The TM4 item containes the move 'Calm Mind', and can only be bought at the Battle Park for 48 Battle Points. Pokemon such as Meditite and Bronzong can learn it though, as it is a Psychic Move.The Battle Park is available to travel to after beating the Elite Four andChampion.
nowhere
Pikachu will know thundershock and growl when caught. Then he/she will learn tail whip at level 6, thunder wave at level 8, quick attack at level 11, double team at level 15, slam at level 20, thunderbolt at level 26, agility at level 33, thunder at level 41, and light screen at level 50. And in gold he/she can learn TM1, TM2, TM3, TM4, TM6, TM7, TM10, TM13, TM17, TM18, TM20, TM21, TM23, TM25, TM27, TM31, TM32, TM34, TM35, TM39, TM40, TM41, TM43, TM44, TM45, HM04, HM05, and HM 03. Through breeding you can get a pichu that would know encore, doubleslap, bide, reversal, and present. I'm not sure if this is for gold or ruby and saphire, but I thought I would put it any way.