The　adsorption　of　cis　and　trans　2-butenes　on　Pt(111)　has　been　studied　as　a　function　of　hydrogen　coverage　OH　by　means　of　calculations　based　on　density　functional　theory　(DFT)　with　the　inclusion　of　dispersion　forces.　All　hydrogen　coverages　have　been　considered,　from　0　to　1.00　monolayer　(ML).　For　each　case,　the　di-sigma　and　pi　adsorption　geometries　of　the　olefins　have　been　compared　at　a　surface　coverage　of　theta(C4H8)　=　0.11　ML.　Calculations　of　the　Gibbs　free　energies　of　these　systems　have　identified　the　most　stable　2-butene　isomer　(cis　or　trans)　as　a　function　of　coverage,　temperature,　and　pressure.　In　particular,　focus　was　placed　on　two　sets　of　conditions,　namely,　one　with　a　pressure　of　10(-7)　Torr,　a　temperature　of　80　K,　and　a　gas　ratio　(P-H2/P-butene)　of　25,　similar　to　the　conditions　used　in　surface　science　studies,　and　a　second　with　a　pressure　of　1　bar,　a　temperature　range　of　300-400　K,　and　a　gas　ratio　(P-H2/P-butene)　of　10,　similar　to　catalytic　hydrogenation　conditions.　With　all　selected　functionals　(PW91,　PBE-TS,　and　optPBE),　di-sigma　bonding　was　found　to　be　the　most　stable　for　both　isomers　of　2-butene　and　for　all　hydrogen　coverages　except　for　OH　=　1.00　ML.　At　low　pressures,　2-butene　is　physisorbed　at　low　temperatures　(＜=　125　K　with　PBE-TS　and　＜=　90　K　with　optPBE);　however,　when　the　temperature　increases,　coadsorption　of　the　butene　with　6　H　atoms　becomes　the　most　stable　configuration　of　the　system　(OH　=　0.67　ML),　and　finally,　2-butene　desorbs　around　380　K,　as　estimated　with　PBE-TS　(or　around　325　K　with　optPBE).　Interestingly,　a　switch　in　stability　was　observed　with　hydrogen　coverage,　from　the　adsorbed　trans　isomer　being　the　more　stable　for　theta(H)　＜　0.44　ML　to　the　adsorbed　cis　isomer　becoming　the　more　stable　at　higher　hydrogen　coverages,　in　agreement　with　the　cis-trans　isomerization　behavior　previously　reported　for　this　system.　At　high　pressures,　the　behavior　is　similar,　but　with　transitions　occurring　at　higher　temperatures.　2-Butene　is　physisorbed　until　the　temperature　reaches　250　K,　and　desorbs　above　500　K　At　hydrogenation　reaction　temperatures　(between　300　and　500　K),　a　hydrogen　coverage　of　roughly　half　a　monolayer　was　calculated　(0.66　and　0.44　for　300　and　500　K,　respectively).　Our　results　confirm　that　dispersion　effects　must　be　included　to　properly　describe　the　2-butene　and　hydrogen　coadsorption　on　Pt(111),　as　PW91　predicts　that　2-butene　is　never　adsorbed　on　the　platinum　surface.　On　the　other　hand,　DFT　calculations　including　dispersion　forces　such　as　PBE-TS　or　optPBE　afford　a　good　understanding　of　catalytic　systems　under　both　ultra-high-vacuum　conditions　and　catalytic　hydrogenation　conditions.　For　this　system,　the　PBE-TS　results　are　in　good　agreement　with　experiments:　they　correctly　reproduce　the　coverage　in　hydrogen　and　the　configuration　of　the　2-butene　adsorbate　(cis-trans　isomer).