carboxyphosphate is 
 an elusive intermediate in the atp - dependent 
 carboxylase superfamily of enzymes , which is involved in critical 
 pathways related to obesity , diabetes , and microbial infections . recently , we found that carboxyphosphate exists in a unique  closed  
 or pseudochair  conformation ( figure 1 ) stabilized by more than 14 kcal / mol as the monoanion and 
 12 kcal / mol as the dianion over the corresponding lowest energy  open key to understanding the 
 novel pseudochair stability resides in the balance between the stabilizing 
 intramolecular charge - assisted hydrogen bond ( cahb ) , which is a special 
 case of the intramolecular hydrogen bond ( imhb ) , and associated destabilizing interactions . in addition , 
 it is important to delineate carboxyphosphate s cahb strength 
 to understand its stability in nonpolar environments compared to its 
 reactivity in aqueous solution . m06 - 2x / aug - cc - pvtz key distances (  ) 
 and angles of pseudochair 
 carboxyphosphate . the cahb is suspected 
 to be the key element of stabilization for 
 the pseudochair conformation of carboxyphosphate , where the energy 
 minimized pseudochair conformation reveals a hydrogen bond oxygen  oxygen 
 distance of ca . 2.5  that is less than its van der waals sum 
 of 3.04  ( rovdw = 1.52  ) and significant angle expansion across the bridging oxygen ( ca . the geometric changes suggest that 
 pauli repulsion and ring strain could be contributing factors to the 
 overall destabilization of the pseudochair conformation . unlike the intermolecular hydrogen bond that has a convenient reference 
 state , where infinite separation defines its absolute strength , measurement 
 of imhb strength must be determined relative to a nonzero reference 
 system that makes its value ambiguous . determining the strength of 
 an imhb is a nontrivial task due to the reference state selection ; 
 thus , many methods have been proposed and explored with varying degrees 
 of success . the challenge is to isolate an open structure ( no imhb ) , which may 
 not necessarily be stationary , without 
 introducing new or removing essential geometric elements found in 
 the closed conformation . to date , there is no one widely accepted 
 method for identifying a reference structure or for estimating imhb 
 strength . despite its controversial nature , the most common 
 imhb estimation 
 scheme involves the energy difference between the geometry optimized 
 open and closed conformations , otherwise 
 known as the open  closed method . however , geometry optimization 
 has the potential to remove essential energetic contributions in defining 
 an accurate open reference state . subsequently , there has been effort in determining the effects of 
 partially constrained versus full optimization of the open reference 
 system , where significant differences have been reported . nevertheless , it is possible to take an alternative approach , where 
 the energetic terms crucial to the imhb configuration are estimated 
 and then reinserted into the open  closed energy . the process 
 of correcting the open and closed energy difference to estimate cahb 
 strength is referred to here as the additive scheme . jablonski proposed a partial optimization scheme to improve 
 the 
 open reference structure and the predicted accuracy of the imhb energy 
 depending upon the molecular system of interest . only the position of the hydrogen bond donor or the 
 hydrogen bond acceptor is modified , while retaining the closed geometry 
 optimized structure . such an open reference system is not a stationary 
 state and higher in energy . partial geometry optimization on selected 
 degrees of freedom lowers the energy for a possibly more accurate 
 open reference state . since the energy is lowered with increasing 
 relaxation , we coin this technique as the subtractive scheme . systematic and partial relaxation of the starting conformation 
 with the disengaged hydrogen bond leads to a series of partially optimized 
 open reference geometries and energies . selected dihedral angles determined 
 in the closed structure , except the one to break the hydrogen bond , 
 are typically held to their original closed values to prevent the 
 introduction of new repulsive or attractive forces in the partially 
 optimized open form . in this manner , comparison of the closed form 
 to a partially optimized open reference form is suggested to yield 
 an improved imhb estimation . however , 
 selection of the partially optimized open structure is as arbitrary 
 as selecting a completely geometry optimized open structure . careful 
 selection of the open reference state improves the predicted imhb 
 estimate , but the subtractive technique does not isolate , quantitate , 
 nor clearly define any of the possible repulsive energies counterbalancing 
 the attractive imhb . many estimation schemes beyond the open  closed 
