phosphorus heterocycles. In such reactions, for the cleavage of every endocyclic X–Y (or X=Y) bond, a HnX–YHm (or HnX=YHm) reagent is used, the valences of X and Y being completed with H atoms. In reactants and products, the number of every type of bonds (single/double) between X and Y, with the same hybridization states in X and Y, must be conserved, as well as the number of sp3, sp2, and sp-hybridized (and non-hybridized, in case) atoms of every element with 0, 1, 2, or 3 H atoms attached. By averaging the oppositesMolecules 2018 of, 23the, 3341 zero point-corrected energies for the three homodesmotic endocyclic bond cleavage10 of 16 reactions of 1a, a rather high value of RSE (Table 2) was obtained (see Computational Details).

Scheme 5. Homodesmotic and hyperhomodesmotic reaction reactionss used used for the evaluation of the RSE in parent oxaphosphirene 1a..

Table 2. Computed (CCSD(T)/def2-TZVPP//B3LYP-D3/def2-TZVP) RSE (kcal/mol) using Table 2. Computed (CCSD(T)/def2-TZVPP//B3LYP-D3/def2-TZVP) RSE (kcal/mol) using homodesmotic (RC4) or hyperhomodesmotic (RC5) reaction schemes. homodesmotic (RC4) or hyperhomodesmotic (RC5) reaction schemes.

RSERC4 RSERC5 RSERC4 RSERC5 1a 49.90 49.08 1a 2a 49.90 7.53 4.59 49.08 14 36.83 41.99 2a 7.53 4.59

According to a14 recent classification and36.83 redefinition of reaction types41.99 used in thermochemistry [58], homodesmotic reactions (reaction class 4, or “RC4”) is the second to last type in a hierarchy of increasinglyAccording more to a accurate recent classification processes, due and toredefini conservationtion of reaction of larger types fragments. used in thermochemistry In this hierarchy, [58],hyperhomodesmotic homodesmotic reactions reactions (reaction (reaction class class 4, 5, or or “RC4”) “RC5”) is constitutethe second the to toplast quality,type in mosta hierarchy accurate of increasinglytype of processes. more accurate They are processes, defined so due as to to conserve conservation in reactants of larger and fragments. products theIn this same hierarchy, number hyperhomodesmoticof HnX–YHm bonds (X,reactions Y are the (reactio two bondedn class 5, atoms; or “RC5”) n and constitute m are the the number top quality, of H atoms most attachedaccurate typeto them), of processes. for every They type are of defined single, double,so as to orcons tripleerve bond,in reactants as well and as products the same the number same ofnumber sp3, sp of2, HandnX–YH sp-hybridizedm bonds (X, (and Y are non-hybridized, the two bonded in atoms; case) atoms n andof m every are the element number with of H 0, atoms 1, 2, or attached 3 H atoms to attached. The small difference obtained in the RSE (Table2) when using the RC4 and RC5 sets of reactions (ca. 0.8 kcal/mol) justifies the widespread use of homodesmotic reactions for the estimation of RSE without significant loss of accuracy. Moreover, the use of lower levels of theory resulted in an overestimation of RSE (RC4/RC5) for 1a that increases from PWPB95-D3 (50.88/50.15 kcal/mol), B3LYP-D3 (52.05/51.19 kcal/mol) and SCS-MP2 (52.15/51.45 kcal/mol). The RSE for oxaphosphirane-3-ylidene 2a was computed similarly by using the appropriate set of homodesmotic and hyperhomodesmotic reactions (Scheme6). The results point to a very significant decrease in the RSE (more than 40 kcal/mol) compared to 1a, most likely paralleling the decrease in bond order for the P–C linkage. This drop in RSE does not entail an overall stabilization of 2a with respect to 1a in the same magnitude, owing to the presence of very reactive (unstable) centers in 2a, such as the carbene moiety. Molecules 2018, 23, x 11 of 16

