beta - adrenergic antagonists have been established as first line treatment in the medical management of hypertension , as well as acute coronary syndrome , in patients with recent myocardial infarction ( <3 years ) and/or left ventricular systolic dysfunction ( left ventricular ejection fraction 40% ) ; in congestive heart failure , where one of three beta - blockers were proven to reduce mortality ( e.g. , bisoprolol , carvedilol , and sustained - release metoprolol succinate ) ; it is recommended for all patients with current or prior symptoms of hfref ( heart failure with a reduced ejection fraction ) , unless contraindicated , to reduce morbidity and mortality .
beta - blockers have also been well established for the prevention of initial episodes of gastrointestinal bleeding in patients with cirrhosis and esophageal varices , glaucoma , and have recently become the main form of treatment of infantile hemangiomas . in the pharmaceutical field ,
molecular chirality is a property which plays a main role in the activity of drugs , which is also the case of beta - blockers , making the identification and separation of enantiomers extremely important .
the activity of enantiomeric forms of pharmaceuticals is known to be often distinctly different , one of the enantiomers may be biologically active while the other may be inactive , toxic or ballast . furthermore , stereochemistry plays an important role for biodegradability of chemical species but there are no specific rules for how to decide which enantiomer will be preferably degraded .
this is particularly important from an environmental point of view , considering that the presence of active pharmaceutical ingredients in the aquatic environment is increasingly seen as one of the major challenges to the sustainable management of water resources .
stereochemical features of a molecule can have an influence on its stability and reactivity to other chiral molecules . in 2012 ,
five quantum chemical descriptors were applied to pyrrolidin-2-one compounds : hlg ( gap between ehomo and elumo ) , hardness (  ) , softness (  ) and electronegativity (  ) , total energy ( etotal ) , for the prediction of retention factors . based on koopmans theorem ,
the chemical potential m and chemical hardness  can be calculated as : = + 0.5(elumo  ehomo ) and m= 0.5(ehomo + elumo ) .
acebutolol , metoprolol and atenolol were investigated by applying quantum mechanical computer codes and comparison of the same to study the properties associated with their electronic structure .
homo ( highest occupied molecular orbital ) , lumo ( lowest unoccupied molecular orbital ) , stability , sensitivity and chemical hardness were calculated on the optimized structures .
the aim of the present study is to calculate several quantum chemical descriptors ( homo , lumo , hlg , electronegativity , chemical potential , hardness and softness , electrophilicity ) in order to interpret various molecular properties such as electronic structure , conformation , reactivity in the interest of determining how such descriptors could have an impact in our understanding of the experimental observations and describing various aspects of chemical binding of beta - blockers in terms of these descriptors .
the studied molecules are fourteen beta - adrenoceptor blocking agents with the chemical structures depicted below in table i : the 2d chemical structures of the beta - blockers ( 14 molecules with one stereogenic center ) were downloaded from chemicalbook , the chemistry of the structures was checked and they were consequently cleaned in 3d before generating the 3d structures of the stereoisomers using marvinview ( chemaxon ) .
the chirality at the stereogenic centres was verified in accordance to cahn - ingold - prelog priority rules .
the resulting geometries were further refined by means of a low mode dynamics ( lmd ) conformational search using the mmff94x force field and standard settings in moe software ( molecular operating environment ) .
the lowest energy conformations were chosen to further calculate etotal , homo and lumo descriptors . using these ,
homo and lumo descriptors were calculated for each conformation of each enantiomer with moe and then the values corresponding to the conformation with the lowest energy were chosen .
calculations were performed with moe ( molecular operating environment , v. 2014.09 on an intel  core(tm ) i3 - 4005u cpu @ 1.7 ghz personal computer with 12 gb of ram running under microsoft windows 8.1 ) .
further , several quantum chemical descriptors were calculated : hlg ( gap between ehomo and elumo ) , hardness (  , =elumo - ehomo = hlg ) , softness (  , 
 =11 ) , electronegativity (  , 
 =-1122(ehomo+elumo ) ) or chemical potential (  , 
 =-1122  ( ehomo+elumo ) ) , global electrophilicity (  , 
 =11222 ) .
homo and lumo are calculated using three different methods ( am1 , mndo and pm3 ) .
the studied molecules are fourteen beta - adrenoceptor blocking agents with the chemical structures depicted below in table i :
the 2d chemical structures of the beta - blockers ( 14 molecules with one stereogenic center ) were downloaded from chemicalbook , the chemistry of the structures was checked and they were consequently cleaned in 3d before generating the 3d structures of the stereoisomers using marvinview ( chemaxon ) .
the chirality at the stereogenic centres was verified in accordance to cahn - ingold - prelog priority rules .
the resulting geometries were further refined by means of a low mode dynamics ( lmd ) conformational search using the mmff94x force field and standard settings in moe software ( molecular operating environment ) .
the lowest energy conformations were chosen to further calculate etotal , homo and lumo descriptors . using these , the remaining desired descriptors were subsequently calculated .