 method have been developed and implemented 
 for their 
 ability to estimate the strength of the imhb . specifically , isodesmic 
 reactions have been used in order to determine the strength of the 
 imhb . more recent schemes include the 
 investigation of rotation barriers , as well as the relationship between 
 rotamers . the relationship between h nmr 
 shifts and hydrogen bond strength is well - known , and a direct correlation 
 between the two has been discovered . nbo analysis 
 has been implemented to study the interactions of orbitals involved 
 in the imhb . topological analysis by qtaim 
 can be used to monitor changes in the electron density as the reference 
 system is developed . given the physiological importance 
 and controversial understanding 
 of carboxyphosphate s structure , stability , and role in the 
 atp - dependent carboxylase superfamily of enzymes , it is both appropriate 
 and timely to investigate the intramolecular forces responsible for 
 the novel pseudochair conformation of carboxyphosphate . the cahb is 
 estimated through additive corrections for pauli repulsions to the 
 open  closed method using charmm force field nonbond parameters , and compared to a subtractive variant of the open an improved understanding of the cahb strength in relation 
 to the overall stability of the pseudochair conformation in a vacuum 
 is a starting point in dissecting the origin of instability in the 
 aqueous phase and possible existence and meaningful contribution to 
 the mechanism of atp - dependent carboxylases . the importance of pauli 
 repulsion is demonstrated for the accurate prediction of the cahb 
 strength in carboxyphosphate . resources 
 at the center for computational sciences at duquesne 
 university , the gaussian 09 program , and the charmm force field have been used for all calculations . all electronic structure computations 
 utilized truhlar s minnesota m06 - 2x functional with dunning s augmented correlation consistent 
 polarized valence triple- basis set ( aug - cc - pvtz ) . this level of theory has been shown to capture 
 the majority of energetic convergence giving the most consistent agreement 
 with reference mp2 and ccsd(t ) calculations , as shown in figure s1 
 ( supporting information ) . frequency calculations 
 were carried out to confirm all stationary points as minima on the 
 potential energy surface . the atom types with epsilon and rmin values from the charmm force field were used to compute the r pauli repulsion . open , 
 ec  o = eclosed  eopen , which 
 delivers negative values for stabilized closed structures . borrowing 
 from jablonski s notation in the subtractive scheme , several partial optimizations were performed 
 to locate an accurate open reference system . all model structures 
 were modified from the geometry optimized pseudochair structure by 
 changing a single degree of freedom to maintain the original geometric 
 features of the structure without the hydrogen bond , as defined in 
 figure 2 . possible conformational modification of 
 pseudochair carboxyphosphate 
 ( center ) to break the cahb in the monoanion ( top ) and dianion ( bottom ) . for hydrogen bond donors , an idealized 
 180 rotation of the 
 dihedral angle across the hydrogen bond donor to break the hydrogen 
 bond was carried out with all other coordinates held fixed . alternatively 
 for hydrogen bond acceptors , the carboxylic acid was rotated by 90 
 ( dianion ) or the phosphoryl group by 60 ( monoanion ) . the manner 
 of generating open structures with a single conformational change 
 isolated to either the donor or the acceptor results in differences 
 with the lowest energy geometry optimized open structures computed . 
 however , the two schemes are independent approaches so it is not necessary 
 for the open structures to be identical . next , only the bond lengths 
 of sp were geometry optimized in order to yield a structure with a 
 lower energy , which is labeled and referred to as b. finally , geometry 
 optimization of both bond lengths and bond angles with all dihedral 
 angles held constant is carried out , and denoted as ab . the fully 
 geometry optimized structure starting from sp is referred to as opt . however , the lowest energy geometry optimized energy is used as a 
 common reference throughout the study . the open  closed method 
 is one of the most widely used approaches for estimating cahb strength , 
 where the energy of the hydrogen - bonded ( closed ) form is compared 
 to that of an open structure in which the cahb is not present . as previously discussed , the open  closed method typically 
 involves rotation about one or more bonds starting from the closed 
 form in order to disengage the hydrogen bond to produce an open structure . there are many variations to the open  closed method ; however , 
 the most basic procedure involves geometry optimization of the closed 
