I would like to email an invitation for investment to 10 potential investors. Is it legal for the owner of a private C-corporation to recruit potential investors via email?
Is it legal for the owner of a private company to recruit potential investors via email?
Yes. This is no different from making your proposal in person, over the phone or by letter. Depending on the nature or details of the matter, email might be more efficient than other methods for making the proposal.
Sending that email does not create, let alone formalize, legal relations between the addressee(s) and you. Nor does it preclude the subsequent formation of a contract or an agreement. In the case of one-sided contracts, the contract is formed when an addressee meets prior to expiration of his power of acceptance (see Restatement (Second) of Contracts at §§35-36) the conditions you formulate in your email. In all other cases, the formation of the contract happens when you two agree on the terms & conditions of the investment.
A security that is not registered may not be sold or offered in a "public offering." Basically, it can't be advertised for sale to the general public.
Simply sending emails to potential investors without some kind of pre-existing relationship between the party sending the email and the party receiving, is pretty much, by definition, a public offering.
For example, sending an email seeking investors to ten people selected at random from a mailing list that doesn't tell you anything about them would be a securities law violation even if no investments were secured as a result. If you did that, the SEC could issue a "cease and desist order", seek an injunction against you, or seek civil or criminal penalties.
If you did obtain an investor, the investor would have a private cause of action against you even if the only thing wrong with the investments is that they were unregistered and did not fall within any specific exemption authorized by the SEC.
It isn't the use of email itself that is the problem. It is the lack of any reason to send it to these particular investors stated in the question that falls within an SEC approved private placement exception that is the problem. This is due to the Securities Act of 1933, as amended, and the regulations issued by the Securities and Exchange Commission to enforce and implement the Act.
For an offer to sell securities (stock in a C-corporation is the prototypical type of security), to not constitute a public offering and instead constitute a private placement of securities, one must comply with one or more of the exemptions from registration of securities promulgated by the Securities and Exchange Commission (mostly under Regulation D) and also under any parallel state securities regulations (which sometimes apply even when federal securities laws do not).
Most of these exemptions either limit the amount of investment that may be sought in the offering as a whole, limit the offering to people who are known to be "accredited investors" (basically affluent people or institutional investors), limit the number of unaccredited investors (and require that they either be sophisticated or have a professional advisor assisting them), or require that the investor be actively involved in the business. Some exemptions are available as a matter of course, but only if expressly registered with the SEC. But, the full set of exemptions that are available is a complicated and technical matter. The SEC summarizes some of the main exemptions and provides numerous additional references here.
It is possible that the course of action proposed may fall within, for example, Rule 504, Rule 505, or Rule 506 of Regulation D that permits private offerings. But on the face of the information in the question it is not possible to determine that.
For example, if you sought to secure $6,000,000 of investments over twelve months, with some of the investments sought from non-accredited investors, that would not fall within the scope of any of the Regulation D exemptions and would violate federal securities laws.