homo and lumo descriptors were calculated for each conformation of each enantiomer with moe and then the values corresponding to the conformation with the lowest energy were chosen .
calculations were performed with moe ( molecular operating environment , v. 2014.09 on an intel  core(tm ) i3 - 4005u cpu @ 1.7 ghz personal computer with 12 gb of ram running under microsoft windows 8.1 ) .
further , several quantum chemical descriptors were calculated : hlg ( gap between ehomo and elumo ) , hardness (  , =elumo - ehomo = hlg ) , softness (  , 
 =11 ) , electronegativity (  , 
 =-1122(ehomo+elumo ) ) or chemical potential (  , 
 =-1122  ( ehomo+elumo ) ) , global electrophilicity (  , 
 =11222 ) .
homo and lumo are calculated using three different methods ( am1 , mndo and pm3 ) .
the 2d chemical structures of the beta - blockers ( 14 molecules with one stereogenic center ) were downloaded from chemicalbook , the chemistry of the structures was checked and they were consequently cleaned in 3d before generating the 3d structures of the stereoisomers using marvinview ( chemaxon ) .
the chirality at the stereogenic centres was verified in accordance to cahn - ingold - prelog priority rules .
the resulting geometries were further refined by means of a low mode dynamics ( lmd ) conformational search using the mmff94x force field and standard settings in moe software ( molecular operating environment ) .
the lowest energy conformations were chosen to further calculate etotal , homo and lumo descriptors . using these , the remaining desired descriptors were subsequently calculated .
homo and lumo descriptors were calculated for each conformation of each enantiomer with moe and then the values corresponding to the conformation with the lowest energy were chosen .
calculations were performed with moe ( molecular operating environment , v. 2014.09 on an intel  core(tm ) i3 - 4005u cpu @ 1.7 ghz personal computer with 12 gb of ram running under microsoft windows 8.1 ) .
further , several quantum chemical descriptors were calculated : hlg ( gap between ehomo and elumo ) , hardness (  , =elumo - ehomo = hlg ) , softness (  , 
 =11 ) , electronegativity (  , 
 =-1122(ehomo+elumo ) ) or chemical potential (  , 
 =-1122  ( ehomo+elumo ) ) , global electrophilicity (  , 
 =11222 ) .
homo and lumo are calculated using three different methods ( am1 , mndo and pm3 ) .
homo represents the ability to donate an electron , while lumo as an electron acceptor represents the ability to accept an electron .
homo and lumo are considered to be the main orbitals taking part in chemical stability , also known as frontier orbitals .
homo energy is closely related to reactivity to electrophilic attack , being the highest energy orbital containing electrons ; lumo energy is closely related to reactivity to nucleophilic attack , since it is the lowest energy orbital that can accept electrons .
the homo - lumo band gap ( hlg ) explains the structure and conformation barriers in many molecular systems .
the hlg for each representative of the set of studied beta - blockers , calculated using values of homo and lumo energy can be visualized in table ii ; the values for the orbital energies were obtained using semi - empirical molecular orbital methods am1 , mndo and pm3 . the energy and symmetry type and the charge distribution in homo and in lumo are known to determine the structures of molecules .
moreover , pearson showed that the homo - lumo gap represents the chemical hardness of the molecule .
increases in hardness lead to increases in the movement of the system towards a more stable configuration .
the chemical hardness is related to the resistance towards deformation or polarization of the electron cloud of our study molecules . bearing this in mind , and the results given in table i
, it is shown that according to homo - lumo gap and the chemical hardness the most stable compounds are alprenolol , bisoprolol and esmolol .
it is correlated with complex stability with respect to bonding in the molecule , chemical reactivity and solubility of molecules .
the softness values calculated for the study molecules revolve around 0.1 , suggesting low reactivities .
associated within the framework of scf mo ( self - consistent field molecular orbital ) theory , the ionization energy ( i ) and electron affinity ( a ) can be expressed through homo and lumo orbital energies as i = -ehomo and a= -elumo .
the electron affinity can be used in combination with ionization energy to give electronic chemical potential , the global electrophilicity , 
 =11222 , where  represents the softness is also calculated .
the values for electrophilicity , calculated with am1 , mndo and pm3 methods are illustrated in table iii .
as seen in table iii , propranolol , sotalol and timolol have among the highest electrophilicity index of the studied beta - blocker molecules .
results obtained show that acebutolol , atenolol , timolol and sotalol have the highest values for the electronegativity index .
useful theoretical insights into chemical reactivity and selectivity parameters may be obtained by determining global qualitative chemical concepts such as the electronegativity (  ) , chemical potential (  ) , hardness (  ) , softness (  ) , and electrophilicity index (  ) . in order to analyze molecular stability
, we calculated the global hardness value , which is calculated as the hlg , considering that the charge transfer resistance equals the energy gap between the highest occupied and lowest unoccupied molecular orbital .
the large band gap means that a high - energy is needed to be fed into a molecule to kick it from the ground state into an excited state .