 and opened forms with subsequent energetic comparison . structural 
 relaxation of the open form can either add or remove important interactions 
 indigenous to the closed cahb structure , thereby distorting the accuracy 
 of the cahb estimate , which has been recognized and criticized before . in the open  closed method , the open configuration of 
 carboxyphosphate is selected to be the geometry optimized , lowest 
 energy conformation without the intramolecular hydrogen bond . the 
 m06 - 2x / aug - cc - pvtz geometry optimized structures are shown in figure 3 . stabilization of the pseudochair is defined to 
 be the energy difference between the closed and open conformations 
 in both the monoanionic and dianion states . cahb strength is commonly 
 estimated from the open  closed method and defined by the computed 
 stabilization energies of 14.5 kcal / mol for the monoanion 
 and 12.0 kcal / mol for the dianion . m06 - 2x / aug - cc - pvtz open 
 ( bottom ) and closed ( top ) monoanionic ( left ) 
 and dianionic ( right ) conformations . the open structures defined in figure 2 are 
 slightly different than the geometry optimized open structures using 
 m06 - 2x / aug - cc - pvtz shown in figure 3 . the differences 
 are a consequence of how the two techniques generate the open structure 
 to estimate independently the same cahb strength . in this fashion , 
 a more practical comparison is undertaken to represent approaches 
 reported in the literature . change in the lowest energy geometry optimized 
 open structures affirms that essential geometric elements can differ 
 from the closed conformation in the standard implementation of the 
 open  closed method . the geometry minimized 
 pseudochair 
 conformations , in comparison to the open structures , reveal that , 
 in addition to the cahb , pauli repulsion interactions and ring strain 
 are possible contributors to differences in energetics between the 
 two forms , as shown in figure 3 . to gauge the 
 effect of each type of contribution to the overall stability of the 
 pseudochair , a series of model systems were developed and applied . in order to study the differential ring 
 strain ( ec  ors = eclosedrs  eopenrs ) between 
 the closed and open forms of carboxyphosphate , dihydrogen phosphate 
 was used as a model system for its ability to resemble the phosphate 
 side and bridging oxygen of carboxyphosphate . geometry optimized dihydrogen 
 phosphate has an hop angle of 105.9 ( m06 - 2x / aug - cc - pvtz ) 
 and was used as the strain free reference , as shown in figure 4 . angle representing ring strain in the dihydrogen phosphate 
 model 
 of carboxyphosphate . to model the ring strain in the closed and open forms , the 
 hop 
 angle of 105.9 in dihydrogen phosphate was adjusted and fixed 
 to that of the bridging oxygen in the different states and conformations 
 of carboxyphosphate . the dihydrogen phosphate model systems were allowed 
 to optimize constrained to the bridging oxygen angle . the relative 
 energies ( ec  ors ) of the different constrained geometries 
 are given in table 1 . even though ring strain from a ca . . 4.0 kcal / mol , 
 the angle and subsequent energy difference between the open and closed 
 forms is found to be small . in fact , the computed energy difference 
 is less than 1 kcal / mol . the angles between the open and closed structures 
 are too small to generate appreciable ring strain differences , making 
 model selection irrelevant . consequently , ring strain is determined 
 to play only a minor role in the accurate prediction of the cahb from 
 the open  closed method . comparison of the geometry optimized 
 open and closed conformations using m06 - 2x / aug - cc - pvtz reveals a significant 
 shortening of the distance between the oxygen atoms ( roo ) and between the hydrogen bonded oxygen and hydrogen 
 ( rho ) involved in the cahb , as highlighted 
 in figure 5 . specific nonbond interactions ( red ) computed 
 to determine the pauli 
 repulsion in carboxyphosphate . optimized closed 
 conformations of both charge states , 
 the roo distance of ca . 2.5  is 
 less than its van der waals sum of 3.04  ( rovdw = 1.52 
  ) . in addition , the hydrogen bond rho distances are 1.49 and 1.61  for the 
 monoanion and dianion , respectively , which are shorter than the idealized 
 van der waals sum of 2.61  ( rhvdw = 1.09  ) , as given in table 2 . in the geometry optimized open conformations , the hydrogen bond 
 is broken , and the distances between atoms change to relieve intramolecular 
 nonbond interactions . the distances are computed to become greater 
 than the van der waals sum , as shown in figure 5 . however , two roo distances in the open 
 structures are close to the van der waals sum , as given in table 2 . thus , two interactions for each conformation were 
 computed to determine the difference in pauli repulsion between the 
 closed and open conformations , as defined in figure 5 . the difference in the pauli 
