While　the　hydrogen　evolution　reaction　obtained　during　photocatalytic　water　splitting　is　easily　facilitated　by　existing　photocatalysts,　the　oxygen　evolution　reaction　(OER)　exhibits　very　sluggish　reaction　kinetics　because　it　involves　multi-proton-coupled　electron-transfer　steps.　Therefore,　the　most　important　goal　for　developing　efficient　photocatalysts　for　overall　water　splitting　is　to　design　photocatalysts　for　which　the　valence　band　edge　is　sufficiently　less　than　the　oxidation　potential　of　O-2/H2O　to　meet　the　thermodynamic　requirements　of　the　OER.　This　is　addressed　in　the　present　work　by　applying　first-principles　density　functional　theory　calculations　to　systematically　investigate　the　effect　of　B,　N-codoping　on　the　electronic　band　structure,　thermal　stability,　dynamic　stability,　and　optical　properties　of　two-dimensional　graphdiyne　monolayers,　which　is　a　relatively　new　carbon　allotrope　consisting　of　sp-　and　sp(2)-hybridized　carbon　atoms　that　provides　a　bandgap　of　similar　to　1.0　eV.　The　results　indicate　that　the　bandgap　energy　increases　with　an　increasing　number　of　BN　pair　substitutions　and　that　some　of　the　B,　N-codoped　graphdiyne　configurations　representative　of　a　BCN　ternary　structure　provide　direct　bandgaps　with　energies　of　2-3　eV　appropriate　for　visible　light　absorption.　Moreover,　the　valence　and　conduction　band　edges　are　appropriately　matched　with　the　oxidation　and　reduction　potentials　of　water.　We　also　demonstrate　that　the　optimal　B,　N-codoped　graphdiyne　monolayers　have　excellent　charge　carrier　mobilities　and　provide　good　separation　between　photogenerated　electrons　and　holes.