But I think Tear of the Goddess is more effective for Mana regen than chalice of harmony
False. Totally false.
They give the same mana regen / 5 second, except for the Chalice's Passive, of course. The main reason of why Tear of the Goddess seams an attractive option is that you actually gain mana when you spam, and you can convert that item into another one (The Archangel Staff) that will give you ap depending of your total mana, impressive mana regen per second and a massive mana pool. However ...

Archangel staff costs three times more than a chalice of harmony.

Chalice of harmony gives Magic Resist, while Archangel don't give any defensive stat

A Sona (for exemple) with a chalice of harmony will have the same teamfight presence as one with an Archangel Staff.

Chalice of Harmony boost your total mana regen, which means it will have a synergy with items you will probably have like Soul Shroud, Shurelya's Rêverie and Morello's Evil Tome.

Most of the harass you will get in early, laning phase (or even in teamfight) will come from a magic damage source. Caitlyn's traps and net deal magic damage. Nidalee's spear deals magic damage. Zilean's bombs deal magic damage. Miss Fortune's Impure shots bonus and Bullet Time deal magic damage. Lux's spells and passive deal magic damage. Tristana's Explosive shot is a magic damage DoT. Corki's Phosphorus bomb is magic-based... You get it?

*** EXCEPTION : One of the only cases where I think Tear of the Goddess is honestly better than a Chalice of Harmony is when you play champions like Taric, Sona, Nidalee, Janna or Alistar that WILL benefit the AP bonus and when you plan to build a Frozen Heart, and various mana-giving items (another exemple; Sheen for nidalee and Alistar) or need to make a ryze-ish build. But this is a rare, isolated case.

It's the kind of things you do when you are bored at 3:00 am ... at least for me.

So sorry for the inconveniance.