 repulsion between the closed and open 
 conformations of carboxyphosphate was estimated by using the sum of 
 the repulsive r part of the 
 lennard - jones approximation , as given in eq 1.1the atomic lennard - jones parameters  
 and r are combined with the appropriate 
 mixing rules for a pair of atoms i and j. in the current charmm force field , the parameters are ij = ( ij ) ( geometric mean ) 
 and rijmin = ( rimin + rjmin)/2 ( arithmetic mean ) , as listed in 
 table 3 . the charmm atom types defining the 
 parameters used in eq 1 for the computation 
 of the pauli repulsion ( ec  opauli = eclosedpauli  eopenpauli ) are shown 
 in figure 5 and table 3 . the computed pauli repulsion for the closed and open forms of the 
 dianion are 6.48 and 0.78 kcal / mol , respectively . therefore , the difference 
 in the pauli energies for the dianion is 5.70 kcal / mol . likewise , 
 the computed pauli repulsions for the closed and open forms of the 
 monoanion are 9.96 and 0.78 kcal / mol , respectively . thus , the difference 
 in the pauli energies for the monoanion is 9.18 kcal / mol . analyses 
 of the differential ring strain and pauli repulsions in the open and 
 closed forms uncover contributions that impact the estimated cahb 
 strength of the open  closed method , as described in eq 2.2 the results of eq 2 are 
 given in table 4 in order to estimate 
 the range of cahb strength . according to the additive correction for 
 the pauli repulsion to the open  closed method , the cahb strength 
 is 22.9 kcal / mol for the monoanion , whereas the cahb strength 
 is 18.4 kcal / mol for the dianion . the additive corrective 
 terms for pauli repulsion significantly increase the predicted cahb 
 strength compared to that predicted by the standard implementation 
 of the open  closed method . it has been reported that geometry 
 optimization of the open form may lead to an inappropriate reference 
 system . jablonski has shown that the calculated strength of an imhb with 
 the open  closed method is highly dependent on the degree of 
 optimization . as previously discussed , 
 the idea is to create an open structure by modifying the closed geometry 
 optimized structure with minimal structural changes to break the imhb 
 and improve the cahb estimate . typically , adjustment of a dihedral 
 angle to reposition the hydrogen shared in the imhb is made ( figure 2 ) . a single point energy evaluation ( sp ) is carried 
 out , giving an upper bound to the imhb estimation . at the other extreme , 
 geometry relaxation starting from the sp structure gives a geometry 
 optimized ( opt ) structure . ideally , two pathways to break the imhb 
 can be taken by modifying either the hydrogen bond donor or the hydrogen 
 bond acceptor . both result in a different reference and range of imhb 
 values . analogous to the partial optimizations of jablonski , 
 the sp , b , ab , and opt computations were carried out . first , the cahb 
 was removed by an idealized 180 rotation of the hydrogen bond 
 donor ( hoco for the monoanion and hopo for the dianion ) 
 starting from the closed geometry optimized structure . our second 
 method of breaking the cahb also started with the closed geometry 
 optimized structure but with a rotation of the hydrogen bond acceptor 
 ( 60 for opoc for the monoanion and 90 for hopo 
 for the dianion ) . however , only modification of the donor structure 
 leads to an appropriate open state that removes the cahb . modification 
 of the acceptor leads to a structure that connects closed states ( figures 
 s2 and s3 , supporting information ) , which 
 does not represent a desirable open reference state and is referred 
 to as inappropriate in table 5 . as such , analysis is carried out only on the cahb estimation from 
 the donor - modified structure . as reported in table 5 , the sp calculations were found to give the highest estimations 
 and the opt geometry optimizations the lowest . removal of the bond 
 and angle constraints ( b and ab ) reduced the energies as compared 
 to the sp value . inappropriate reference state that 
 is not open . according to 
 the subtractive method , the cahb strength is between 
 17.8 and 25.4 kcal / mol for the monoanion , whereas 
 the cahb strength is between 15.7 and 20.9 kcal / mol 
 for the dianion . the estimated ranges from the subtractive scheme 
 are in good agreement with the additive corrections to the open the transition structures for 
 each process in breaking the cahb were computed and verified using 
 m06 - 2x / aug - cc - pvtz , as shown in table 5 as 
 ts . the computed transition structure is at the highest point on the 
 potential energy surface along the reaction coordinate to break the cahb separating the closed and 
 open conformations . as such , the activation energy defined from the 
 pseudochair structure represents the energy to break the cahb . the 
