The following spells do not require somatic or material components (these spells get around the need to have a free hand):
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Cantrips:
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Thaumaturgy [Transmutation] (V) (Cleric)
Vicious Mockery [Enchantment] (V) (Bard)
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Level 1 Spells:
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Command [Enchantment] (V) (Cleric, Paladin)
Compelled Duel [Enchantment] (V; Concentration) (Paladin)
Dissonant Whispers [Enchantment] (V) (Bard)
Ensnaring Strike [Conjuration] (V; Concentration) (Ranger)
Faerie Fire [Evocation] (V; Concentration) (Bard, Druid)
Hail of Thorns [Conjuration] (V) (Ranger)
Healing Word [Evocation] (V) (Bard, Cleric, Druid)
Hunter's Mark [Divination] (V; Concentration) (Ranger)
Searing Smite [Evocation] (V; Concentration) (Paladin)
Thunderous Smite [Evocation] (V; Concentration) (Paladin)
Wrathful Smite [Evocation] (V; Concentration) (Paladin)
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Level 2 Spells:
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Blindness/Deafness [Necromancy] (V) (Bard, Cleric, Sorcerer, Wizard)
Blur [Illusion] (V; Concentration) (Sorcerer, Wizard)
Branding Smite [Evocation] (V; Concentration) (Paladin)
Knock [Transmutation] (V) (Bard, Sorcerer, Wizard)
Misty Step [Conjuration] (V) (Sorcerer, Warlock, Wizard)
Prayer of Healing [Evocation] (V) (Cleric)
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Level 3 Spells:
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Aura of Vitality [Evocation] (V; Concentration) (Paladin)
Blinding Smite [Evocation] (V; Concentration) (Paladin)
Crusader's Mantle [Evocation] (V; Concentration) (Paladin)
Mass Healing Word [Evocation] (V) (Cleric)
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Level 4 Spells:
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Aura of Life [Abjuration] (V; Concentration) (Paladin)
Aura of Purity [Abjuration] (V; Concentration) (Paladin)
Dimension Door [Conjuration] (V) (Bard, Sorcerer, Warlock, Wizard)
Guardian of Faith [Conjuration] (V) (Cleric)
Staggering Smite [Evocation] (V; Concentration) (Paladin)
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Level 5 Spells:
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Banishing Smite [Abjuration] (V; Concentration) (Paladin)
Circle of Power [Abjuration] (V; Concentration) (Paladin)
Contact Other Plane [Divination] (V; Ritual) (Warlock, Wizard)
Destructive Wave [Evocation] (V) (Paladin)
Geas [Enchantment] (V) (Bard, Cleric, Druid, Paladin, Wizard)
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Level 6 Spells:
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Otto's Irresistible Dance [Enchantment] (V; Concentration) (Bard, Wizard)
Word of Recall [Conjuration] (V) (Cleric)
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Level 7 Spells:
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Divine Word [Evocation] (V) (Cleric)
Teleport [Conjuration] (V) (Bard, Sorcerer, Wizard)
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Level 8 Spells:
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Glibness [Transmutation] (V) (Bard, Warlock)
Power Word Stun [Enchantment] (V) (Bard, Sorcerer, Warlock, Wizard)
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Level 9 Spells:
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Power Word Kill [Enchantment] (V) (Bard, Sorcerer, Warlock, Wizard)
Time Stop [Transmutation] (V) (Sorcerer, Wizard)
Wish [Conjuration] (V) (Sorcerer, Wizard)