the high stability in turn indicates low chemical reactivity , which could probably mean that the interactions of molecules from the beta - blocker class with other molecules , for example polysaccharides or cyclodextrins , would result in very weak bonds , like van der waals or possibly hydrogen bonds . according to homo - lumo gap and the chemical hardness the most stable compounds are alprenolol , bisoprolol and esmolol . to gain insight into the molecular reactivities of the studied beta - blockers we calculated the global softness values of each molecule .
the low values for softness , all revolving around 0.1 ev , support the fact that the reactivity of these molecules is very low . among the studied beta - blockers
this could probably be due to the presence of a c = o double bond and one other electronegative element attached to the same c atom , in the case of atenolol and acebutolol , where we have an amide functional group in the side chain , the heteroatom attached to the same c atom is nitrogen . in the case of sotalol and timolol ,
it is probably explained by the presence of highly electronegative heteroatoms such as sulphur , nitrogen and oxygen .
the lowest calculated value for electronegativity is that of betaxolol , which has only one oxygen heteroatom in the molecule , apart from the heteroatoms of the substructure common to all beta - blocker molecules .
the differences in electronegativity between the lowest and highest value vary between the methods of calculation used . using am1 ,
the difference between betaxolol and timolol is 0.655 ev , while using pm3 , the difference between betaxolol and sotalol is 1.540 ev , but between betaxolol and timolol is 0.610 ev .
the electrophilicity contains information about structural , reactivity and selectivity patterns of many electron systems in both ground and excited electronic states .
it represents the stabilization energy of the system when it becomes saturated by electrons coming from the surroundings .
a good electrophile is characterized by a high value of  ( chemical potential ) and a low value of  ( chemical hardness ) .
the chemical potential and chemical hardness are key indicators of the overall reactivity of the molecule and are the most fundamental descriptors of charge transfer during a chemical reaction .
the lowest electrophilicity index was obtained for betaxolol and metoprolol , so they are the most likely to accept electrons until the molecule is saturated with electrons from its surroundings , thus energetically stabilizing the molecule .
the highest values were obtained for propranolol , sotalol and timolol molecules , meaning these are the least chemically reactive of all the selected molecules .
the large band gap means high excitation energies , good stability and a large chemical hardness for the beta - blocker enantiomer molecules .
the high stability in turn indicates low chemical reactivity , supported by the fact that the softness values calculated for the studied molecules revolve around 0.1 .
a high electronegativity was obtained in case of atenolol , acebutolol , timolol and sotalol , probably due to the functional groups and electronegative heteroatoms present in these molecules . in the future ,
the aim is to determine whether it is possible to find a valid correlation between these descriptors and the physicochemical behavior of the molecules from this class .
homo could be correlated to the observed oxidation potential , since the required voltage is related to the energy of the homo , because only the electron from this orbital is involved in the oxidation process .
the values obtained in the study were calculated in silico / in vacuum , and as such the real significance is limited .
nevertheless , for comparative purposes within the same class of substances ( beta - blockers ) , they could be used successfully , for example for obtaining correlations between chromatographic behavior and chemical structure ( molecular descriptors ) .
 background and aimbeta - adrenergic antagonists have been established as first line treatment in the medical management of hypertension , acute coronary syndrome and other cardiovascular diseases , as well as for the prevention of initial episodes of gastrointestinal bleeding in patients with cirrhosis and esophageal varices , glaucoma , and have recently become the main form of treatment of infantile hemangiomas.the aim of the present study is to calculate for 14 beta - blockers several quantum chemical descriptors in order to interpret various molecular properties such as electronic structure , conformation , reactivity , in the interest of determining how such descriptors could have an impact on our understanding of the experimental observations and describing various aspects of chemical binding of beta - blockers in terms of these descriptors.methodsthe 2d chemical structures of the beta - blockers ( 14 molecules with one stereogenic center ) were cleaned in 3d , their geometry was preoptimized using the software mopac2012 , by pm6 method , and then further refined using standard settings in moe ; homo and lumo descriptors were calculated using semi - empirical molecular orbital methods am1 , mndo and pm3 , for the lowest energy conformers and the quantum chemical descriptors ( hlg , electronegativity , chemical potential , hardness and softness , electrophilicity ) were then calculated.resultsaccording to homo - lumo gap and the chemical hardness the most stable compounds are alprenolol , bisoprolol and esmolol . 
 the softness values calculated for the study molecules revolve around 0.100 . 
 propranolol , sotalol and timolol have among the highest electrophilicity index of the studied beta - blocker molecules . 
 results obtained from calculations showed that acebutolol , atenolol , timolol and sotalol have the highest values for the electronegativity index.conclusionsthe future aim is to determine whether it is possible to find a valid correlation between these descriptors and the physicochemical behavior of the molecules from this class . the hlg could be correlated to the experimentally recorded electrochemical properties of the molecules . 
 homo could be correlated to the observed oxidation potential , since the required voltage is related to the energy of the homo , because only the electron from this orbital is involved in the oxidation process . 
Background and aim
Methods
1. Analytes
2. Computational details
2.1. Molecular Modeling and Geometry Optimization
2.2. Generation of Descriptors
Results
Conclusions