 computed activation energy for breaking the monoanion cahb through 
 the donor is 19.5 kcal / mol , while it was 9.0 kcal / mol for a different 
 process through the acceptor , where the computed transition structure 
 is a cahb switch between the two equivalent phosphate oxygens . as 
 a result , the 9.0 activation energy is inappropriate for cahb strength 
 assessment , as with the subtractive scheme of table 5 , since the transition structure does not connect the pseudochair 
 and open conformations ( figure s2 , supporting 
 information ) . therefore , the predicted cahb strength for the 
 monoanion is 19.5 kcal / mol . the computed activation energy for breaking 
 the dianion cahb through the acceptor is 13.0 kcal / mol , and 12.1 kcal / mol 
 through the donor ( figure s3 , supporting information ) . analogously , the transition structure interconnecting the pseudochair 
 and open structures is through the donor change in geometry . thus , 
 the predicted cahb strength for the dianion is 12.1 kcal / mol . the geometries of the computed 
 transition structures , the ab minimized structures suggested by jablonski , 
 and the geometry optimized closed structures ( figure 3 ) were compared , as shown in figure 6 . it is of interest to analyze the key 
 geometric features of the closed structure and the change observed 
 in the cahb models . dianionic transition structure computed using m06 - 2x / aug - cc - pvtz 
 for the breaking of the cahb donor ( tsdd ) and the partially minimized 
 dianion donor ( abdd ) reference structure . monoanionic transition structure 
 for the breaking of the cahb donor ( tsdm ) and the partially minimized 
 monoanion donor ( abdm ) reference structure . the m06 - 2x / aug - cc - pvtz geometry optimized closed structures 
 ( monoanion 
 and dianion ) have the hydrogen bond proton positioned directly in 
 between the donor and the acceptor ( figure 3 ) . the structural consequence is that there is reduced lone - pair 
 congestion between the donor and acceptor oxygens . in addition , the 
 closed structures involve two nonbond interactions that could lead 
 to strong pauli repulsion , involving the hydrogen bond donor and acceptor 
 oxygens , and the hydrogen bond hydrogen and noncovalent oxygen . the 
 dianion models ( tsdd and abdd ) maintain the eclipsing hydrogen bond 
 donor and acceptor , as found in the closed structure . however , the 
 main geometric difference in the dianion models is in the position 
 of the hydrogen . tsdd directs the lone pairs away from the acid group 
 ( hopo = 63 ) , whereas abdd directs the lone pairs toward 
 the acid ( hopo = 151 ) . thus , the dianion abdd model 
 should overestimate the repulsion in the estimation of the cahb . the 
 additional repulsion is seen by the lengthening of the hydrogen bond 
 donor and acceptor oxygens from 2.48  in the closed dianion 
 to 3.07  ( tsdd ) and 2.87  ( abdd ) . the monoanion models 
 ( tsdm and abdm ) result in different orientations between the hydrogen 
 bond donor and acceptor . 60 
 from the closed structure , lengthening the donor and acceptor oxygen 
 difference from 2.48  in the closed to 2.85  and generating 
 a second weak interaction at 3.31  . the hydrogen rotates to 
 hoco = 114 reorienting its lone pairs away from the 
 phosphate group . however , abdm maintains the eclipsing hydrogen bond 
 donor and acceptor interaction , since it is constrained to that of 
 the closed structure . the hydrogen bond oxygen to oxygen distance 
 lengthens to 2.77  , and the hydrogen adopts a position of hoco 
 = 180 that increases the congestion of lone pairs between the 
 donor and the acceptor . the net result should overestimate the repulsion 
 in the estimation of the cahb , as in the dianion model . however , the 
 overestimation is somewhat mitigated when the energy difference is 
 determined in reference to the opt structures with open geometries . in a final comparison of the activation energies with the subtractive 
 and additive corrections to the open  closed method ( table 6 ) , an agreement to the estimated cahb strength is 
 observed , which is greater than the stabilization energy of pseudochair 
 carboxyphosphate from the standard implementation of the open as expected , the predicted cahb values from the computed transition 
 structures are on the lower end of the additive and subtractive schemes 
 for the monoanion , and below the lower bounds for each open  closed 
 method describing the dianion . the dihedral angle constraints , or 
 release of other degrees of freedom , in the partial optimization procedure 
 of the subtractive method are a likely source of error causing an 
 overestimation , as highlighted in the discussion above . the additive 
 corrections to the open  closed method are possibly in error 
 due to the parametrization of nonbond terms , where the parameters 
 were developed for phosphate esters for intermolecular interactions . 