them), for every type of single, double, or triple bond, as well as the same number of sp3, sp2, and sp-hybridized (and non-hybridized, in case) atoms of every element with 0, 1, 2, or 3 H atoms attached. The small difference obtained in the RSE (Table 2) when using the RC4 and RC5 sets of reactions (ca. 0.8 kcal/mol) justifies the widespread use of homodesmotic reactions for the estimation of RSE without significant loss of accuracy. Moreover, the use of lower levels of theory resulted in an overestimation of RSE (RC4/RC5) for 1a that increases from PWPB95-D3 (50.88/50.15 kcal/mol), B3LYP-D3 (52.05/51.19 kcal/mol) and SCS-MP2 (52.15/51.45 kcal/mol). The RSE for oxaphosphirane-3-ylidene 2a was computed similarly by using the appropriate set of homodesmotic and hyperhomodesmotic reactions (Scheme 6). The results point to a very significant decrease in the RSE (more than 40 kcal/mol) compared to 1a, most likely paralleling the decrease in bond order for the P–C linkage. This drop in RSE does not entail an overall stabilization Molecules 2018of, 2a23 ,with 3341 respect to 1a in the same magnitude, owing to the presence of very reactive (unstable) 11 of 16 centers in 2a, such as the carbene moiety.

Homodesmotic (RC4) Hyperhomodesmotic (RC5)

CH C-OH HP HC PH2 HO-C PHOH HP O C-P cleavage C-P cleavage O H2P (i) (i) HOHP

OH H OH HC-HP OH PH H2P OH P PH P-O cleavage O P-O cleavage O O PH 2 (ii) 2a (ii) PH-CH

H H P HC OH H2P-C OH P O C-O cleavage C-O cleavage O PH2 HO CH HO (iii) (iii) Scheme 6.SchemeHomodesmotic 6. Homodesmotic and and hyperhomodesmotic hyperhomodesmotic reaction reactionss used used for the for evaluation the evaluation of the RSE of in the RSE in parent oxaphosphirane-3-ylideneparent oxaphosphirane-3-ylidene2a. 2a. In case of the oxaphosphirenide 14, the required use of anionic reagents for the appropriate In casehomodesmotic of the oxaphosphirenide and hyperhomodesmotic14, thering requiredcleavage reactions use of (Scheme anionic 7) forms reagents cleavage for products the appropriate homodesmoticdianionic and in hyperhomodesmoticnature. As the latter should ring display cleavage an extra reactions Coulombic (Scheme destabilization,7) forms not cleavagepresent in products dianionicthe in nature.(isolated) reagents, As the lattera compensation should displayof the resulting an extra repulsion Coulombic energy was destabilization, needed. This was not present in the (isolated)estimated reagents, via the Coulomb a compensation law formalism. of the With resulting this aim, repulsion the two energynon-consecutive was needed. atoms This was contributing the most to HOMO and HOMO-1 (or even HOMO-2 if the uppermost HOMOs are estimatedconstrained via the Coulomb to the same law part formalism. of the molecule) With are this considered aim, the as twocenters non-consecutive for the two negative atoms charges contributing the mostin to the HOMO cleavage and product. HOMO-1 For this (orparticular even case, HOMO-2 electrostatic if the repulsion uppermost energies HOMOsin the range are of 80 constrained to the samekcal/mol part are of obtained. the molecule) The principa arel limitation considered of this as methodology centers for is that the the two use negative of point charges charges in the cleavage product.located at Forparticular this particularatom centers case, is nothing electrostatic but a crude repulsion simplification energies of the inreal the electron range density of 80 kcal/mol distribution and, consequently, some minor source of inaccuracy must be assumed. Thus, by using are obtained.only Thethe homodesmotic principal limitation C–O cleavage of reaction this methodology (type iii RC4, Scheme is that 7) the that use results of in point a monoanionic charges located at particularacyclic atom centersproduct and is nothing therefore but nota needing crude simplificationany further Coulombic of the realenergy electron correction, density an RSE distribution and, consequently,estimation of some 38.56 minor kcal/mol source was obtained. of inaccuracy After averaging must be with assumed. the other Thus, two byCoulomb using only the homodesmoticterm-corrected C–O cleavage homodesmotic reaction reactions (type (i and iii RC4, ii), a slightly Scheme lower7) that final results value (less in athan monoanionic 2 kcal/mol acyclic away) was obtained (Table 2). All three hyperhomodesmotic ring cleavage reactions proposed for 14 product andsuffer therefore from the Coulomb-term not needing corr anyection further limitation Coulombic and, hence, a energy moderate correction, inaccuracy, in an the RSE range estimation of 38.56 kcal/molof some 3–4 waskcal/mol, obtained. must be expected. After averaging with the other two Coulomb term-corrected homodesmoticMolecules reactions2018, 23, x (i and ii), a slightly lower final value (less than 2 kcal/mol12 of 16 away) was obtained (Table 2). All three hyperhomodesmotic ring cleavage reactions proposed for 14 suffer from the Coulomb-termDespite correctionthese limitations limitation mentioned and, beforehand, hence, a a rough moderate estimation inaccuracy, of RSE in the in range the range36–42 of some kcal/mol for oxaphosphirenide 14 (Table 2) is enough to conclude that a small decrease in the bond 3–4 kcal/mol,order mustof the P–C be expected. bond (after formal C-deprotonation 1a→14, Table 1) parallels a decrease in the RSE.

