I'm tired of hearing the phrase "invisible hand" used as though it refers to so-called "free markets" (as though that phrase is a technical term with a clear definition).
To put it to rest: Smith's argument in the Wealth of Nations is a sociological argument about economic investment. Smith wrote:
"By preferring the support of domestic to that of foreign industry, [a merchant] intends only his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention (1776 : 456)."
In the paragraphs before and after, Smith is arguing that business people prefer to use their capital on domestic rather than foreign trade because they lack familiarity with capitalists in other countries and their legal systems. Thus, a sociocultural preference for one's home country combined with a self-interested desire to increase profits -- which together Smith calls an "invisible hand" -- results in higher employment and growth in that country.
The odd part is that the reality now is the complete opposite of Smith's justification for the "invisible hand." Multinational corporations move investment everywhere, and business people have few sociocultural preferences for their home countries. Thus the "invisible hand" doesn't exist except as a distortion of Smith's arguments.
-- Your economic historian