 despite overestimating the cahb strength compared to those predicted 
 by the transition structures , the importance of pauli replusion interactions is highlighted for the first time by the additive corrections to the 
 open  closed method . on the basis of the above estimation 
 schemes , the cahb can be classified 
 as strong ( greater than 12 kcal / mol ) . the class of hydrogen 
 bonds known as short - strong hydrogen bonds ( sshbs ) is often associated 
 with those that are also low barrier ( lbhbs ) . although hydrogen bonds may be both short - strong and low barrier , 
 these classifications are made on the basis of separate criteria . classification as sshb is based on the distance between the heteroatoms 
 ( less than 2.5  for an oho hydrogen bond ) . however , classification 
 as an lbhb is based on the equivalence of the pka s of the two donor atoms , resulting in a low barrier 
 to proton transfer between the two . the estimated cahb strengths 
 from each of the three independent 
 estimation schemes result in a bond strength greater than 12 kcal / mol 
 used to classify a short - strong hydrogen bond . the heteroatom 
 distance is 2.48  in the monoanion and 2.56  in the dianion . thus , considering the sources of error , carboxyphosphate meets the 
 geometric and energetic criteria for short - strong hydrogen bonding . thus , there is no double - well potential 
 found , and the bond can not be considered low barrier . in summary , 
 the bond is considered to be short - strong but not low barrier in both 
 charge states of pseudochair carboxyphosphate . the cahb strength of the pseudochair conformation of monoanionic 
 and dianionic carboxyphosphate in a vacuum has been estimated by independent 
 additive and subtractive corrections to the open  closed method . our additive correction scheme shows differential pauli repulsion 
 contributions between the pseudochair ( closed ) and open conformations 
 of carboxyphosphate that are significant in estimating the cahb strength . our cahb estimate is 22.9 kcal / mol for the monoanion and 18.4 
 kcal / mol for the dianion . results from the subtractive technique reinforce 
 those from our additive procedure , where the predicted cahb strength 
 ranges from 17.8 to 25.4 kcal / mol for the monoanion 
 and from 15.7 to 20.9 kcal / mol for the dianion . ultimately , 
 we find the cahb in carboxyphosphate meets the criteria for short - strong 
 hydrogen bonds . however , carboxyphosphate has a unique energy profile 
 that does not result in the symmetric double - well behavior of low - barrier 
 hydrogen bonds . the cahb in carboxyphosphate is short - strong but can not 
 be considered to be low barrier , as the proton is not shared equally 
 between the donor and acceptor groups . the strong hydrogen bond coupled 
 with the fact that the hydrogen prefers to be on the phosphate group 
 provides a previously unrecognized mechanism by which protons can 
 be shuttled from the carboxylic acid side of carboxyphosphate to the 
 phosphate . such a proton shuttling mechanism has previously unconsidered 
 implications for the catalytic mechanism of the carboxylase enzymes . the present analysis delivers a fundamental report on the strength 
 of the cahb in the ionized forms of carboxyphosphate , which has the 
 potential to realign and improve the mechanistic understanding of 
 this intermediate in atp - dependent carboxylases .
carboxyphosphate , 
 a suspected intermediate in atp - dependent carboxylases , 
 has not been isolated nor observed directly by experiment . 
 consequently , 
 little is known concerning its structure , stability , and ionization 
 state . 
 recently , carboxyphosphate as either a monoanion or dianion 
 has been shown computationally to adopt a novel pseudochair conformation 
 featuring an intramolecular charge - assisted hydrogen bond ( cahb ) . 
 in this work , 
 additive and subtractive correction schemes to the commonly 
 employed open 
 closed method are used to estimate the strength 
 of the cahb . 
 truhlar s minnesota m06 - 2x functional with dunning s 
 aug - cc - pvtz basis set has been used for geometry optimization , energy 
 evaluation , and frequency analysis . 
 the charmm force field has been 
 used to approximate the pauli repulsive terms in the closed and open 
 forms of carboxyphosphate . from our additive correction scheme , 
 differential 
 pauli repulsion contributions between the pseudochair ( closed ) and 
 open conformations of carboxyphosphate are found to be significant 
 in determining the cahb strength . 
 the additive correction modifies 
 the cahb prediction ( eclosed  open ) of 14 kcal / mol for the monoanion and 12 kcal / mol 
 for the dianion to 22.9 and 18.4 kcal / mol , respectively . 
 results from the subtractive technique reinforce those from our additive 
 procedure , where the predicted cahb strength ranges from 17.8 
 to 25.4 kcal / mol for the monoanion and from 15.7 to 
 20.9 kcal / mol for the dianion . ultimately , we find that the 
 cahb in carboxyphosphate meets the criteria for short - strong hydrogen 
 bonds 
 . however , carboxyphosphate has a unique energy profile that 
 does not result in the symmetric double - well behavior of low - barrier 
 hydrogen bonds . 
 these findings provide deeper insight into the pseudochair 
 conformation of carboxyphosphate , and lead to an improved mechanistic 
 understanding of this intermediate in atp - dependent carboxylases .