Scheme 7.SchemeHomodesmotic 7. Homodesmotic and hyperhomodesmoticand hyperhomodesmotic reaction reactionss used used for the for evaluation the evaluation of the RSE of in the RSE in oxaphosphirenideoxaphosphirenide anion 14anion. 14. 3. Materials and Methods

Computational Details. DFT calculations were performed with the ORCA program (version 3.0.3, Mülheim/Ruhr, Germany) [59]. All geometry optimizations were run in redundant internal coordinates in the gas phase, with tight convergence criteria, and using the B3LYP functional [60,61] together with the def2-TZVP basis set [62] and the speeding up algorithm RIJCOSX [63]. The latest Grimme’s semiempirical atom-pair-wise London dispersion correction (DFT-D3) was included in all calculations [64]. Harmonic frequency calculations verified the nature of ground states or transition states (TS) having all real (positive) frequencies or only one imaginary (negative) frequency, respectively. Relaxed force constants were computed at the optimization level and obtained by inversion of the Hessian matrix and appropriate unit conversion of the reciprocal of the resulting diagonal elements. From these optimized geometries all reported data were obtained by means of single-point (SP) calculations using the more polarized def2-TZVPP [65] basis set. Basis sets may be obtained from the Basis Set Exchange (BSE) software and the EMSL Basis Set Library [66,67] Reported energies were corrected for the zero-point vibrational term at the optimization level and obtained by means of the recently developed near linear scaling domain-based local pair natural orbital (DLPNO) method [68] to achieve coupled cluster theory with single-double and perturbative triple excitations (CCSD(T)) [69]. For comparative purposes, local correlation schemes of type LPNO (Local Pair Natural Orbital) for high level single reference methods, such as CEPA (Coupled Electron-Pair Approximation) [70,71], here the slightly modified NCEPA/1 version [72] implemented in ORCA, was used, as well as the spin-component scaled second-order Möller–Plesset perturbation theory (SCS-MP2) level [73,74] and the double-hybrid-meta-GGA functional PWPB95 [75,76], together with the D3 correction (PWPB95-D3) (see the SI). Due to the unavailability of unrestricted formalism for DLPNO/CCSD(T) calculations in the working version of ORCA, the corresponding values in the case of triplet electronic states were taken from the LPNO/NCEPA1 level, making use of the reported small differences between the results in these two levels for closed-shell systems [77]. Figures 2, 3, and 7 were drawn with VMD [78].

Molecules 2018, 23, 3341 12 of 16

Despite these limitations mentioned beforehand, a rough estimation of RSE in the range 36–42 kcal/mol for oxaphosphirenide 14 (Table2) is enough to conclude that a small decrease in the bond order of the P–C bond (after formal C-deprotonation 1a→14, Table1) parallels a decrease in the RSE.

