Exhibit 4.1

NUMBER U-

SEE REVERSE FOR CERTAIN DEFINITIONS

CUSIP 039562 202

ARCHIMEDES TECH SPAC PARTNERS CO.

UNITS CONSISTING OF (I) ONE SUBUNIT, CONSISTING OF ONE SHARE OF COMMON STOCK AND ONE-QUARTER OF ONE REDEEMABLE WARRANT,

AND (II) ONE-THIRD OF ONE REDEEMABLE WARRANT,

EACH WHOLE WARRANT ENTITLING THE HOLDER TO PURCHASE ONE SHARE OF COMMON STOCK

THIS CERTIFIES THAT                    is the owner of                    Units.

Each Unit (“Unit”) consists of (i) one (1) subunit (“Subunits”), consisting of one share of common stock, par value $0.0001 per share (“Common Stock”), of Archimedes Tech SPAC Partners Co., a Delaware corporation (the “Company”), and one-quarter of one (1) warrant (“Warrant”), and (ii) one-third of one (1) Warrant. Each whole Warrant entitles the holder to purchase one share of Common Stock for $11.50 per share (subject to adjustment). Each whole Warrant will become exercisable 30 days after the Company’s completion of an initial merger, capital stock exchange, asset acquisition, or other similar business combination with one or more businesses or entities (a “Business Combination”), and will expire unless exercised before 5:00 p.m., New York City Time, on the fifth anniversary of the completion of an initial Business Combination, or earlier upon redemption or liquidation. The Subunit(s) and Warrant(s) comprising the Unit(s) represented by this certificate are not transferable separately until ninety days following the IPO, unless EarlyBirdCapital, Inc. informs the Company of its decision to allow earlier separate trading, except that in no event will the Common Stock and Warrants be separately tradeable until the Company has filed an audited balance sheet reflecting the Company’s receipt of the gross proceeds of its initial public offering and issued a press release announcing when such separate trading will begin. The terms of the Warrants are governed by a Warrant Agreement, dated as of ___________, 2021, between the Company and Continental Stock Transfer & Trust Company, as Warrant Agent, and are subject to the terms and provisions contained therein, all of which terms and provisions the holder of this certificate consents to by acceptance hereof. Copies of the Warrant Agreement are on file at the office of the Warrant Agent at 1 State Street, 30th Floor, New York, New York 10004, and are available to any Warrant holder on written request and without cost.

This certificate is not valid unless countersigned by the Transfer Agent and Registrar of the Company. Witness the facsimile seal of the Company and the facsimile signatures of its duly authorized officers.

Archimedes Tech SPAC Partners Co.

The Company will furnish without charge to each unitholder who so requests, a statement of the powers, designations, preferences and relative, participating, optional or other special rights of each class of stock or series thereof of the Company and the qualifications, limitations, or restrictions of such preferences and/or rights.

The following abbreviations, when used in the inscription on the face of this certificate, shall be construed as though they were written out in full according to applicable laws or regulations:

Additional abbreviations may also be used though not in the above list.

For value received,                      hereby sell, assign and transfer unto                     

PLEASE INSERT SOCIAL SECURITY OR OTHER IDENTIFYING NUMBER OF ASSIGNEE

(PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS, INCLUDING ZIP CODE, OF ASSIGNEE)

___________________represented by the within Certificate, and do hereby irrevocably constitute and appoint

__________________to transfer the said Units on the books of the within named Company with full power of substitution in the premises.

Dated:  _________________________                

Signature(s) Guaranteed:

The holder(s) of this certificate shall be entitled to receive a pro-rata portion of the funds from the trust account with respect to the Subunits underlying this certificate only in the event that (i) the Corporation is forced to liquidate because it does not consummate an initial business combination within the period of time set forth in the Corporation’s Amended and Restated Certificate of Incorporation, as the same may be amended from time to time (the “Charter”) or (ii) if the holder seeks to convert his subunits upon consummation of, or sell his subunits in a tender offer in connection with, an initial business combination or in connection with certain amendments to the Charter. In no other circumstances shall the holder(s) have any right or interest of any kind in or to the trust account with respect to the subunit underlying the unit.