Exhibit 10.4


 


RICE ACQUISITION CORP. II

RICE ACQUISITION HOLDINGS II LLC

102 East Main Street, Second Story

Carnegie, PA 15106


 


June 15, 2021


 


Rice Acquisition Sponsor II LLC


102 East Main Street, Second Story


Carnegie, PA 15106


 


Re: Administrative
Services Agreement 


 


Gentlemen:


 


This letter agreement by and
between Rice Acquisition Corp. II (the “Company”), Rice Acquisition Holdings
II LLC (“Opco”) and Rice Acquisition Sponsor II LLC (“Sponsor”),
dated as of the date hereof, will confirm our agreement that, commencing on the date the securities of the Company are first listed on
the New York Stock Exchange (the “Listing Date”), pursuant to a Registration
Statement on Form S-1 and prospectus filed with the Securities and Exchange Commission (the “Registration
Statement”) and continuing until the earlier of the consummation by the Company of an initial business combination or
the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as
the “Termination Date”):


 


(i)       Sponsor
shall make available to the Company, at 102 East Main Street, Second Story, Carnegie, PA 15106 (or any successor location of Sponsor),
certain office space, utilities, secretarial support and administrative services as may be reasonably required by the Company and Opco.
In exchange therefor, the Company shall cause Opco to pay Sponsor the sum of $10,000 per month on the Listing Date and continuing monthly
thereafter until the Termination Date; and


 


(ii)       Sponsor
hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind (each, a “Claim”)
in or to, and any and all right to seek payment of any amounts due to it out of, the trust account established for the benefit of the
public shareholders of the Company and the holders of Class A Units of Opco (other than the Company) of Opco and into which substantially
all of the proceeds of the Company’s initial public offering will be deposited (the “Trust
Account”), and hereby irrevocably waives any Claim it may have in the future as a result of, or arising out of, this
letter agreement, which Claim would reduce, encumber or otherwise adversely affect the Trust Account or any monies or other assets in
the Trust Account, and further agrees not to seek recourse, reimbursement, payment or satisfaction of any Claim against the Trust Account
or any monies or other assets in the Trust Account for any reason whatsoever.


 


This letter agreement constitutes
the entire agreement and understanding of the parties hereto in respect of its subject matter and supersedes all prior understandings,
agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter
hereof or the transactions contemplated hereby.


 




     


     


    

 


This letter agreement may
not be amended, modified or waived as to any particular provision, except by a written instrument executed by the parties hereto.


 


No party hereto may assign
either this letter agreement or any of its rights, interests, or obligations hereunder without the prior written approval of the other
party. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign
any interest or title to the purported assignee.


 


This letter agreement, the
entire relationship of the parties hereto, and any litigation between the parties (whether grounded in contract, tort, statute, law or
equity) shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the State of New York, without giving
effect to its choice of laws principles.


 


[Signature page follows]


 




    2


     


    

 


	 	Very truly yours,
	 	 
	 	RICE ACQUISITION CORP. II
	 	 	 	 
	 	By: 	/s/ Daniel Joseph Rice, IV
	 	 	Name: 	Daniel Joseph Rice, IV
	 	 	Title:	Chief Executive Officer
	 	 	 	 
	 	RICE ACQUISITION HOLDINGS II LLC
	 	 	 	 
	 	By: 	/s/ Daniel Joseph Rice, IV
	 	 	Name: 	Daniel Joseph Rice, IV
	 	 	Title:	Chief Executive Officer


 


	AGREED TO ACCEPTED BY:	 
	 	 
	RICE ACQUISITION SPONSOR II LLC	 
	 	 	 	 
	By:	/s/ Daniel Joseph Rice, IV	 
	 	Name: 	Daniel Joseph Rice, IV	 
	 	Title:	Chief Executive Officer	 



 


[Signature Page to Administrative Services Agreement]