3. Materials and Methods

Computational Details DFT calculations were performed with the ORCA program (version 3.0.3, Mülheim/Ruhr, Germany) [59]. All geometry optimizations were run in redundant internal coordinates in the gas phase, with tight convergence criteria, and using the B3LYP functional [60,61] together with the def2-TZVP basis set [62] and the speeding up algorithm RIJCOSX [63]. The latest Grimme’s semiempirical atom-pair-wise London dispersion correction (DFT-D3) was included in all calculations [64]. Harmonic frequency calculations verified the nature of ground states or transition states (TS) having all real (positive) frequencies or only one imaginary (negative) frequency, respectively. Relaxed force constants were computed at the optimization level and obtained by inversion of the Hessian matrix and appropriate unit conversion of the reciprocal of the resulting diagonal elements. From these optimized geometries all reported data were obtained by means of single-point (SP) calculations using the more polarized def2-TZVPP [65] basis set. Basis sets may be obtained from the Basis Set Exchange (BSE) software and the EMSL Basis Set Library [66,67] Reported energies were corrected for the zero-point vibrational term at the optimization level and obtained by means of the recently developed near linear scaling domain-based local pair natural orbital (DLPNO) method [68] to achieve coupled cluster theory with single-double and perturbative triple excitations (CCSD(T)) [69]. For comparative purposes, local correlation schemes of type LPNO (Local Pair Natural Orbital) for high level single reference methods, such as CEPA (Coupled Electron-Pair Approximation) [70,71], here the slightly modified NCEPA/1 version [72] implemented in ORCA, was used, as well as the spin-component scaled second-order Möller–Plesset perturbation theory (SCS-MP2) level [73,74] and the double-hybrid-meta-GGA functional PWPB95 [75,76], together with the D3 correction (PWPB95-D3) (see the SI). Due to the unavailability of unrestricted formalism for DLPNO/CCSD(T) calculations in the working version of ORCA, the corresponding values in the case of triplet electronic states were taken from the LPNO/NCEPA1 level, making use of the reported small differences between the results in these two levels for closed-shell systems [77]. Figures2,3 and7 were drawn with VMD [78].

4. Conclusions In total, a full picture of the potential energy surfaces (PES) for oxaphosphirene and oxaphosphirenide anion has been presented, including remarkable isomers in the triplet electronic state for the first time. Furthermore, ground state structures of fluorinated derivatives are detailed. The PES of the neutral CHOP system includes important derivatives, such as phosphaketene (phosphaisocyanic acid, H-PCO), linear isomers such as phosphacyanic (H-OCP), and phosphafulminic (H-CPO) acids, as well as two other cyclic isomers and fragmentation products. In the case of the anionic derivatives, the phosphaethynolate anion is the most stable. The electronic structures of the most representative isomers were described using MO theory, NBO analysis, and bond strength descriptors. Using both homodesmotic and hyperhomodesmotic reactions, ring strain energies were estimated for the parent 1H-oxaphosphirene, oxaphosphirane-3-ylidene, and the oxaphosphirenide anion, the latter requiring an additional electrostatic energy-correction term.

Supplementary Materials: The following are available online, Tables S1 and S2: Computed zero-point corrected relative energies (kcal/mol) at various computational levels, Computed geometries (Cartesian coordinates, in Å), energies (in hartree) and imaginary frequencies (for TS, in cm−1) for all computed species. Molecules 2018, 23, 3341 13 of 16

Author Contributions: Conceptualization, methodology, supervision, writing—original draft preparation, review and editing of final version A.E.F. and R.S.; calculation of the PES for neutral compounds, A.E.F.; calculation of all RSEs and PES for anionic derivatives, A.R. Funding: This research was funded by the Deutsche Forschungsgemeinschaft, grant number STR 411/29-3. Acknowledgments: The authors acknowledge the computation centre at Servicio de Cálculo Científico (SCC—University of Murcia) for their technical support and the computational resources used. Conflicts of Interest: The authors declare no conflict of interest.

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Sample Availability: Samples of the compounds are not available from the authors.

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